888 MONTHLY WEATHER REVIEW VOLUME 128

A Clari®cation of Breakdown and Tornadogenesis

R. JEFFREY TRAPP National Severe Storms Laboratory, NOAA, and Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma, Norman, Oklahoma

31 March 1999 and 9 August 1999

ABSTRACT Recent and past observations of a central downdraft within a have been misinterpreted as evidence of vortex breakdown on the mesocyclone scale. In this note, the literature is reviewed and model examples are provided in order to demonstrate that the mesocyclone dynamics likely precludes mesocyclonic vortex breakdown. It is shown that an adverse vertical pressure gradient, induced by vertical that decreases in intensity with height, leads to the formation of a central downdraft, hence, two-celled vortex, in absence of vortex breakdown. Two-celled , then, may form when low-level vertical vorticity, generated by the vertical tilting of horizontal baroclinic vorticity, exceeds that generated at midlevels. Tor- nadogenesis occurs in a two-celled mesocyclonic vortex if an instability to which the vortex is susceptible is released.

1. Introduction 2. Two-celled vortices and vortex breakdown a. Background Vortex breakdown, a rather well-known phenomenon in ¯uid mechanics, has been documented in tornadoes Swirl ratio (S) is the ratio of the tangential velocity (Pauley and Snow 1988; see also Lugt 1989). The ex- at the outer edge of the updraft hole of a laboratory istence of vortex breakdown in tornadic mesocyclones chamber (or the atmospheric analogue thereof), has been inferred from observations of a downdraft near to the average vertical velocity through such an updraft the central axis of the mesocyclonic vortex (Brandes hole (Davies-Jones 1973). The dependence on swirl ra- 1978; Wakimoto and Liu 1998); tornadogenesis was at- tio of tornadic vortex structure has been demonstrated tributed by these authors to the purported mesocyclonic in tornado chambers (e.g., Ward 1972; Church et al. vortex breakdown. Numerical models, however, have 1979) and numerical models thereof (e.g., Rotunno 1977; Howells et al. 1988). Indeed, the vortex ¯ow un- simulated the formation of such a central or axial down- dergoes a remarkable metamorphosis as S increases draft and, thus, of a two-celled vortex in the absence of (e.g., see Snow 1982; Davies-Jones 1986). Brie¯y, small vortex breakdown. values of S support a laminar, one-celled vortex: air rises The purpose of this note is to (i) demonstrate that throughout the vortex. Moderate swirl ratios support an vortex breakdown likely is precluded in mesocyclones, intense vortex, within which axial or vertical motions and (ii) provide a simple reinterpretation of these past now take the form of a jet that erupts out of the boundary and recent observations of central downdrafts and, layer. The vertical jet terminates aloft at a stagnation hence, of two-celled mesocyclonic vortices. These tasks point along the central axis, above which (i) the vortex are accomplished through a review of the literature and core broadens substantially, (ii) the ¯ow becomes tur- through a consideration of the observations and of an- bulent, and (iii) recirculatory or downward motion re- alytic and numerical model solutions (section 2). A the- sides along the axis (Fig. 1a): these are characteristics orized tornadogenesis process in two-celled mesocy- of the breakdown of a columnar vortex that terminates clones is recalled in section 3. Conclusions are given at a solid boundary (or end wall), in accordance with in section 4. the accepted de®nition of vortex breakdown observed in nature and technology (Lugt 1989). With subsequent increases in S, the vortex breakdown point becomes positioned successively closer to the lower surface until Corresponding author address: Dr. R. Jeffrey Trapp, NCAR/ ultimately, the vortex breakdown penetrates to the lower MMM, P.O. Box 3000, Boulder, CO 80307-3000. surface. This results in a broadly rotating, two-celled E-mail: [email protected] vortex with down¯ow along its central axis, terminating

