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1-2005 Body-Induced Vortical Flows: A Common Mechanism for Self-Corrective Trimming Control in Boxfishes Ian K. Bartol Old Dominion University, [email protected]

Morteza Gharib

Paul W. Webb

Daniel Weihs

Malcolm S. Gordon

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Repository Citation Bartol, Ian K.; Gharib, Morteza; Webb, Paul W.; Weihs, Daniel; and Gordon, Malcolm S., "Body-Induced Vortical Flows: A Common Mechanism for Self-Corrective Trimming Control in Boxfishes" (2005). Biological Sciences Faculty Publications. 207. https://digitalcommons.odu.edu/biology_fac_pubs/207 Original Publication Citation Bartol, I. K., Gharib, M., Webb, P. W., Weihs, D., & Gordon, M. S. (2005). Body-induced vortical flows: A common mechanism for self-corrective trimming control in boxfishes. Journal of Experimental Biology, 208(2), 327-344. doi:10.1242/jeb.01356

This Article is brought to you for free and open access by the Biological Sciences at ODU Digital Commons. It has been accepted for inclusion in Biological Sciences Faculty Publications by an authorized administrator of ODU Digital Commons. For more information, please contact [email protected]. The Journal of Experimental Biology 208, 327-344 327 Published by The Company of Biologists 2005 doi:10.1242/jeb.01356

Body-induced vortical flows: a common mechanism for self-corrective trimming control in boxfishes Ian K. Bartol1,*, Morteza Gharib2, Paul W. Webb3, Daniel Weihs4 and Malcolm S. Gordon5 1Department of Biological Sciences, Old Dominion University, Norfolk, VA 23529-0266, USA, 2Options of Bioengineering and Aeronautics, California Institute of Technology, Pasadena, CA 91125, USA, 3School of Natural Resources and Department of Biology, University of Michigan, Ann Arbor, MI 48109, USA, 4Department of Aerospace Engineering, Technion, Haifa, 3200, Israel and 5Department of Ecology and Evolutionary Biology, University of California, Los Angeles, CA 90095-1606, USA *Author for correspondence (e-mail: [email protected])

Accepted 22 October 2004

Summary Boxfishes (Teleostei: Ostraciidae) are marine fishes In the spotted boxfish, which is largely trapezoidal in cross having rigid carapaces that vary significantly among taxa section, consistent dorsal vortex growth posterior to the in their shapes and structural ornamentation. We showed eye ridge was also present. When all three boxfishes were previously that the keels of the carapace of one species of positioned at various yaw angles, regions of strongest tropical boxfish, the smooth trunkfish, produce leading concentrated vorticity formed in far-field locations of the edge vortices (LEVs) capable of generating self-correcting carapace compared with near-field areas, and vortex trimming forces during swimming. In this paper we show circulation was greatest posterior to the center of mass. In that other tropical boxfishes with different carapace general, regions of localized low pressure correlated well shapes have similar capabilities. We conducted a with regions of attached, concentrated vorticity, especially quantitative study of flows around the carapaces of three around the ventral keels. Although other features of morphologically distinct boxfishes (spotted boxfish, the carapace also affect flow patterns and pressure scrawled cowfish and buffalo trunkfish) using distributions in different ways, the integrated effects of the stereolithographic models and three separate but flows were consistent for all forms: they produce trimming interrelated analytical approaches: digital particle image self-correcting forces, which we measured directly using velocimetry (DPIV), pressure distribution measurements, the force balance. These data together with previous work and force balance measurements. The ventral keels of all on smooth trunkfish indicate that body-induced vortical three forms produced LEVs that grew in circulation along flows are a common mechanism that is probably the bodies, resembling the LEVs produced around delta- significant for trim control in all species of tropical winged aircraft. These spiral vortices formed above the boxfishes. keels and increased in circulation as pitch angle became more positive, and formed below the keels and increased in circulation as pitch angle became more negative. Key words: vortex, boxfish, leading edge vortices (LEV), digital Vortices also formed along the eye ridges of all boxfishes. particle image velocimetry (DPIV), stability, pressure, pitch, yaw.

Introduction The boxfishes (Teleostei: Ostraciidae) are marine, mostly with a minimal turning radius, and hold precise control of their shallow-water, mostly tropical reef-dwelling fishes that have positions and orientations (Walker, 2000; Hove et al., 2001). the anterior 2/3 to 3/4 of their bodies encased in rigid bony The demonstration of some of the smallest amplitude recoil carapaces consisting of hexagonal plates (or scutes; Tyler, movements associated with swimming among fishes is one of 1980). These fishes swim by employing coordinated the most notable qualities of boxfishes (Hove et al., 2001). In movements of their five fins. A detailed study of swimming short, these fishes are remarkably stable, i.e. they can maintain dynamics and kinematics in one species, the spotted boxfish desired swimming trajectories during steady and intentionally Ostracion meleagris, revealed that it uses distinct gaits to unsteady motions of maneuvers while being affected by both produce surprisingly constant costs of transport over a wide external and self-generated perturbations. range of speeds (Gordon et al., 2000; Hove et al., 2001). The bony carapaces of different species of boxfishes vary Although they appear ungainly, boxfishes are capable of significantly in their cross-sections, longitudinal shapes and swimming rapidly [>6·body·lengths·(BL)·s–1], can spin around structural ornamentation, with some boxfishes having horns,

THE JOURNAL OF EXPERIMENTAL BIOLOGY 328 I. K. Bartol and others spikes and pointed extensions of the carapace. The carapaces boxfishes having different carapace morphologies have similar are generally not streamlined, but have longitudinal keels and self-correcting mechanisms? To make this determination, shapes that appear to orient and control water flows over their flows around the bodies of three morphologically distinct surfaces in beneficial ways. Bartol et al. (2003) determined that boxfishes were investigated. The species were: (1) the spotted the carapace of one boxfish, the smooth trunkfish Lactophrys boxfish Ostracion meleagris, which has a trapezoidal cross- triqueter, plays an integral role in the hydrodynamic stability section and no significant ornamentation; (2) the scrawled of swimming. The ventro-lateral keels of this species of cowfish Acanthostracion quadricornis, which has a pentagonal boxfish, which is broadly triangular in cross-section, produce cross-section and has sharp anterior horns and bony projections leading edge vortical flows that increase in magnitude when extending from the ventral keels; and (3) the buffalo trunkfish the carapace pitches and yaws at greater angles. The vortices Lactophrys trigonus, which has a triangular cross-section, a are strongest at posterior regions of the carapace and produce hump on its back, and ornamentation along the ventral keels self-correcting trimming forces that probably help L. triqueter (Fig.·1). Three separate but interrelated techniques were maintain smooth swimming trajectories in turbulent employed to investigate flow development along the carapaces environments. (Bartol et al., 2003). For each approach, anatomically exact, In this paper, we address a related question: do other stereolithographic models were used. The three techniques

Spotted boxfish Ostracion meleagris Two dorsal keels Convexity

Concavity Concavity

Two ventral keels Convexity Center of mass Trapezoidal cross-section

Scrawled cowfish Acanthostracion quadricornis Dorsal keel Narrow width Horns Pronounced Pronounced convexity convexity

Concavity Concavity

Two ventral keels Ventral keel extensions Center of mass Pentagonal cross-section

Buffalo trunkfish Lactophrys trigonus Dorsal keel Dorsal hump

Concavity

Two ventral keels Ventral keel extensions Center of mass Triangular cross-section

Smooth trunkfish Lactophrys triqueter Dorsal keel

Concavity

Two ventral keels Triangular cross-section Concavity Center of mass

Fig.·1. Anterior, posterior, and lateral views of a spotted boxfish, scrawled cowfish, buffalo trunkfish, and smooth trunkfish. The smooth trunkfish was examined in Bartol et al. (2003). Some distinguishing features of each boxfish are highlighted in the figure. Scale bars, 1·cm.

THE JOURNAL OF EXPERIMENTAL BIOLOGY Flows around rigid-bodied boxfishes 329 were: (1) digital particle image velocimetry (DPIV), which A dual pulsed ND:YAG laser (New Wave Research, Inc., provides global data on flow structures at selected planar Fremont, CA, USA; pulse duration=0.02·ms, pulse sections along the carapaces; (2) pressure distribution separation=1·ms), a series of front-surface mirrors, and a measurements, which provide information on conditions at the cylindrical lens were used to generate and align an illuminated surface of the carapaces, a region that is difficult to resolve sheet ~1.0·mm thick. The laser sheet was projected underneath using DPIV; and (3) force balance measurements, which the water tunnel in a transverse (YZ) plane. The laser sheet was provide an integrated measurement of the forces and moments adjusted to illuminate planes in the wake of the models (5·cm acting on the carapaces. downstream from the caudal fin) and at five locations along the carapace: the eye ridge, the point of maximum girth, the midpoint between the point of maximum girth and the posterior Materials and methods edge of the carapace, the posterior edge of the carapace, and Model construction the caudal peduncle. An Hawaiian spotted boxfish Ostracion meleagris Shaw Using PixelFlow™ software (FG Group LLC, San Marino, [12.1·cm total length (TL), 48.5·g] and two Puerto Rican CA, USA) and a customized timing box, we phase-locked the boxfishes, a buffalo trunkfish Lactophrys trigonus L. dual laser and a frame grabber to the video camera, and (23.4·cm·TL, 261.2·g) and a scrawled cowfish Acanthostracion collected 30 paired images at each pitch/yaw angle for all quadricornis L. (16.4·cm·TL, 18.8·g), were captured, frozen planar locations described above. In all images, except those immediately, and shipped frozen to the University of collected in the wake, the model was subtracted out of the field California, Los Angeles (UCLA), where they were stored in a of view prior to processing. The displacement of particles freezer at –70°C. Computed tomography (CT) scans were within interrogation windows [322 pixels with a 16 pixel offset] performed on still frozen (–70°C) specimens with the dorsal comprising the paired images was calculated by cross- and anal fins removed, the pectoral fins positioned flush against correlation (Willert and Gharib, 1991). Mean velocity and the body, and the caudal fin aligned with the longitudinal axis mean vorticity fields were determined for each trial. of the body. The scans and subsequent stereolithographic Circulation of regions of concentrated vorticity attached to the model construction were performed using procedures model were determined by carefully tracing along the outline described in Bartol et al. (2003). To improve resolution of of the model where the region of concentrated vorticity was DPIV and force balance measurements and accommodate present, tracing along an iso-vorticity contour of magnitude more ports in pressure experiments, the 12.1·cm spotted 2·s–1 found external to the model, and integrating the vorticity boxfish was enlarged to 17.0·cm during model construction. within the selected area. For detached vortices in the wake, All proportions were kept constant. circulation was computed by integrating vorticity within an iso-vorticity contour of magnitude 2·s–1 surrounding each Digital particle image velocimetry (DPIV) vortex. Tracings and circulation calculations were performed The basic 2-D DPIV technique for flow field measurements using PixelFlow software. is described in Willert and Gharib (1991) and Raffel et al. (1998), and a more detailed description of our techniques is Pressure measurements included in Bartol et al. (2003). The models were positioned Surface pressures along the boxfish carapaces were measured at pitch angles (±30° at 2° intervals) and yaw angles (0–30° at at multiple locations. Series of 36–48 holes, most often aligned 10° intervals) in a water tunnel with a 30·cm30·cm100·cm in dorso-ventral transects at intervals along the carapaces, were test section (Model 503, Engineering Laboratory Design, Inc., drilled in sections of models that were fabricated in halves. It Lake City, MN, USA). The pitch angle refers to the angle was necessary to drill some ports below the ventral keel slightly between free-stream flow and a line connecting the center of out of alignment with respect to other ports along a transect so mass and the center of the caudal peduncle (centerline of fish). as not to damage the delicate ventral keel extensions and/or The yaw angle refers to the angle between free-stream flow and provide viable channels for tubing. Urethane tubing (0.068·cm the dorsal keel (for those fishes with one keel) or a line i.d., 0.129·cm o.d.) was inserted into the holes and glued in equidistant between the dorsal keels (for the spotted boxfish). place so that it was flush with the surface of the models. The The water tunnel was seeded with 14·µm silver-coated, hollow tubing was threaded through a rod attached to the posterior glass spheres (Potter Industries Inc., Carlstadt, NJ, USA) and section of the models, and the model halves were glued set at a speed of 44·cm·s–1 (1.9–2.7·BL·s–1) for all experimental together. The rod was used to mount the models caudally to a trials. The water tunnel also was set at lower and higher speeds sting in a 61·cm wind tunnel (model 407, Engineering periodically to confirm that DPIV results at the intermediate Laboratory Design, Inc., Lake City, MN, USA). Tubing exiting speed above were qualitatively applicable over the range of the models was connected to a Scanivalve 48-channel rotating swimming speeds of the fish. pressure scanner (Scanivalve Inc., Liberty Lake, WA, USA) A Pulnix TM-1320 digital video camera (Sunnyvale, CA, and a barocel electric manometer and capacitative differential USA; 30·Hz frame rate, 480768 pixel frame size) with a pressure sensor (Barocel Datametrics, Wilmington, MA, USA). 35·mm or 85·mm Nikkor lens (Nikon, USA) was positioned Static pressure (N·m–2) at each of the ports was expressed downstream of the working section to record oncoming flows. relative to static pressure at a tunnel wall port.

THE JOURNAL OF EXPERIMENTAL BIOLOGY 330 I. K. Bartol and others

Data were collected while each model was positioned at 2° above the ventral keels at positive pitch angles, regions of increments for pitch angles of –30 to +30°. For the angles concentrated vorticity formed below the ventral keels at considered, data were acquired at 100·Hz for 10·s using negative pitch angles (Fig.·3). Furthermore, when compared to LabVIEW software (National Instruments, Inc., Austin, TX, flow patterns at positive pitch angles, vortical flow rotation USA). Wind tunnel speed was set according to the Reynolds reversed in direction (i.e. vortices around the right ventral keel number considered in water tunnel trials. Mean pressure were rotated counterclockwise when viewed from the rear at coefficients (CP) were calculated at each port for each pitch positive pitch angles but clockwise at negative pitch angles). angle using the equation described in Bartol et al. (2003). Therefore, an upwash of flow developed in the wake at negative pitch angles. Force measurements Although the location and pattern of vortex development did Each of the three models was mounted to a sting in a large not change appreciably for different positive pitch angles or for water tunnel (test section 61·cm46·cm244·cm), and force different negative pitch angles, the magnitude of vortex measurements were collected using an in-house force balance circulation and peak vorticity did. At a pitch angle close to 0°, (Lisoski, 1993) containing two load cells for measuring lift and peak vorticity and circulation of ventral vortices were lowest one for measuring drag (Interface, Inc. Scottsdale, AZ, USA). for all three boxfishes (Fig.·4). At 0° the direction of vortex Force data were collected in 2° increments from pitch angles rotation was similar to that at positive pitch angles, and a of at least –30 to +30°. Flow speed during trials was identical downwash of flow was observed in velocity vector plots. to that considered in DPIV experiments (44·cm·s–1; i.e. As the carapace was positioned at increasingly more positive 1.9–2.7·BL·s–1). At each pitch angle considered, data output pitch angles, ventral vortices increased in peak vorticity and was recorded at 200·Hz for 10·s using a Dash 8 Series data circulation. Similarly, as the carapace was positioned at recorder (Astro-Med, Inc., West Warwick, RI, USA). increasingly more negative pitch angles, ventral vortices Coefficients of drag (CD), lift (CL) and pitch moment (CM) increased in peak vorticity and circulation. were calculated using equations described in Bartol et al. In the scrawled cowfish and buffalo trunkfish, the cores of (2003). vortices always formed approximately above or below the ventral keel extensions at the posterior edge of the carapace at positive and negative pitch angles, respectively (Fig.·4). Results However, in the spotted boxfish, which lacks ventral keel Digital particle image velocimetry extensions, the cores of regions of concentrated vorticity were Ventral keels – pitch not always directly above or below the ventral keel at the When all three boxfish models were positioned at positive posterior edge of the carapace. pitch angles, regions of concentrated vorticity (leading edge vortices; LEVs) began to develop near the anterior edges of the Dorsal keels – pitch ventral keels at a longitudinal location corresponding to the eye Regions of attached, concentrated vorticity formed dorsally ridge (Fig.·2). These regions of concentrated vorticity around the eye ridges of all three boxfishes at positive pitch intensified in peak vorticity and circulation posteriorly along angles (Fig.·2). At the eye ridge dorso-ventral transect, dorsal the ventral keels until two well-developed, counter-rotating regions of concentrated vorticity were greater in circulation vortices ultimately formed above the ventral keels at the and peak vorticity than ventral regions of concentrated posterior edge of the carapace. These ventral vortices left the vorticity. However, at the posterior edge of the carapace where body at the caudal peduncle, where vortices increased in terms both dorsal and ventral attached vortices were strongest in of circulation and peak vorticity relative to attached vortices at circulation, dorsal vortices had less circulation and lower peak the posterior edge of the carapace (Fig.·2). In the wake, ventral vorticity than ventral vortices. Some regions of weaker, vortices either merged with dorsal vortices or were in the concentrated, attached vorticity also formed around the eye process of merging. Clockwise rotation was present on the left ridges at negative pitch angles (Fig.·3). side of the carapaces (when viewed from the rear), while In the spotted boxfish, dorsal regions of attached vorticity counterclockwise rotation was present on the right side of the grew consistently in terms of peak vorticity and circulation carapaces, resulting in the development of a downwash of flow posterior to the eye ridges both at positive and negative pitch in the wake. angles (Figs·2, 3). Although there was some migratory At negative pitch angles, regions of concentrated, attached movement of concentrated vorticity around the dorsal keels at vorticity also began to develop around the ventral keels at a low positive pitch angles, dorsal vortices generally grew along longitudinal location corresponding to the eye ridge in all three and above the dorsal keels at positive pitch angles until two boxfishes (Fig.·3). As was the case for positive pitch angles, well-developed vortices ultimately formed at the posterior circulation and peak vorticity of ventral, concentrated, attached edge of the carapace. Dorsal vortex circulation growth was vorticity increased posteriorly, developing into two counter- particularly pronounced in the posterior quarter of the rotating vortices at the posterior edge of the carapace and carapace, sometimes even outpacing ventral vortex growth. At ultimately leaving the body close to the caudal peduncle. negative pitch angles, dorsal vortices also grew along the However, while regions of concentrated vorticity developed dorsal keels, but two well-developed vortices formed below the