᭧ 2000 American Meteorological Society

Unauthenticated | Downloaded 09/24/21 07:11 PM UTC MARCH 2000 NOTES AND CORRESPONDENCE 889

mentioned, appears to be tied in some way to the ex- istence of an upstream1 axial jet. Such a jet that exceeds the axial motions outside the vortex core, perhaps by a factor of Ն3 (Leibovich 1984), affords the condition of supercriticality. In a supercritical vortex, centrifugal waves cannot propagate upstream. This condition con- trasts that of subcriticality that exists downstream of the breakdown point and allows for upstream and down- stream propagation of centrifugal waves (Benjamin 1962). According to Leibovich (1984), the general con- cept of critical ¯ow is the consistent element in ``all formations of criteria for onset of breakdown in purely axisymmetric theories.'' Summarizing, a supercritical vortex and moderate-to- high swirl ratio2 are necessary for vortex breakdown. Supercriticality in tornadoes is provided through a boundary layer±erupting axial jet in the vortex core. We consider next if the mesocyclone dynamics supports such an axial jet and hence the condition of supercrit- icality.

b. Analytic models With the reasonable assumption that the velocity dis- tribution of a Rankine-combined vortex3 approximates that of a mesocyclone (and that of a tornado), the so- lution due to Bodewadt (1940) represents the effects of a low-level mesocyclone core and its boundary layer. FIG. 1. Schematic of (a) vortex breakdown in a tornado-like vortex Bodewadt examined a ¯uid that rotates as a solid-body and (b) a two-celled vortex (see text). Vectors indicate radial-vertical above a ®xed plate, and found that the resulting vertical motion. Shading represents azimuthal or tangential motion, with high- velocity distribution is independent of the radial dis- er windspeeds denoted by darker shading. tance from the axis of rotation (see Schlichting 1979, 225±230). This result implies the existence, at the top of the boundary layer, of a uniform updraft distributed in low-level radial out¯ow that turns vertical in an an- throughout the mesocyclone core (of a few-kilometer nular updraft at an outer radius (Fig. 1b). radius) rather than of a narrow vertical jet on the me- The dynamics attendant with a rotating ¯ow above a socyclone axis (see Rotunno 1986, p. 430). Such a ver- rigid boundary (like the earth's surface) is crucial to tical jet does appear, however, in solutions of Burgraff development of an axial jet within simulated vortex et al.'s (1971) model of a potential vortex above a ®xed cores and, presumably, within tornadoes. Assume that plate; their model represents reasonably well a narrow the rotating ¯ow is in cyclostrophic balance, well above tornado and its boundary layer, since the presumed po- the rigid boundary and, hence, also above the boundary tential ¯ow of the tornadic vortex is large compared to layer. Within the boundary layer, the cyclostrophic bal- its core. ance condition is upset because friction reduces the tan- A swirling, boundary layer±erupting jet as in Burgraff gential wind and centrifugal force to zero at the ground; et al.'s solution (and in some tornadoes) is much more friction does not alter the radial pressure gradient force, likely to be supercritical than is a broadly rotating however. The consequential unbalanced inward pressure updraft as in Bodewadt's solution (and hence in some gradient drives a strong in¯ow that transports parcels (that nearly conserve angular momentum) much closer to the central axis than is possible without friction. At a radial distance on the order of the boundary layer 1 In this context of axial jets within tornadoes or tornado-like vor- tices, upstream is in the Ϫz (vertical) direction. With reference to depth, inward transport of mass and angular momentum the axial stagnation point, upstream is below the height of the stag- ceases as the ¯ow turns vertical, erupting into an intense nation point, and downstream is above the height of the stagnation axial jet (Burgraff et al. 1971); this rotating jet may point. break down under certain conditions. 2 The swirl condition typically is imposed and external or ambient to the vortex core and will receive no further discussion. Although vortex breakdown ``is still considered a ba- 3 The Rankine-combined vortex is characterized by a core of solid- sic, largely unexplained phenomenon in modern ¯uid body rotation [wherein tangential velocity (␷) ϳ radius (r)], sur- dynamics'' (Rusak et al. 1998), its existence, as just rounded by an outer region of potential ¯ow (wherein ␷ ϳ 1/r).