THE JOURNAL OF EXPERIMENTAL BIOLOGY Flows around rigid-bodied boxfishes 331 D Γ –1 –1 –1 –1 –1 =26.5 s =5.5 s =7.5 s =31.3 s =6.5 s D V D D V ω ω ω ω ω P P P P P ; ; ; ; ; –1 –1 –1 –1 –1 s s s s s 2 2 2 2 2 , respectively) are included V ω P =24.3 cm =69.0 cm =42.4 cm =11.0 cm =35.0 cm D V D D V Γ Γ Γ Γ Γ and –1 –1 V –1 –1 –1 –1 Γ =34.3 s =11.5 s D V =32.7 s =11.1 s =21.3 s =17.7 s D V ω ω D V ω ω P P ω ω ; ; P P P P ; ; –1 –1 ; ; –1 –1 s s –1 –1 2 2 s s s s 2 2 2 2 0 =24.7 cm =63.7 cm 2 D V e =16.4 cm =33.0 cm =24.1 cm =28.3 cm + s D V Γ Γ D V i Γ Γ Γ Γ w k c –1 –1 –1 –1 o –1 l –1 0 c 1 r + e =28.0 s =9.2 s t D V =22.0 s =10.8 s =19.5 s =9.3 s n D V ω ω D V u P P ω ω ω ω ; ; o P P P P ; ; –1 –1 ; ; C s s –1 –1 –1 –1 2 2 , respectively) and a ventral vortex ( s s s s 2 2 2 2 D 0 ω P =14.5 cm =56.9 cm D V =12.1 cm =23.3 cm =16.8 cm =26.7 cm Γ Γ D V D V beneath the plots. In wake of spotted boxfish, ventral and dorsal vortices merge and thus dorsal ventral distinctions are not necessary. and shadows beneath the models represent areas that were shielded from laser light. White dots in scrawled cowfish and buffalo trunkfish figures are the tips of ventral keel extensions. Mean circulation magnitude and mean peak vorticity for a dorsal vortex ( Γ Γ Γ Γ 0 –1 e –1 1 s –1 –1 –1 i – –1 w k =21.7 s =16.5 s c V =6.2 s =13.0 s =9.1 s V =11.1 s D o ω D V D ω l ω Pitch angle +10° P ω ω ω P P ; C P P P ; ; 0 –1 ; ; ; –1 –1 2 s –1 –1 –1 s 2 s 2 s s – s 2 2 2 2 ) =5.3 cm =29.8 cm 1 =8.5 cm =10.7 cm D V – =13.4 cm =19.0 cm D V Γ Γ D V s Γ Γ ( Γ Γ y t –1 i –1 –1 –1 c –1 i –1 t r =13.5 s =7.0 s o =15.4 s =11.8 s =5.3 s D V D V D =6.7 s ω ω ω ω V V ω P P P P ω P ; ; ; ; P ; –1 –1 –1 –1 ; –1 s s s s –1 2 2 s 2 2 2 s 2 =7.5 cm =9.2 cm =8.1 cm =5.2 cm D V D V =10.6 cm =6.8 cm Γ Γ Γ Γ D V Γ Γ –1 –1 –1 –1 –1 –1 =9.1 s =5.8 s =12.7 s =12.3 s h =1.3 s =5.1 s h D V D V s D V s i i ω ω ω ω f ω ω h f P P P P s P P k w i ; ; ; ; ; ; f o n –1 –1 –1 –1 x –1 –1 c u s s s s r o s s 2 2 2 2 t d 2 2 b e o l d l e a w t f a t f r o u c =9.6 cm =4.1 cm =9.3 cm =3.3 cm =9.5 cm =4.4 cm p D V D V D V S B S Γ Γ Γ Γ Γ Γ 2. Vorticity contour fields around and in the wake of spotted boxfish (upper row), · scrawled cowfish (middle row), and buffalo trunkfish (bottom row) models positioned at a pitch angle of +10°. The data are viewed in transverse planes at various locations along the body and in wake. Each plot is mean result of 30 paired images (1 representative trial). From left to right, the locations, which are highlighted in upper corner of figures, are: eye ridge, maximum girth, midpoint between girth and posterior edge of the carapace, posterior caudal peduncle, and wake. The Fig.

THE JOURNAL OF EXPERIMENTAL BIOLOGY 332 I. K. Bartol and others , L ω P and L Γ –1 –1 –1 –1 , respectively) are V =8.3 s =18.4 s =7.0 s D =30.1 s D V ω D ω ω ω P P ω P P ; P ; ; ; –1 –1 –1 s –1 s s 2 and 2 2 s 2 V Γ =40.6 cm =11.9 cm =27.3 cm D =57.9 cm D V Γ D Γ Γ Γ –1 –1 –1 –1 –1 –1 =14.5 s =13.5 s D V ω ω =18.0 s V =3.4 s P P =19.2 s =9.2 s D D V ; ; ω ω –1 –1 P ω ω P ; P P s s 2 2 ; ; ; –1 –1 –1 –1 s 2 s s s 2 2 2 0 2 + e =20.0 cm =34.1 cm D V s i Γ Γ =8.0 cm =24.9 cm D V =17.0 cm =48.5 cm w Γ Γ D V k –1 –1 Γ Γ c o l 0 –1 c , respectively) and a ventral vortex ( 1 –1 r =12.3 s =11.8 s –1 D + e D V –1 t ω ω ω n P P P =17.7 s u ; ; V =3.7 s =17.6 s o –1 –1 D ω V =0.0 s s s ω D P C ω 2 2 P ; and ω P ; –1 P ; D –1 ; s 0 –1 2 s Γ –1 s 2 2 s 2 =15.3 cm =22.0 cm D V Γ Γ =5.5 cm =22.0 cm D V =0.0 cm =41.4 cm included beneath the vorticity contour plots. In scrawled cowfish, mean circulation magnitude and mean peak vorticity for a lateral vortex ( respectively) also are included. In the wake, dorsal and ventral distinctions not necessary for the spotted boxfish and buffalo trunkfish since ventral dorsal vortices merge. dots in scrawled cowfish and buffalo trunkfish figures are the tips of ventral keels extensions. Mean circulation magnitude and mean peak vorticity for a dorsal vortex ( Γ Γ D V Γ Γ 0 –1 e –1 1 s i – –1 –1 w –1 –1 –1 =11.5 s =5.7 s k D V c ω ω o =16.8 s =16.3 s P P l V =5.7 s V =5.7 s =6.2 s ; ; D L D C ω ω –1 –1 0 ω Pitch angle –10° ω P ω P s s 2 P ; 2 2 P P ; ; ; ; – –1 –1 –1 –1 –1 s s 2 2 s s s 2 2 2 ) 1 – =14.3 cm =16.2 cm D V s Γ Γ ( =5.8 cm =13.8 cm =7.8 cm =6.5 cm =20.8 cm D L V D V y Γ Γ Γ Γ Γ t i c i –1 t –1 r –1 –1 –1 o –1 –1 =6.5 s V V =3.7 s D =14.2 s ω =15.8 s V =1.3 s ω V =0.0 s =12.1 s P D L D ω P ; ω ω ; ω P ω –1 P P ; P –1 P ; s ; 2 ; ; –1 s –1 2 –1 –1 –1 s s 2 2 s s s 2 2 2 =5.6 cm =11.8 cm D V =1.1 cm =10.3 cm Γ Γ =9.0 cm =0.0 cm =15.9 cm D L V D V Γ Γ Γ Γ Γ –1 –1 –1 –1 –1 –1 =5.7 s =2.1 s =1.6 s =2.2 s =6.2 s =2.6 s D V D V D V ω ω ω ω h ω ω P P P P s P P i ; ; ; ; f ; ; –1 –1 –1 –1 x –1 –1 s s s s o 2 2 s s 2 2 2 2 b Buffalo trunkfish d e t t o =3.1 cm =9.4 cm =1.8 cm =2.7 cm p =2.6 cm =2.2 cm D V D V D V S Γ Γ Γ Γ Scrawled cowfish Γ Γ 3. Vorticity contour fields around and in the wake of spotted boxfish (upper row), · scrawled cowfish (middle row) and buffalo trunkfish (bottom models positioned at a pitch angle of –10°. The data are viewed in transverse planes at various locations along the body and in wake. Each plot is mean result of 30 image pairs (1 representative trial). From left to right, the locations, which are highlighted in upper corner of figures, are: eye ridge, maximum girth, midpoint between girth and posterior edge of the carapace, posterior edge of caudal peduncle, and wake. The shadows on the sides of or beneath models represent areas that were shielded from laser light. White Fig.

THE JOURNAL OF EXPERIMENTAL BIOLOGY Flows around rigid-bodied boxfishes 333 –1 –1 –1 –1 –1 –1 –1 –1 –1 –1 –1 –1 =–13.9 s , respectively) and a =–20.1 s =–1.1 s D =–12.4 s =–11.1 s =–4.7 s D =17.1 s D D V =–4.6 s D =17.6 s =2.8 s =–7.1 s D ω V =6.5 s ω D V V V ω ω ω V ω P ω ω P ω P ω ω ω P ; P P ω P ; P P ; P ; P ; P –1 ; ; –1 ; ; ; ; –1 –1 –1 ; s –1 –1 s 2 –1 –1 –1 –1 s s s 2 –1 s s 2 2 2 s 2 s s 2 s and P s 2 2 2 2 2 D Γ =–28.9 cm =19.8 cm =–0.8 cm =2.2 cm =–57.8 cm =23.4 cm =–3.6 cm =7.4 cm D V D V =–27.1 cm =30.0 cm =–4.8 cm =–7.7 cm D V D V D V D V Γ Γ Γ Γ Γ Γ Γ Γ Γ Γ Γ Γ –1 –1 –1 –1 –1 –1 =43.0 s =23.0 s =26.5 s =13.5 s V =0.0 s V =6.8 s D V D D ω ω ω ω ω P ω P P P P ; P ; ; ; ; ; –1 –1 –1 –1 –1 –1 s s 2 s s 2 s s 2 2 2 2 =0.0 cm =90.3 cm =7.1 cm =32.7 cm =22.2 cm =54.4 cm , respectively) are included beneath the vorticity contour plots. D V D V D V V Γ Γ Γ Γ Γ Γ ω 0 P –1 –1 e –1 2 –1 s i + –1 –1 and w k =12.3 s =11.8 s V =17.6 s D V c =17.7 s V =0.0 s Γ V =3.7 s ω ω o D D ω l ω P P ω P ω c P ; ; P ; r P 0 ; –1 –1 ; e –1 ; 1 –1 s s t –1 2 2 s –1 s + 2 n s 2 s 2 2 u o C =15.3 cm =22.0 cm =0.0 cm =41.4 cm D V =5.5 cm =22.0 cm Pitch angle –10° D V D V Γ Γ areas that were shielded from laser light. White dots in scrawled cowfish and buffalo trunkfish figures are the tips of ventral keels extensions. Mean circulation magnitude and mean peak vorticity magnitude for a dorsal vortex ( For the yaw angles, circulation and peak vorticity values for each side of carapace are included (right side, in normal text = far-field; left italicized near-field). ventral vortex ( Γ Γ Γ Γ 0 –1 –1 –1 –1 –1 –1 =6.5 s =4.7 s D V ω ω =3.1 s =4.4 s P P =3.7 s =4.4 s D V ; ; D V 0 ω ω –1 –1 ω ω 1 P P s s P P e 2 2 ; ; – ; ; s i –1 –1 –1 –1 s s s s w 2 2 2 2 k c o =3.02 cm =4.35 cm l D V 0 Γ Γ =4.7 cm =1.6 cm C =2.9 cm =4.3 cm D V 2 D V Γ Γ – Γ Γ ) –1 1 –1 – –1 –1 –1 –1 s ( =19.5 s =9.3 s y D V t =28.0 s =9.2 s =22.0 s =10.8 s i ω ω D V D V c P P ω ω ω ω i ; ; P P t P P –1 –1 ; ; r ; ; s s –1 –1 –1 –1 o 2 2 s s s s 2 2 2 2 V =16.8 cm =26.7 cm D V =14.5 cm =56.9 cm =12.1 cm =23.3 cm Γ Γ D V D V Γ Γ Γ Γ –1 –1 –1 –1 –1 –1 =21.2 s =18.6 s =25.3 s =8.6 s =36.0 s =11.4 s D V D V D V ω ω ω ω ω ω P P P P P P ; ; ; ; ; ; –1 –1 –1 –1 –1 –1 s s 2 2 s s s s 2 2 2 2 =32.7 cm =40.7 cm =10.3 cm =32.8 cm =23.7 cm =84.4 cm D V Pitch angle +20° Pitch angle +10° Pitch angle 0° Pitch angle –20° Yaw angle 10° D V D V Γ Γ Spotted boxfish Scrawled cowfish Buffalo trunkfish Γ Γ Γ Γ 4. Vorticity contour fields around the posterior edge of carapace spotted · boxfish (upper row), scrawled cowfish (middle and buffalo trunkfish (bottom row) models positioned (from left to right) at pitch angles of +20°, +10°, 0°, –10° and –20°, and a yaw angle of 10°. The data are viewed in transverse planes, sampling locations are highlighted in the upper corner of figures. Each plot is mean result 30 image pairs (1 representative trial). The shadows underneath or to the side of models represent Fig.

THE JOURNAL OF EXPERIMENTAL BIOLOGY 334 I. K. Bartol and others

Positive pitch angles Negative pitch angles A 0.50 0.40

.6 0.20 7 0 . 0 . 8 . 9 . –0.50 –0.20 .10 . 11† –0.40 12 –1.00 –0.60 *1% –1.50 –0.80 6 7 8 9 10 11 12 6 7 8 9 10 11 12 B 0 –0.10 –0.20 15 –0.20 . 16 –0.30 . 17 . 18 –0.40 –0.40 . 19 . 20 –0.50 –0.60 . 21 –0.60 . 22 23 –0.80 –0.70 *40% –0.80 –1.00 15 16 1718 19 20 21 22 23 –0.90 C –0.1 –0.2 15 16 1718 19 20 21 22 23

–0.2 –0.3 . 24 –0.3 –0.4 –0.4 . 25 –0.5 . 26 –0.5 Pitch angle (deg.) . 27 P –0.6 . C –0.6 28 0 –0.7 –0.7 +4 or –4 51% –0.8 –0.8 +10 or –10 2425 26 27 28 2425 26 27 28 D –0.10 –0.20 +14 or –14 +20 or –20 –0.20 –0.25 . 29 +24 or –24 . 30 –0.30 +30 or –30 . 31

Pressure coefficient, –0.30 . 32 . 33 –0.35 . 34 –0.40 . 35 –0.40 . 36† . –0.50 37 –0.45 *64% –0.60 –0.50 29 30 3132 33 34 35 36 37 29 30 3132 33 34 35 36 37 E 0.10 –0.05

0 –0.10 –0.15 . 38 –0.10 –0.20 . 39 . 40 –0.20 –0.25 . 41 . –0.30 .42† –0.30 43 –0.35 –0.40 79% –0.40 –0.50 –0.45 F 38 39 40 41 42 43 38 39 40 41 42 43 0.20 0.10

0.10 0

. 44 0 –0.10 . 45 . 46 –0.10 –0.20 . 47† . 48 –0.20 –0.30

*94% –0.30 –0.40 –0.40 –0.50 44 45 46 47 48 44 45 46 47 48 Pressure port

THE JOURNAL OF EXPERIMENTAL BIOLOGY Flows around rigid-bodied boxfishes 335 dorsal keels, reaching maximum strength at the posterior edge greater circulation and peak vorticity in far-field regions of the of the carapace. Peak vorticity and circulation of dorsal carapace (i.e. portions of the carapace that are shielded vortices increased with more positive and negative pitch angles somewhat from oncoming flow) than in near-field locations (Fig.·4). At both positive and negative pitch angles, dorsal (i.e. portions of the carapace that are directly exposed to vortices always merged with ventral vortices in the wake of the oncoming flow; Fig.·4). In general, one vortex formed along spotted boxfish. the dorsal keel and one vortex formed along the ventral keel In the other boxfishes, dorsal vortex formation posterior to of each boxfish at the far-field side of the carapace. Vortex the eye ridge was less well defined. In the scrawled cowfish, development in these far-field locations began at anterior regions of attached vorticity shed from the anterior horns/eye regions of the dorsal and ventral keels and grew along the body ridges persisted on either side of the dorsal keel at positive before detaching from the body at either the posterior edge of pitch angles (Fig.·2). These vortices remained relatively the carapace or caudal peduncle. In contrast to pitch angles constant in circulation along the body, forming above lateral where vortex rotation was in the same direction on a particular regions of high convexity, before increasing slightly along the side of the carapace, dorsal and ventral vortices on the far-field posterior quarter of the carapace. At negative pitch angles, side of the carapaces rotated in different directions. For multiple regions of concentrated vorticity often developed in example, when viewed from the rear of the carapace and when lateral locations (Fig.·3). The strongest region of concentrated the far-field region is on the right side of the carapace, a vorticity frequently formed below the region of maximum clockwise and counterclockwise vortex developed around the convexity and merged with weaker dorsal regions of dorsal and ventral keels, respectively (Fig.·4). As yaw angles concentrated vorticity at the posterior edge of the carapace. No increased from 0°, peak vorticity and circulation of far-field consistent increase in circulation of dorsal vortices with more vortices intensified. As was the case with pitch angles, peak positive or negative pitch angle was observed in the scrawled vorticity and circulation of attached vortices were always cowfish, but circulation of dorsal vortices was generally higher greatest at the posterior edge of the carapace, irrespective of for positive compared with negative pitch angles (Fig.·4). At angle. both positive and negative pitch angles, dorsal/lateral and ventral vortices were often in the process of merging at the Pressure measurements wake sampling location (i.e. 5·cm from the caudal fin), but Terminology and figure format vortex unification was not always complete (Figs·2, 3). Throughout this section, dorso-ventral transects in Figs·5–7 In the buffalo trunkfish, regions of concentrated dorsal will be referenced. These transects are expressed as vorticity sometimes detached from the body and did not remain percentages of distance along the ventral keel beginning at the constant or grow in a consistent pattern posteriorly at either anterior end. Transects that coincide with those considered in positive or negative pitch angles (Figs·2, 3). In fact, circulation DPIV experiments are denoted by asterisks in the figures to and peak vorticity decreased frequently at certain locations facilitate cross-referencing with DPIV data. The term ‘local along the carapace when moving antero-posteriorly. Not pressure minimum’ will be used throughout this section. A surprisingly, no consistent increase in circulation of dorsal local pressure minimum refers to low pressure at a port relative vortices with more positive or negative pitch angle was to its immediate dorsal and ventral neighbors (if present) along observed in the buffalo trunkfish (Fig.·4). In most cases, ventral a selected dorso-ventral transect. and dorsal vortices, if present, merged in the wake. Ventral keels Ventral and dorsal keels – yaw For all three boxfishes, local pressure minima were often When the carapaces of each of the three boxfishes were detected near the ventral keels in locations where regions of positioned at yaw angles, regions of concentrated vorticity had attached, concentrated vorticity were observed, with the more acutely keeled scrawled cowfish and buffalo trunkfish having

Fig.·5. Pressure coefficients (Cp) plotted as a function of location more detectable minima than the spotted boxfish. At positive along various dorso-ventral transects (A–F) on the spotted boxfish pitch angles, local pressure minima generally were detected at model positioned at positive (left) and negative (right) pitch angles. ports just above the ventral keels. Ports where local pressure The locations of the pressure ports included in each graph are minima were consistently detected at positive pitch angles are highlighted in images to the left of the graphs. The location of each highlighted in red boxes (see positive pitch angle column in dorso-ventral transect is expressed as a percentage of ventral keel Figs·5–7). The lack of local pressure minima at ports 11 and length (measured from the anterior leading edge) in the lower left- 46 in the spotted boxfish is likely the product of port hand corner of each image. Ports in blue, red and black are located misalignment (e.g. port 11 is more anterior than neighboring on the dorsum, sides, and ventrum of the model, respectively. ports and port 46 is more posterior than its ventral neighbor, †Denotes ports that were slightly out of alignment with other ports along the dorso-ventral transect; * represent transects that were port 47). In the spotted boxfish and buffalo trunkfish, local low considered in DPIV studies. Blue and red rectangles highlight ports pressure was detected in lateral regions above the ventral keels, where local pressure minima were consistently detected at dorsal and as well as regions just above the ventral keels, at positive pitch ventral locations, respectively. An ambient pressure line (Cp=0) was angles. For example, in the spotted boxfish, local low pressure included in the most posteriorly located transect (F). was detected at pressure port 34 for pitch angles 24° and

THE JOURNAL OF EXPERIMENTAL BIOLOGY 336 I. K. Bartol and others

Positive pitch angles Negative pitch angles A 0.50 0 –0.10 . 6 0 . 7 –0.20 . 8 . 9 –0.30 . 10 –0.50 –0.40 . 11 . 12 –0.50 –1.00 *1% –0.60 –1.50 –0.70 6 7 8 9 10 11 12 6 7 8 9 10 11 12 B 0.20 0 . . 18 0 –0.20 . 19 20 –0.20 –0.40 . 21 . –0.40 . 22 –0.60 23 –0.60 . 24 . –0.80 *38% 25 –0.80 –1.00 –1.00 18 19 2021 22 23 24 25 18 19 2021 22 23 24 25 C 0.20 –0.10