Unauthenticated | Downloaded 09/24/21 07:11 PM UTC 890 MONTHLY WEATHER REVIEW VOLUME 128 low-level mesocyclone cores) (R. Davies-Jones 1999, sence of a boundary layer) is motivated by the presumed personal communication). Thus, by the discussion in relevance of the boundary layer to the scale of the vortex section 2a, it is correspondingly more unlikely for a being considered, as suggested by the model solutions mesocyclone to develop a vortex breakdown. Two-di- in section 2b: the boundary layer of a mesocyclone ap- mensional (2D), axisymmetric, numerical-model exper- parently has only a minor effect on the mesocyclone iments now are used to illustrate the formation of an core dynamics, whereas the boundary layer of a tornado axial downdraft and, thus, of a two-celled vortex in the has a profound effect on the tornado core dynamics. absence of vortex breakdown.

1) FREE-SLIP LOWER BOUNDARY CONDITION c. Numerical model results When a free-slip lower boundary condition is im- Consider the primitive equation version of the tor- posed, the model produces a subcritical vortex that be- nado-chamber numerical model developed by Fiedler comes two-celled in absence of a vortex breakdown (Fig. (1993), used recently by Trapp and Davies-Jones (1997); 2). Rapid development of an axial downdraft and con- the reader is referred to these papers for model details. sequential evolution toward the two-celled vortex so- The impermeable, cylindrical4 (r, ␪,z), model domain lution can be explained as follows (see also Rotunno rotates at a constant rate ⍀. Within the rotating cylinder, 1984): Radially inward (outward) transport of angular convection is driven by a constant body force, b(r, z). momentum (⌫ϭr␷) surfaces by the low-level (upper- Also referred to as buoyancy, the body force is modi®ed level) branch of the buoyancy-forced meridional cir- here to simulate better the through¯ow in the tornado culation results in angular momentum surfaces that chamber due to Ward (1972) (and in a numerical model slope outward with height (Rotunno 1977). Such radi- thereof, due to Rotunno 1977). Accordingly, we let ally outward-sloping ⌫ surfaces imply that tangential [(r(␷rץ/ץ(velocity and hence vertical vorticity [␨ ϭ (1/r ␲  f (r) cos(␲zЈ), zЈ Յ 0.5 decrease with height; rotationally induced pressure that b(r, z) ϭ 2 (1)  is lower near the ground than aloft is furthermore im- 0, zЈϾ0.5, plied. An adverse vertical pressure gradient force results along the central axis, which through the vertical mo- where zЈϭ[(z Ϫ 0.5)2]1/2, and mentum equation drives the axial down¯ow. This pro- 1, r Յ 0.5 cess, incidentally, represents the choking or vortex valve  effect discussed by Lewellen (1971) and later applied  f (r) ϭ 1 Ϫ 2(r Ϫ 0.5), 0.5 Ͻ r Յ 1 (2) by Lemon et al. (1975). 0, r Ͼ 1 A relevant atmospheric analogue can be identi®ed. (see Fig. 2a); the model of dimensionless domain size Mesocyclones form at midlevels within a storm through 0 Յ z Յ 1 and 0 Յ r Յ 3 is nondimensionalized as tilting and subsequent stretching of the horizontal vor- described by Trapp and Davies-Jones (1997). The pri- ticity associated with vertical shear of the ambient hor- mary meridional (radial-vertical) ¯ow forced by b(r, z) izontal wind. At low levels, mesocyclones form through tilting of horizontal vorticity associated presumably is fully developed just after dimensionless time t ϭ 0, and is approximately irrotational inside the region r Յ with horizontal buoyancy gradients. Cloud model sim- 0.5, our subdomain of interest; this is similar to Rotun- ulations (e.g., Klemp and Rotunno 1983) and obser- no's (1977) initial condition in the streamfunction. This vations (Cai and Wakimoto 1998) have shown that the resultant vertical vorticity in the low-level mesocyclone meridional ¯ow has positive azimuthal vorticity (␩ ϭ can become larger than that of the midlevel mesocy- r) that is generated via the radial gradientץ/wץz Ϫץ/uץ of b. clone. As just explained, this vertical distribution of ␨ and, hence, pressure affords axial downdraft formation The upper boundary (z ϭ 1) and outer wall (r ϭ 3) and a transition to a two-celled vortex; two-celled me- are rigid, impermeable, and no slip; the central axis (r socyclones have been simulated (Rotunno 1984; Klemp ϭ 0) is a symmetry axis; and the bottom boundary (z and Rotunno 1983), observed by Doppler radar (Bran- ϭ 0) is rigid, impermeable, and can be made no slip or des 1978; Wakimoto and Liu 1998; Trapp 1999), and free slip. There is no viscous boundary layer (like the documented visually (Bluestein 1985). steady Ekman layer over the solid earth or the unsteady vortex boundary layer simulated herein) when the free- slip boundary condition is imposed. Thus, the two sim- 2) NO-SLIP LOWER BOUNDARY CONDITION ulations presented below examine the behavior of a vor- When a no-slip lower boundary condition is imposed, tex, with and without a viscous boundary layer. The the model produces, relative to the free-slip case, an choice of boundary condition (hence presence or ab- intense tornado-like vortex with a narrow core (Fig. 3); this result is consistent with modeling results presented by Rotunno (1977), Howells et al. (1988), Fiedler 4 These and the other variables have their traditional meanings. (1993), and others. Within the vortex core is a vertical

Unauthenticated | Downloaded 09/24/21 07:11 PM UTC MARCH 2000 NOTES AND CORRESPONDENCE 891

FIG. 2. Contours of (a) body force b, and of radial velocity u, tangential velocity ␷, and vertical velocity w, at (b) t ϭ 2.0, and (c) t ϭ 4.5, for the free-slip experiment. Contour interval is indicated in the top right-hand corner of each plot, contour value begins at one-half the interval, and dashed lines indicate negative values. jet with windspeeds that are more than twice those out- abruptly broadened core and axial down¯ow; the axial side the core (Fig. 3c). At time t ϭ 6, the vertical jet down¯ow is present due to the decrease with height of stagnates on the axis at a height of z ϭ 0.3. Below this tangential velocity, as similarly explained previously. height, the vortex is supercritical. Above this height, the It is important to note here that the axial downdrafts vortex is subcritical and exhibits the de®nitive break- within the two-celled vortex in the free-slip case and down features [e.g., according to Hall (1972), Leibovich downstream of vortex breakdown in the no-slip case (1978), Leibovich (1984), and Lugt (1989)] like an both are associated with adverse vertical pressure gra-

Unauthenticated | Downloaded 09/24/21 07:11 PM UTC 892 MONTHLY WEATHER REVIEW VOLUME 128

FIG. 3. As in Fig. 2, except for the no-slip experiment, and for u, ␷, and w at (a) t ϭ 2.0, (b) t ϭ 4.5, and (c) t ϭ 6.0.