0 –0.15 . 26 –0.20 –0.20 . 27 –0.25 Pitch angle (deg.) . 28 –0.40 . –0.30 0 29 –0.60 . 30 P –0.35 +4 or –4 C –0.80 52% –0.40 +10 or –10 +14 or –14 –1.00 –0.45 2627 28 29 30 31 2627 28 29 30 31 +20 or –20 D 0 –0.05 +24 or –24 –0.10 . –0.10 +30 or –30 . 32 –0.20 . 33 . 34 –0.30 –0.15 . 35 Pressure coefficient, 36 –0.40 . 37 –0.20 . 38 –0.50 –0.25 *64% –0.60 –0.70 –0.30 3233 34 35 36 37 38 3233 34 35 36 37 38 E 0.10 0.10 0 0.05 –0.10 0 . 39 –0.05 . 40 –0.20 –0.10 –0.30 . 42 –0.15 . 43† –0.40 –0.20 . 44 76% –0.50 –0.25 –0.60 –0.30 3940 42 43 44 3940 42 43 44 F 0.15 0.12 0.10 0.10 0.05 0.08 . 45 0 0.06 . –0.05 0.04 46 –0.10 0.02 –0.15 0 *93% –0.20 –0.02 –0.25 –0.04 45 46 45 46 Pressure port

THE JOURNAL OF EXPERIMENTAL BIOLOGY Flows around rigid-bodied boxfishes 337 ports 40 and 45 for pitch angles 18° (Fig.·5). In the buffalo for scrawled cowfish; and port 47 (positive pitch) for buffalo trunkfish, local low pressure was observed at ports 35 and 41 trunkfish]. at pitch angles 26° (Fig.·7). At negative pitch angles, local pressure minima generally Dorsal keels were detected at ports just below the ventral keels, which is Correlations between localized low pressure and where regions of concentrated vorticity were detected. Ports concentrated vorticity were less apparent in dorsal locations, where local pressure minima were consistently detected at where vortices were lower in circulation magnitude than in negative pitch angles are highlighted in red boxes (see negative ventral locations. The most consistent correlations in dorsal pitch angle column in Figs·5–7). The absence of local pressure locations occurred in the trapezoidal spotted boxfish, especially minima below the ventral keel at various transects was often a at higher pitch angles. At the 1%, 40% and 64% transects, local product of misalignment (e.g. ports 36 and 42 in spotted pressure minima were detected above the dorsal keel at boxfish and port 43 in buffalo trunkfish) or the absence of ports positive pitch angles in regions where concentrated vorticity below the ventral keel (e.g. 93% transect in scrawled cowfish, also was observed (see ports highlighted in blue in Fig.·5). 87% transect in buffalo trunkfish). In the scrawled cowfish, Local pressure minima were not detected above the dorsal keel local low pressures often were detected both at port 43, which at the 51% and 94% transects because no ports were sampled is located just below the ventral keel extension (see 76% just above the dorsal keel. At negative pitch angles, local transect), and port 44, which is located near the midline of the pressure minima were detected along most transects where ventrum in a region of high concavity. Low pressures at ports ports just below the dorsal keel were present (see ports 43 and 44 were particularly pronounced at pitch angles of –10 highlighted in blue in Fig.·5). Interestingly, along the 40% and –14°, where pressures were lower than at the other angles. transect local pressure minima were sometimes located at port For all three boxfishes, pressure generally decreased at the 18 (below the dorsal keel) at certain positive pitch angles, and ports above when pitch angles became more positive or more at port 17 (above the dorsal keel) at certain negative pitch negative, just as regions of concentrated vorticity increased in angles. This finding is consistent with the observed migratory circulation with increased pitch angle (Figs·5–7). Although movement of concentrated vorticity in DPIV experiments. peak vorticity and vortex circulation increased consistently In the scrawled cowfish, regions of concentrated vorticity along the ventral keels of the boxfishes from the anterior edge formed around the eye ridges and at lateral locations along the of the keel to the posterior edge of the carapace, pressure carapace at positive/negative pitch angles. Local pressure values at these locations did not decrease antero-posteriorly at minima were present near the eye ridges (see ports 7 and 8, either positive or negative pitch angles, and pressure was not Fig.·6). In lateral locations, there was evidence of local lowest at posterior regions of the carapace. Instead pressure pressure minima at the 38–76% transects, but the minima were above/below ventral keels was most often lowest near subtle relative to dorsal pressure minima detected in the spotted maximum girth (see 40% transect for spotted boxfish, 38% boxfish (see blue boxes, Fig.·6). At positive and negative pitch transect for scrawled cowfish, and 32% transect for buffalo angles, regions of concentrated vorticity formed most trunkfish in Figs·5–7). consistently around the eye ridges of the buffalo trunkfish. In general, pressure adjacent to the ventral keels at the Local pressure minima were present at the buffalo trunkfish posteriormost regions of the carapaces of the three boxfishes eye ridge at the 1% transect at positive pitch angles (see port (where regions of concentrated vorticity were observed) was 7 highlighted in the blue box). At pitch angles >–6° and –24°, not above ambient levels for positive and negative pitch there was also evidence of local pressure minima at the eye angles (i.e. pressure coefficients were <0). Examples are ridge, but not at moderate (–10 to –20°) pitch angles. However, found in Figs·5–7 [see port 46 (positive pitch) and port 47 local pressure minima could well have been present at port 8 (negative pitch) for spotted boxfish; port 46 (positive pitch) at these moderate negative pitch angles (port 8 was defective and thus was not included in the analysis).

Fig.·6. Pressure coefficients (Cp) plotted as a function of location At positive pitch angles, dorsal pressure was lowest at the along various dorso-ventral transects (A–F) on the scrawled cowfish eye ridge for all three boxfishes (see 1% transects, Figs·5–7), model positioned at positive (left) and negative (right) pitch angles. which is where concentrated vorticity was observed. At The locations of the pressure ports included in each graph are negative pitch angles in regions where concentrated dorsal highlighted in images to the left of the graphs. The location of each vorticity was detected, dorsal pressure was not always lowest dorso-ventral transect is expressed as a percentage of ventral keel at the eye ridge, however. For example, dorsal pressure was length (measured from the anterior leading edge) in the lower left- lowest at port 18 (maximum girth) for pitch angles of 0 to –16° hand corner of each image. Ports in red and white are located on the and at port 44 (posterior region of carapace) for pitch angles sides and ventrum of the model, respectively. †Denotes ports that were of –22 to –30° in the spotted boxfish (Fig.·5). For the scrawled slightly out of alignment with other ports along the dorso-ventral transect; * represent transects that were considered in DPIV studies. cowfish, dorsal pressure was lowest at port 21 (maximum Blue and red rectangles highlight ports where local pressure minima girth) for pitch angles –10° and for the buffalo trunkfish, were consistently detected at dorsal and ventral locations, dorsal pressure was lowest at port 17 (maximum girth) for respectively. An ambient pressure line (Cp=0) was included in the pitch angles –12° (Figs·6, 7). most posteriorly located transect (F). Dorsal pressures at the posteriormost regions of the carapace

THE JOURNAL OF EXPERIMENTAL BIOLOGY 338 I. K. Bartol and others

Positive pitch angles Negative pitch angles A 0.50 0.10 0 0 –0.10 . 6 . 7 –0.20 . 8 –0.50 –0.30 . 9 . 10 –0.40 . 11 –1.00 –0.50 .12 *1% –0.60 –1.50 –0.70 6 7 8 9 10 11 12 6 7 8 9 10 11 12 B 0.50 0

.16 –0.50 . 0 . 17 18 –0.50 –1.00 . 19 . 20 . 21 –1.00 –1.50 . 22 . 23 –1.50 –2.00 *32% . 24 –2.00 –2.50 16 1718 19 20 21 22 23 24 16 1718 19 20 21 22 23 24 C 0 0 Pitch angle (deg.) –0.20 . 25 0 –0.40 –0.50 +4 or –4 –0.60 . 26 +10 or –10 . 27 –0.80 +14 or –14 . 28 P –1.00 . C –1.00 +20 or –20 29 +24 or –24 46% –1.20 +30 or –30 –1.40 –1.50 2526 27 28 2925 26 27 28 29 D 0 0 –0.10 –0.20 .30 –0.20 . 31

. 32 Pressure coefficient, –0.40 –0.30 . 33 –0.40 . 34 . 35 –0.60 –0.50 . 36 . 37 –0.80 –0.60 . 38 *59% –0.70 –1.00 –0.80 30 3132 33 34 35 36 37 38 30 3132 33 34 35 36 37 38 E 0.20 0.05

0 0 . 39 –0.05 –0.20 . 40 –0.10 . 41 –0.40 . 42 –0.15 . 43† . 44 –0.60 –0.20 71% –0.80 –0.25 39 40 41 42 43 44 39 40 41 42 43 44 F 0.10 0.12 0.05 0.10 0 0.08 45 . –0.05 0.06 . 46 . 47 –0.10 0.04 –0.15 0.02