Unauthenticated | Downloaded 09/24/21 07:11 PM UTC MARCH 2000 NOTES AND CORRESPONDENCE 893 dients. Moreover, the adverse pressure gradients are, in 2315 UTC, upward vertical motion and positive vertical turn, associated with rotation that decreases in strength vorticity that are correlated through a 5 km depth, and, with height. A distinction can be made, however, be- a vertical velocity ®eld with a maximum at 5 km and tween the two processes that result in this vertical dis- small values in the lowest kilometer (their Fig. 10d). A tribution of ␨ in a tornadic vortex undergoing breakdown similar vertical distribution of vertical velocity can be (analogous to the no-slip case) and in a two-celled me- inferred at 2313±2318 UTC, from time±height pro®les socyclone (analogous to the no-slip case). In the former, of vertical velocity and vertical vorticity (their Fig. 13). boundary layer processes act to amplify ambient (or Hence, prior to the development of an axial downdraft mesocyclonic) ␨ selectively at low levels, and in the and two-celled vortex, the data present no evidence of latter, low-level ␨ is generated in amounts greater than a supercritical vortex and associated breakdown. One that at midlevels presumably by the vertical tilting of may conclude, therefore, that the OD in the two-celled horizontal baroclinic vorticity, as discussed previously. mesocyclone formed analogously to that in the vortex The two model solutions lead to the following im- in the free-slip simulation. portant conclusion: the existence of a subcritical vortex Of course, one could argue that the hypothetical me- with an axial downdraft does not imply that, at some socyclonic vortex breakdown developed aloft and sub- previous time, the vortex necessarily had a breakdown sequently penetrated the boundary layer within 5 min, and was supercritical. This conclusion is exempli®ed by the approximate time difference between successive air- the vortex in the free-slip case that was at all times borne volumetric radar scans. While this possibility can- subcritical, and, is used to help reinterpret the obser- not be ruled out, a dimensionalization of the no-slip vations presented next. model results suggests that it is unlikely. Consider a convective timescale of 7 min, which is derived from a convective velocity scale of 30 m sϪ1 and a length d. Observations of two-celled mesocyclones scale of 13 km; the velocity and length scales are in- Recall that the existence of vortex breakdown in the ferred from Garden City storm data presented by Wak- tornadic mesocyclones of the 16 May 1995 Garden City, imoto et al. This timescale is used to dimensionalize the Kansas, tornadic (Wakimoto and Liu 1998; time difference between the incipient and well-devel- Wakimoto et al. 1998) and the 8 June 1974 Harrah, oped vortex breakdown stages depicted in Figs. 3b and Oklahoma, tornadic supercell (Brandes 1978) were in- 3c, respectively. The resultant difference of 11.5 min ferred from observations of a downdraft near the central implies that the radar data have suf®cient temporal res- axis of the mesocyclonic vortex. In light of the preced- olution to capture the development and evolution of a ing discussion, the interpretation of such mesocyclonic hypothetical breakdown. vortex breakdown is now evaluated. Consider the two-celled mesocyclone in the Garden 3. Discussion City supercell. Wakimoto and Liu retrieved the three- dimensional air¯ow of the storm from airborne Doppler The two-celled mesocyclonic vortex is susceptible to radar data, and observed a central or occlusion down- a cylindrical vortex-sheet instability (Rotunno 1984). draft (OD) within the storm's mesocyclone. Wakimoto Once/if this instability is released, vortices (or vertical and Liu equated such axial down¯ow to that found vorticity maxima; Fig. 7d, Klemp and Rotunno 1983) downstream of a vortex breakdown: ``It is likely that that are smaller in scale than the parent vortex form the breakdown reaches the surface (leading to a rapid outside the central downdraft, in an annular region expansion of the core radius) after the 2324±2329 vol- where both vertical velocity and its radial gradient are ume time.'' positive (Fig. 11, Rotunno 1984). Tornadogenesis oc- The Garden City data indicate that if a hypothetical curs if one or more of these submesocyclone-scale vor- mesocyclonic vortex breakdown had formed and con- tices interact with the ground and consequently intensify sequently reached the surface, it would have done so into tornadoes (Rotunno 1986). prior to the 2324±2329 UTC airborne radar scan: ver- The tornadogenesis mechanism just described does tical cross-sections in Fig. 10 of Wakimoto et al. show not explain those tornadoes that develop near the me- weak-to-moderate down¯ow throughout the entire depth socyclone axis or, in other words, those within one- of the mesocyclone already at 2324±2329 UTC (just celled mesocyclones. Moreover, it is unclear how often before tornadogenesis; their Fig. 10f) and even at 2319± such a mechanism may be active: the percentage of all 2324 UTC (their Fig. 10e). If a mesocyclonic vortex tornadoes that form from two-celled mesocyclones is breakdown had existed prior to these times, the data unknown, as is the percentage of all mesocyclones that would show a marked axial ¯ow transition aloft or near become two-celled some time during their life cycle the ground, and at least the semblance of a boundary (Trapp 1999). Yet another uncertainty regards the role(s) layer±erupting vertical jet or updraft core; the data af- of ODs in tornadogenesis. Indeed, one may ask, ``Is this ford the resolution of these features, based on the ϳ2 downdraft a by-product of the tornadic vortex, or, is it km mesocyclone core radius at times preceding down- necessary for the tornadogenesis process?'' A proper draft development. However, one instead ®nds at 2308± evaluation of this question requires temporal and spatial

Unauthenticated | Downloaded 09/24/21 07:11 PM UTC 894 MONTHLY WEATHER REVIEW VOLUME 128 data point/model gridpoint spacing that nominally can through tilting and subsequent stretching of the hori- resolve a tornado; without such resolution, it is impos- zontal vorticity associated with vertical shear of the am- sible to distinguish the cause from the effect. This cri- bient horizontal wind. Tornadogenesis may occur in a terion disquali®es most of the apparently relevant stud- two-celled mesocyclonic vortex owing to an instability ies in the literature. Consider the relatively high-reso- to which the vortex is susceptible. lution modeling study of Grasso and Cotton (1995), which with its 111-m gridpoint spacing still does not Acknowledgments. Discussions with Drs. Rich Ro- really satisfy this criterion. This study appears to show tunno, Brian Fiedler, and Bob Davies-Jones were in- a ``tornado'' that developed in absence of (or at least strumental in helping the author ``clarify'' his thoughts prior to) an OD. In Trapp and Fiedler (1995), the OD on this topic. Additional comments by Dr. Chuck Dos- did not appear until after a tornado-like vortex was well well and two anonymous reviewers led to further im- formed, hence, the OD was an effect. On the other hand, provements in the manuscript. The work was performed Klemp and Rotunno (1983) and Wicker and Wilhelmson while the author was a visiting scientist with the Me- (1995) simulated submesocyclone-scale vortices that soscale and Microscale Meteorology Division of the Na- proceeded OD formation. tional Center for Atmospheric Research. The National Further insight into occlusion downdrafts, two-celled Center for Atmospheric Research is sponsored by the mesocyclones, and attendant tornadogenesis awaits nu- National Science Foundation. merical modeling experiments performed with very high-resolution grids, and, high-resolution data collect- ed for example by two Doppler On Wheels radars (Wur- REFERENCES man et al. 1997) or by a millimeter-wavelength mobile Benjamin, T. B., 1962: Theory of vortex breakdown phenomena. J. radar (Bluestein et al. 1997). Fluid Mech., 12, 593±629. Bluestein, H. B., 1985: Wall clouds with eyes. Mon. Wea. Rev., 113, 1081±1085. 4. Summary and conclusions , S. G. Gaddy, D. C. Dowell, A. L. Pazmany, J. C. Galloway, R. E. McIntosh, and H. Stein, 1997: Doppler radar observations In a one-celled vortex, air rises throughout the vortex of substorm-scale vortices in a supercell. Mon. Wea. Rev., 125, and may take the form of a jet that erupts out of the 1046±1059. boundary layer. If this vortex undergoes vortex break- Bodewadt, V. T., 1940: Die Drehstromung uber festem Grunde. Z. Angew. Math. Mech., 20, 241±253. down, the vertical jet terminates aloft at a stagnation Brandes, E. A., 1978: Mesocyclone evolution and tornadogenesis: point, downstream of which the vortex core broadens Some observations. Mon. Wea. Rev., 106, 995±1011. substantially, the core ¯ow becomes turbulent, and re- Burgraff, O. R., K. Stewartson, and R. Belcher, 1971: Boundary layer circulatory or downward motion develops along the cen- induced by a potential vortex. Phys. Fluids, 14, 1821±1833. tral axis (Fig. 1a). In a two-celled vortex, down¯ow Cai, H., and R. M. Wakimoto, 1998: Comparison between the Garden City tornadic and Hays nontornadic during VOR- pervades the central axis of the vortex core, and ter- TEX95. Preprints, 19th Conf. on Severe Local Storms, Minne- minates in low-level radial out¯ow that turns vertical apolis, MN, Amer. Meteor. Soc., 108±111. in an annular updraft at an outer radius (Fig. 1b). Church, C. R., J. T. Snow, G. L. Baker, and E. M. Agee, 1979: Observations of a downdraft near the central axis of Characteristics of tornado-like vortices as a function of swirl ratio: A laboratory investigation. J. Atmos. Sci., 36, 1755±1766. a two-celled mesocyclonic vortex have been misinter- Davies-Jones, R. P., 1973: The dependence of core radius on swirl preted as evidence of vortex breakdown in tornadic me- ratio in a tornado simulator. J. Atmos. Sci., 30, 1427±1430. socyclones. The argument that supports this statement , 1986: Tornado dynamics. Morphology and Dy- is as follows. A supercritical vortex and a moderate-to- namics, 2d ed., E. Kessler, Ed., University of Oklahoma Press, high swirl ratio are necessary for vortex breakdown. 197±236. Fiedler, B. H., 1993: Numerical simulation of axisymmetric torna- The supercriticality condition in tornadoes is provided dogenesis in buoyant convection. The Tornado: Its Structure, through a boundary layer±erupting axial jet in the vortex Dynamics, Prediction, and Hazards. Geophys. Monogr., No. 79, core. Analytic model solutions suggest that an axial jet, Amer. Geophys. Union, 41±48. driven by the boundary layer of the mesocyclone, un- Grasso, L, D., and W. R. Cotton, 1995: Numerical simulation of a tornado vortex. J. Atmos. Sci., 52, 1192±1203. likely forms in the mesocyclone core. Accordingly, the Hall, M. G., 1972: Vortex breakdown. Annu. Rev. Fluid. Mech., 4, supercriticality condition unlikely is satis®ed in meso- 195±218. cyclones, therefore precluding a mesocyclonic vortex Howells, P. A. C., R. Rotunno, and R. K. Smith, 1988: A comparative breakdown. study of atmospheric and laboratory-analogue numerical tor- Numerical model solutions demonstrate that an ad- nado-vortex models. Quart. J. Roy. Meteor. Soc., 114, 801±822. Klemp, J. B., and R. Rotunno, 1983: A study of the tornadic region verse vertical pressure gradient, induced by vertical vor- within a supercell thunderstorm. J. Atmos. Sci., 40, 359±377. ticity that decreases in intensity with height, leads to Leibovich, S., 1978: The structure of vortex breakdown. Annu. Rev. the formation of an axial downdraft, hence, two-celled Fluid. Mech., 10, 221±246. vortex, in absence of vortex breakdown. Two-celled me- , 1984: Vortex stability and breakdown: Survey and extension. AIAA J., 22, 1192±1206. socyclones, then, may form when low-level vertical vor- Lemon, L. R., D. W. Burgess, and R. A. Brown, 1975: Tornado ticity, generated by the vertical tilting of horizontal bar- production and storm sustenance. Preprints, Ninth Conf. on Se- oclinic vorticity, exceeds that generated at midlevels vere Local Storms, Norman, OK, Amer. Meteor. Soc., 100±104.