–0.20 0 87% –0.25 –0.02 45 46 47 45 46 47 Pressure port

THE JOURNAL OF EXPERIMENTAL BIOLOGY Flows around rigid-bodied boxfishes 339 were most consistently below ambient pressure in the spotted pitching moment coefficients increased in absolute magnitude. boxfish, especially at negative pitch angles (see port 44 for Moreover, changes in pressure and pitching moment spotted boxfish and port 45 for scrawled cowfish and buffalo coefficients at various pitch angles were highly correlated. As trunkfish). With few exceptions, ambient pressure (Cp=0) pressure coefficients deviated farther from ambient conditions, occurred between ports positioned immediately anterior and pitching moment coefficients increased farther from zero. posterior to the eye at negative pitch angles. However, at positive pitch angles >10°, ambient pressure did not occur consistently between ports positioned immediately anterior and Discussion posterior to the eye for the spotted boxfish and buffalo General findings trunkfish. Only in the scrawled cowfish was ambient pressure Although three very different carapace morphologies were consistently detected between the ports. examined, several important similarities in how the bodies direct flows emerged. The carapaces of all three boxfishes Force balance measurements generated vortical, spiral flows, most consistently in locations No obvious stall, i.e. the condition at which lift does not adjacent to the ventral keels, but also to varying degrees in grow with increased pitch angle, occurred at any of the pitch dorsal locations at various pitch angles. In general, ventral angles examined for the three boxfishes (Fig.·8A). The absence vortices were stronger in terms of circulation than those of stall at pitch angles of ±30° is characteristic of delta wings, detected in dorsal locations and had larger effects on localized as is the general shape of the lift coefficient curves for all three pressures along the carapace, as was evident by the consistent boxfishes. Lift coefficients were closest to a value of 0 at 0°, detection of pronounced local pressure minima in areas where the coefficients were all positive. These positive adjacent to the ventral keels. Leading edge vortices (LEVs) coefficients are consistent with the observed downwash of flow developed first at the anterior edges of the ventral keels and detected at 0° in DPIV experiments. At 0°, the spotted boxfish then grew in circulation as they traveled posteriorly along the had a CL=0.00908, the scrawled cowfish had a CL=0.00126, body until the posterior edge of the carapace, where boundary and the buffalo trunkfish had a CL=0.00620. Drag coefficients layer vorticity fed into the LEV and where the LEV began to were lowest at –4° for the spotted boxfish (CD=0.272), –2° leave the body. Additional growth in circulation of the LEVs for the scrawled cowfish (CD=0.125) and –2° for the buffalo also was observed at the caudal peduncle, which probably trunkfish (CD=0.101) (Fig. 8B). Generally, nose-down and occurred as even more of the body’s boundary layer vorticity nose-up pitching moment coefficients CM occurred at positive was shed into the LEVs. As pitch angles increased from 0° in and negative pitch angles, respectively. The transition between the positive direction, LEVs with stronger peak vorticity and nose-up and nose-down pitching moments occurred at circulation developed above ventral keels, often within approximately +2° for the spotted boxfish and between 0 and concavities that served to hold vortices in place, and reached –2° for the scrawled cowfish and buffalo trunkfish (Fig.·8C). maximum strength (while attached) at postero-lateral regions Furthermore, the absolute magnitude of CM increased as pitch of the carapace. As pitch angles increased from 0° in the angles became more positive and more negative. negative direction, LEVs with stronger peak vorticity and circulation developed below ventral keels often within adjacent Correlations of vortex strength, pressure and pitch moments concavities, reaching maximum strength (while attached) at Clear correlations among vortex circulation, pressure postero-ventral regions of the carapace. coefficients and pitching moment coefficients were detected at Low pressure correlated well with regions of concentrated the posterior edge of the carapace (Table·1). As pitch angle vorticity. Local pressure minima were observed when vortex deviated farther from 0° and circulation of vortices at the cores were close to the carapace surface, and pressure posterior edge of carapace increased, pressure coefficients and decreased as pitch angles deviated from 0°, either in the negative or positive direction. This was expected based on

Fig.·7. Pressure coefficients (Cp) plotted as a function of location Bernoulli’s principle, which states that higher local speeds along various dorso-ventral transects (A–F) on the buffalo trunkfish result in lower static pressure. With this principle in mind, low model positioned at positive (left) and negative (right) pitch angles. static pressure should be detected along the carapace when the The locations of the pressure ports included in each graph are core of a vortex, a region in which flow speeds are higher than highlighted in images to the left of the graphs. The location of each the surrounding fluid, is close to the surface. As the vortex dorso-ventral transect is expressed as a percentage of ventral keel intensifies in strength and local speeds increase, surface length (measured from the anterior leading edge) in the lower left- pressures should become increasingly more negative and hand corner of each image. Ports in red and black are located on the conspicuous (McCormack and Crane, 1973; Tritton, 1998; sides and ventrum of the model, respectively. †Denotes ports that were Vogel, 2003). slightly out of alignment with other ports along the dorso-ventral transect; * represent transects that were considered in DPIV studies. One fairly consistent finding among the boxfishes was that Blue and red rectangles highlight ports where local pressure minima surface pressures generally did not continue to decrease along were consistently detected at dorsal and ventral locations, antero-posterior transects where regions of concentrated respectively. An ambient pressure line (Cp=0) was included in the vorticity were detected and were found to increase in most posteriorly located transect (F). circulation. Instead, lowest pressures along these transects

THE JOURNAL OF EXPERIMENTAL BIOLOGY 340 I. K. Bartol and others often were detected in more anterior regions, such as at energize flow close to the carapace surface and presumably maximum girth. This is because the vortex cores began to prevented flow separation in posterior regions of the carapace move away from the body in posterior locations, thus having (pressure coefficients were <0 in postero-ventral regions). This less effect on surface pressures. (Of course, it should be noted finding is important because it suggests that fin motion is not that the vortex cores are also larger in posterior regions and necessary to keep flow attached to the body. Interestingly, all thus affect larger areas, as observed in the spotted boxfish and of the patterns described above also were detected in the buffalo trunkfish.) Nonetheless, based on pressure coefficients, smooth trunkfish Lactophrys triqueter, a boxfish with a broadly posterior vortices associated with the ventral keels appeared to triangular cross-section, but with no significant ornamentation (Bartol et al., 2003).

1 Species-specific differences Cowfish Buffalo trunkfish Several noteworthy differences in flow patterns around the Spotted boxfish Smooth trunkfish three boxfishes were observed. The most obvious difference 0.5 Delta wing was that dorsal vortices most consistently formed, grew posteriorly, and were of the highest magnitude in the spotted boxfish compared with the other boxfishes. This is not

L 0 surprising given that the spotted boxfish has two widely C separated dorsal keels that extend longitudinally from the eye ridges to the posterior edge of the carapace. These keels, which become more acute in posterior regions, provide structure for –0.5 vorticity build-up and intensification, similar to that provided by the ventral keels (Bartol et al., 2002). In fact, vortices A around the dorsal keels energized flow close to the carapace –1 –40 –30 –20 –10 0 1020 30 40 surface and prevented flow separation in postero-dorsal regions of the carapace, just as ventral vortices did. In the other 1.4 Cowfish boxfishes, the eye ridges do not extend posteriorly as sharp Buffalo trunkfish lateral keels. Instead the eye ridges terminate along the body, 1.2 Spotted boxfish Smooth trunkfish while the single dorsal keel forms between the ridges. 1 The effects of localized dorsal vortex formation in spotted boxfish were most pronounced at high positive and negative 0.8 pitch angles, when strong attached vortices and low pressures

D were detected at the posteriormost regions of the carapace. At C 0.6 more anterior regions (e.g. 40% transect), DPIV and pressure results indicate that attached concentrated vorticity migrates 0.4 above and below the dorsal keel at certain pitch angles. This may occur because the vortex shedding point on the eye ridge 0.2 moves as the pitch angle changes, such that the vortex slides B up and down. The convexity of the dorsum and/or rounded 0 nature of the keel at maximum girth (Bartol et al., 2002) also –40 –30 –20 –10 0 1020 30 40 may facilitate vortex migration. Interestingly, there was 2 significantly less vortex migration at the posterior quarter of Cowfish the carapace, where the dorsal keels sharpen, and there is a 1.5 Buffalo trunkfish Spotted boxfish pronounced region of concavity above and below the keel 1 Smooth trunkfish (Bartol et al., 2002). These features facilitate vortex generation and retention during pitching, as evident by the consistent 0.5

M 0 Fig.·8. Lift coefficients C (A), drag coefficients C (B), and pitching C L D moment coefficients about the center of mass CM (C) for four –0.5 boxfishes (smooth trunkfish, buffalo trunkfish, scrawled cowfish and spotted boxfish) positioned at various pitch angles. In A, C values –1 L for a delta wing of similar aspect ratio (0.83) to that of the boxfishes –1.5 are also depicted. Delta wing data are from Schlichting and C Truckenbrodt (1969), and smooth trunkfish data are from Bartol et al. –2 (2003). Positive CM values indicate a nose-down pitching moment –40 –30 –20 –10 0 1020 30 40 about the center of mass, whereas negative CM values indicate a nose- Angle of attack (degrees) up pitching moment about the center of mass.

THE JOURNAL OF EXPERIMENTAL BIOLOGY Flows around rigid-bodied boxfishes 341

Table·1. Correlations of vortex circulation, pressure coefficients and pitching moment coefficients for various boxfishes Boxfish Comparison Count Z-value P-value r 95% lower C.I. 95% upper C.I. SB C vs P 7 4.35 <0.0001 0.974 0.832 0.996 SB C vs M 7 4.61 <0.0001 0.980 0.868 0.997 SB P vs M 7 3.84 0.0001 0.958 0.735 0.994 SC C vs P 7 3.72 0.0002 0.953 0.706 0.993 SC C vs M 7 4.84 <0.0001 0.984 0.894 0.998 SC P vs M 7 5.19 <0.0001 0.989 0.924 0.998 BT C vs P 7 4.13 <0.0001 0.968 0.796 0.995 BT C vs M 6 5.35 <0.0001 0.996 0.961 1.000 BT P vs M 6 3.66 0.0003 0.971 0.754 0.997

SB, spotted boxfish; SC, scrawled cowfish; BT, buffalo trunkfish. C, vortex circulation; P, pressure coefficient; M, pitching moment coefficient; r, correlation coefficient. Circulation of vortices found above (positive pitch angles) and below (negative pitch angles) the ventral keels at the posterior edge of the carapace were used in the correlations. Pressure coefficients at ports just above (positive pitch angles) or just below (negative pitch angles) the ventral keels, at the posterior edge of the carapace in locations where vortex circulation was measured, were used in the correlations. Data at pitch angles of 30, 20, 10, 0, –10, –20 and –30° were considered in correlations for the spotted boxfish and scrawled cowfish. These angles also were considered in the buffalo trunkfish for correlations between vortex circulation and pressure coefficient, but –30° was omitted from correlations involving pitching moment coefficients because of a lack of data. observation of strong vortices above and below the keels in the body. Based on the results of this study, these keel extensions, posteriormost carapace locations at positive and negative pitch together with a very pronounced concave ventrum, were angles, respectively. The effect of these vortices on the surface especially effective at facilitating attached vortex growth and was apparent in pressure data for negative pitch angles producing low pressures at the posteriormost sections of the (unfortunately, a lack of pressure ports above the dorsal keels carapace at negative pitch angles, especially those of –10 to in these posterior regions precluded an examination of surface –14°. pressures at positive pitch angles). The buffalo trunkfish generated well-developed ventral Dorsal vortices also formed and were retained around the vortices but produced minimal dorsal vorticity posterior to the carapace of the scrawled cowfish, albeit to a much lesser eye ridge. This is similar to results from a smooth trunkfish, degree than those detected in the spotted boxfish. As which has a similar cross-section (Bartol et al., 2003). The indicated above, the scrawled cowfish does not have two buffalo trunkfish has ventral keel extensions like scrawled dorsal keels that extend along the length of the carapace. cowfish. However, the keel extensions are shaped differently However, it does have two prominent anterior horns, eye in the two species. Rather than extending parallel to the ridges, and strong lateral convexity that extends along the longitudinal axis of the fish and being very close to the body, sides of the carapace, producing a somewhat pentagonal the keel extensions in the buffalo trunkfish extend more cross-section (Bartol et al., 2002). The horns and eye ridges laterally and are farther away from the body. Consequently, the generated vortices, and these vortices remained attached to keel extensions in the buffalo trunkfish do not appear to keep the body either above or below regions of lateral convexity. vortices as close to the carapace as in the scrawled cowfish. The convex regions lack sharp edges, as in spotted boxfish, Although not detected in this study, it should be noted that but provide perhaps enough geometry to retain and even these more laterally extended keels may facilitate beneficial facilitate minor vortex circulation growth as boundary layer vortex production and produce low pressure along other vorticity from the body feeds into the dorsal LEV. The regions of the carapace that were not sampled (e.g. at the keel observance of low pressure in areas adjacent to regions of extension itself or at regions more aligned with the tip of the convexity is consistent with the DPIV findings. The absence extension). of sharp keels and regions of dorsal concavity to corral The scrawled cowfish, buffalo trunkfish and smooth vorticity led to high migratory movement of lateral vortices. trunkfish all have more triangular cross-sections and sharper Moreover, unlike the spotted boxfish, dorsal vortices in the ventral keels than the trapezoidal spotted boxfish (Bartol et al., scrawled cowfish do not appear to be strong enough to 2002). Consequently, the vortices that developed around the energize flow sufficiently to prevent flow detachment near the ventral keels of the cowfish and trunkfishes were more ordered posterior edge of the carapace (pressure coefficients were and had more pronounced effects on surface pressures. This is often greater than 0). clear when examining pressure distributions. In scrawled The ventral keel extensions in the scrawled cowfish are cowfish, buffalo trunkfish and smooth trunkfish, conspicuous important flow-directing features. These extensions, which are pressure minima were observed adjacent to the ventral keels, close to the body and parallel to the longitudinal body axis, whereas in the spotted boxfish, low-pressure zones were less stimulated vortex formation and kept vortices close to the apparent.

THE JOURNAL OF EXPERIMENTAL BIOLOGY 342 I. K. Bartol and others

Lift coefficients and delta wings pitch angles) or below (negative pitch angles) ventral keels that The vortical flow patterns observed around the ventral keels extend laterally at an angle of 0–40° relative to a horizontal of the three boxfishes resemble flows around delta wings. Delta axis when viewed in cross-section. Consequently, suction wings are symmetrical, triangular wings designed to fly at derived from the presence of a vortex above or below the subsonic or supersonic speeds. Some examples of aircraft with ventral keels, which was evident as low pressure zones in delta wings are the Concorde SST, Lockhead CL-8233, North pressure experiments, should act largely upward and posterior American XB-70 Valkyrie supersonic bomber, and even the to the center of mass at positive pitch angles (which also occurs space shuttle. In delta-winged aircraft, a coiled (spiral) vortex in delta wings) and downward and posterior to the center of sheet with a core of high vorticity forms at the leading edge of mass at negative pitch angles. the wing and grows posteriorly along the wing, inducing a field In spotted boxfish, dorsal vortices, which have their greatest of low pressure above the wing that produces lift (Bertin and circulation and peak vorticity posterior to the center of mass, Smith, 1989). Since lift is created with vortices as opposed to also should play an important role in self-correction. These bound circulation, as in conventional wings, stall, i.e. vortex vortices generally formed above the dorsal keels, which extend bursting, does not occur until high pitch angles. The ventrum at an angle of 0–30° relative to a horizontal axis when viewed of boxfishes differs from delta wings in that its maximum in cross-section at positive pitch angles, and below them along width/span occurs close to the middle of the fish as opposed to the sides of the carapace at negative pitch angles. Low pressure the posterior end, as in delta wings. Nonetheless, vortex derived from these vortices should produce forces that formation is similar. Based on DPIV results, spiral vortices like counteract pitching motions, like those in ventral regions. those observed in delta wings form along the ventral keels and Vortices forming above and below convex regions in the grow in strength as they travel posteriorly and vorticity feeds scrawled cowfish and keel extensions in scrawled cowfish and into the vortices. We can be confident that spirality is present buffalo trunkfish also contribute to self-righting forces that in boxfishes because (a) vortices become stronger moving counteract pitching motions. However, these forces are downstream and (b) each planar slice sampled along the body substantially less than those associated with the main keels, reveals steady, time-independent vorticity. These conditions because the vortices are of lower magnitude or act on a smaller can only occur if added vorticity per unit time is swept surface area. downstream by the axial component of velocity (i.e. there is Pitching moments recorded in force balance experiments, axial streamwise flow). which correlated statistically with both pressure and DPIV Given their differences in shape, it is not surprising that data, support the predictions above. Nose-down pitching boxfishes and delta wings have different lift coefficient moments occurred and became progressively stronger as pitch magnitudes. However, the shapes of the curves, whereby there angles became more positive, and nose-up pitching moments is no evidence of stall at ±30°, is further support that vortex occurred and became progressively stronger as pitch angles generation is similar in boxfishes and delta wings. became more negative. At positive pitch angles, smooth Interestingly, vortex flows above delta wings migrate vertically trunkfish, buffalo trunkfish, and scrawled cowfish all produced above the wing as they travel along the chord of the wing. similar self-correcting forces, with spotted boxfish producing Consequently pressures directly below the vortex cores self-correcting forces of lower magnitude. At negative pitch increase posteriorly (Zohar and Er-El, 1988; Pashilkar, 2001). angles, smooth trunkfish and buffalo trunkfish produced strong This was also observed along the bodies of boxfishes. Based self-correcting forces, while scrawled cowfish and spotted on force measurements, lift coefficients were closest to 0 and boxfish produced correcting forces of lower magnitude. slightly positive at 0°. This too is in agreement with DPIV data. The trunkfishes are particularly effective at generating self- DPIV results indicate that lowest vortex circulation occurs at correcting forces because they have sharper ventral keels along pitch angles near 0°, and vortices are generated above ventro- most of their bodies than the other boxfishes and have broad lateral keels at 0°, producing a downwash of flow in the wake. lateral surface areas above and below the ventral keels onto This downwash provides beneficial lift for counteracting which vortices may act (Bartol et al., 2002). The scrawled negative buoyancy present in rigid-bodied ostraciids (Blake, cowfish also has sharp ventral keels with a pronounced lateral 1977). lip in posterior regions, which certainly aids in generating self- correcting forces at positive pitch angles. However, at negative Self-corrective trimming control pitch angles, the narrow ventrum does not allow the two The vortical flow patterns induced by the carapaces of the counter-rotating vortices forming below the ventral keels to different boxfishes, which were similar around the ventral develop in isolation as in the trunkfishes, which have broad keels but variable in dorsal locations, all should produce bases. Instead ventral vortices interact with one another at trimming forces that self-correct for pitching, i.e. rotation in negative pitch angles, and this may lower the magnitude of the vertical, head-up/down longitudinal plane. In ventral self-correcting forces. Lower magnitude dorsal vortices in locations, attached vortices with the strongest peak vorticity posterior regions of the carapace at negative compared with and circulation developed posterior to the center of mass, positive pitch angles (see Fig.·4) also may contribute to the which is located approximately at maximum girth (Fig.·1; observed asymmetric pitching moment curve for scrawled Bartol et al., 2002). These vortices formed above (positive cowfish. Based on the geometry of the spotted boxfish, which

THE JOURNAL OF EXPERIMENTAL BIOLOGY Flows around rigid-bodied boxfishes 343 has four keels and broad regions both above the dorsal keels generate some lift to counteract the nose-down pitching and below the ventral keels onto which vortices may act, we moment produced by the ventral keels at a 0° pitch angle. This expected these fish to produce the strongest self-correcting allows for more uniform lift production about the center of forces. However, the less acute, often rounded, dorsal and mass to counteract negative buoyancy while swimming in ventral keels of the spotted boxfish simply did not produce straight paths. vortices of the magnitude of those observed for the trunkfishes. Irrespective of the differences in the magnitude of the self- Body-induced flows and their ecological implications correcting forces and the distinctions in carapace morphologies The results of the present study indicate that the rigid keeled among the boxfishes, the integrated effects of the flow patterns carapaces of boxfishes play an important role in the control of around the carapaces result in the production of self-correcting vorticity, producing flows and pressure distributions that forces for pitching motions in all boxfishes. Moreover, the self- comprise an efficient, self-correcting system for pitch and yaw. correcting couple is proportional to the angle to which the fish To date this self-correcting system has been documented in is perturbed from a horizontal swimming trajectory. four morphologically distinct boxfishes: spotted boxfish, Although moments and pressure distributions at various yaw scrawled cowfish, buffalo trunkfish and smooth trunkfish angles were not measured, DPIV results indicate that the (Bartol et al., 2003). This self-corrective trimming system is carapaces of all three boxfishes also generate self-correcting important for several reasons. First it damps large perturbations forces for yawing, i.e. rotations in the left/right horizontal when swimming and when holding position while feeding on frontal plane. Stronger dorsal and ventral vortices clearly prey lodged in complex habitats. This damping is especially formed on the far-field as opposed to the near-field side of important in highly energetic turbulent waters where flows may carapace, especially in areas adjacent to the dorsal and ventral frequently move boxfishes off their desired paths or positions. keels, when the boxfishes were positioned at various yaw Second, it acts quickly and automatically and does not require angles. These differences may be attributed in large part to neural processing, as in powered control systems (e.g. changes in sweep angle. When the boxfish yaws, the near-field asymmetrical pectoral fin beats to correct a rolling moment). side effectively decreases in sweep angle, while the far-field This is especially advantageous for unpredictable velocity side increases in sweep angle. In delta wings, the larger the fields, where accurate phasing of powered correction forces sweep angle up to a reasonable maximum (e.g. 75°), the with perturbations is difficult and requires rapid neural stronger the LEV (Bertin and Smith, 1989). Circulation of processing. Without proper phasing, correction may even these far-field vortices increased posteriorly along the amplify disturbances through ‘pilot induced error’ (Webb, carapace, such that maximum vortex circulation occurred 1998, 2000, 2002). Third, maintenance of smooth swimming posterior to the center of mass. Vortex circulation and peak trajectories improves sensory acuity of both hostile (i.e. vorticity also increased as yaw angles increased. Suction predators) and target objects because it reduces complexity of derived from the presence of vortices at far-field locations of movement, a factor that enhances sensory perception in other the carapace should act largely opposite the direction of the animals (Land, 1999; Kramer and McLaughlin, 2001). yaw and posterior to the center of mass, thus providing In addition to the advantages of the carapace and self- trimming forces that self-correct for yawing motions. As with correcting system, there are some disadvantages. Although the pitching, the self-correcting couple is proportional to the angle keels presumably provide energy savings by providing to which the fish is perturbed. counter-moments to pitching and yawing, it should also be noted that there are some energetic costs associated with the Role of the eye ridges maintenance of keel tissue, although these costs are probably In the three boxfishes examined in the present study and in low relative to the energetic costs of swimming and metabolic the smooth trunkfish, regions of concentrated vorticity formed costs of other physiological functions. The rigid, boxy around the eye ridges, producing pressure distributions where carapace, although effective for producing self-correcting ambient pressure occurs at the eye at low positive pitch angles forces, also incurs high drag. The drag coefficients reported in and negative pitch angles. This may be beneficial for eye this study are indeed high relative to other fishes (Blake, 1981, function because the eyeball is not deformed (i.e. lens of the 1983). The most significant disadvantage of the self-correcting eye is not pushed in or pulled out) as flow moves along the system, however, is that it increases costs for maneuverability. body, and thus the optical properties of the eye are not altered. A self-correcting system by definition means that any change Detection of ambient pressure around the eyes also has been in course, whether voluntary or involuntary, is counteracted by reported in squid, bluefish and tuna (Aleyev, 1977; Dubois et the stabilizing mechanism. Consequently, it presumably al., 1974; Vogel, 1987). Interestingly, ambient pressure was requires more power and time to actuate turning maneuvers. most consistently produced around the eyes of the scrawled This is consistent with Walker’s finding (Walker, 2000) that cowfish at positive and negative pitch angles, suggesting that one species of boxfish, Ostracion meleagris, has slower rates the anterior horns may play an important role in controlling of turning than flexible-bodied fish. flows for eye function. This hypothesis, together with the investigation of flow/pressure field effects on the eyes of Role of the fins swimming fishes, merits further study. The eye ridges also When considering stability control and maneuverability, it

THE JOURNAL OF EXPERIMENTAL BIOLOGY 344 I. K. Bartol and others is important to consider flow interactions between the fins and References body. Movements of the pectoral fins, which are located near Aleyev, Y. G. (1977). Nekton. The Hague: Junk. the path of body-induced ventral vortex formation, will Bartol, I. K., Gharib, M., Weihs, D., Webb, P. W., Hove, J. R. and Gordon, M. S. (2003). Hydrodynamic stability of swimming in ostraciid fishes: role presumably affect body vortex magnitude and structure. For of the carapace in the smooth trunkfish Lactophrys triqueter (Teleostei: example, asymmetric pectoral fin movements could Ostraciidae). J. Exp. Biol. 206, 725-744. strengthen or weaken body-induced vortices on one side of the Bartol, I. K., Gordon, M. S., Gharib, M., Hove, J. R., Webb, P. W. and Weihs, D. (2002). Flow patterns around the carapaces of rigid-bodied, body relative to the other, producing favorable forces for multi-propulsor boxfishes (Teleostei: Ostraciidae). Integ. Comp. Biol. 42, lateral rotations. The dorsal fin also may intercept 971-980. concentrated vorticity in postero-dorsal areas of the carapace, Bertin, J. J. and Smith, M. L. (1989). Aerodynamics for Engineers, 2nd edn. Englewood Cliffs: Prentice Hall. which was detected in all boxfishes, to improve its efficacy in Blake, R. W. (1977). On ostraciiform locomotion. J. Mar. Biol. Assn UK 57, producing stabilizing forces. The capture of vorticity by fins 1047-1055. to improve thrust and swimming efficiency has been Blake, R. W. (1981). Mechanics of ostraciiform propulsion. Can J. Zool. 59, 1067-1071. introduced in previous studies (Lighthill, 1970; Wu, 1971; Blake, R. W. (1983). Fish Locomotion. Cambridge: Cambridge University Weihs, 1989) and has been modeled recently in tunas and Press. danios (Zhu et al., 2002). The interactions of various fins with Dubois, A. B., Cavagna, G. A. and Fox, R. S. (1974). Pressure distribution of the body surface of swimming fish. J. Exp. Biol. 60, 581-591. body-induced flows is the subject of ongoing studies in our Gordon, M. S., Hove, J. R., Webb, P. W. and Weihs, D. (2000). Boxfishes laboratories. as unusually well-controlled autonomous underwater vehicles. Physiol. Biochem. Zool. 73, 663-671. Concluding remarks Hove, J. R., O’Bryan, L. M., Gordon, M. S., Webb, P. W. and Weihs, D. (2001). Boxfishes (Teleostei: Ostraciidae) as a model system for fishes The carapaces of boxfishes, which vary in cross-sectional swimming with many fins: kinematics. J. Exp. Biol. 204, 1459-1471. shape, longitudinal features and ornamentation, play an Kramer, D. L. and McLaughlin, R. L. (2001). The behavioral ecology of intermittent locomotion. Amer. Zool. 41, 137-153. important role in hydrodynamic stability. The ventral keels of Land, M. F. (1999). Motion and vision: why animals move their eyes. J. boxfishes, which often have adjacent regions of concavity for Comp. Physiol. A 185, 341-352. holding vorticity in place, and the dorsal keels in the spotted Lighthill, M. J. (1970). Aquatic animal propulsion of high hydromechanical efficiency. J. Fluid Mech. 44, 265-301. boxfish, are vortex generators, producing flows similar to those Lisoski, D. (1993). Nominally 2-dimensional flow about a normal flat plate. around the leading edges of delta-winged aircraft. The PhD dissertation, California Institute of Technology, USA. resulting surface pressures produced by the flows contribute to McCormack, P. D. and Crane, L. (1973). Physical Fluid Dynamics. New York: Academic Press. integrated forces that self-correct for pitching and probably Pashilkar, A. A. (2001). Surface pressure model for simple delta wings at high yawing movements, allowing these fishes to swim in pitch angles. Sadhana 26, 495-515. remarkably straight paths. The evolution of such a Raffel, M., Willert, C. E. and Kompenhans, J. (1998). Particle Image Velocimetry: A Practical Guide. Berlin: Springer-Verlag. sophisticated self-correcting system in this group of fishes is Schlichting, H. and Truckenbrodt, E. (1969). Aerodynamik des Flugzeuges, beneficial for the varied environmental conditions these Vol. 2, Ch. 7. Berlin: Springer-Verlag. animals face within their natural habitats. This system is useful Tritton, D. J. (1998). Physical Fluid Dynamics, 2nd edn. Oxford: Clarendon Press. for steady swimming in highly turbulent waters where counter- Tyler, J. C. (1980). Osteology, phylogeny, and higher classification of the moments for pitching and yawing are required, or perhaps for fishes of the order Plectognathi (Tetraodontiformes). NOAA Tech. Rep. station-holding in highly variable flows during feeding on coral NMFS Circular 434, 1-422. Vogel, S. (1987). Flow-assisted mantle cavity refilling in jetting squid. Biol. inhabitants. Increased understanding of this self-correcting Bull. 172, 61-68. system, especially in regards to how the fins interact with body- Vogel, S. (2003). Comparative Biomechanics: Life’s Physical World. induced flows, promises to reveal novel mechanisms for Princeton: Princeton University Press. Walker, J. A. (2000). Does a rigid body limit maneuverability? J. Exp. Biol. stability control. 203, 3391-3396. Webb, P. W. (1998). Entrainment by river chub Nocomis micropogon and We thank R. M. Alexander and P. Krueger for valuable smallmouth bass Micropterus dolomieu on cylinders. J. Exp. Biol. 201, 2403-2412. intellectual input, M. McNitt-Gray, J. Carnahan, B. Webb, P. W. (2000). Maneuverability versus stability? Do fish perform well Valiferdowsi, and P. Masson for aid during model in both? 1st Int. Symp. Aqua Bio-mech./Int. Semin. Aqua Bio-mech. 1, 21- construction, D. Lauritzen and S. Bartol for assistance 29. Webb, P. W. (2002). 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