Unauthenticated | Downloaded 09/24/21 07:11 PM UTC MARCH 2000 NOTES AND CORRESPONDENCE 895

Lewellen, W. S., 1971: A review of con®ned vortex ¯ows. NASA Trapp, R. J., 1999: Observations of nontornadic low-level mesocy- Contractor Rep. NASA CR-1772, 219 pp. [Available from Na- clones and attendant tornadogenesis failure during VORTEX. tional Technical Information Service, Spring®eld, VA 22151.] Mon. Wea. Rev., 127, 1693±1705. Lugt, H. J., 1989: Vortex breakdown in atmospheric columnar vor- , and B. H. Fiedler, 1995: Tornado-like vortexgenesis in a sim- tices. Bull. Amer. Meteor. Soc., 70, 1526±1537. pli®ed numerical model. J. Atmos. Sci., 52, 3757±3778. Pauley, R. L., and J. T. Snow, 1988: On the kinematics and dynamics , and R. Davies-Jones, 1997: Tornadogenesis with and without of the 18 July 1986 Minneapolis tornado. Mon. Wea. Rev., 116, a dynamic pipe effect. J. Atmos. Sci., 54, 113±133. 2731±2736. Wakimoto, R. M., and C. Liu, 1998: The Garden City, Kansas, storm Rotunno, R., 1977: Numerical simulation of a laboratory vortex. J. during VORTEX 95. Part II: The and tornado. Mon. Atmos. Sci., 34, 1942±1956. Wea. Rev., 126, 393±408. , 1984: An investigation of a three-dimensional asymmetric vor- , , and H. Cai, 1998: The Garden City, Kansas, storm during VORTEX 95. Part I: Overview of the storm's life cycle and tex. J. Atmos. Sci., 41, 283±298. mesocyclogenesis. Mon. Wea. Rev., 126, 372±392. , 1986: Tornadoes and tornadogenesis. Mesoscale Meteorology Ward, N. B., 1972: The exploration of certain features of tornado and Forecasting, P. S. Ray, Ed., Amer. Meteor. Soc., 414±436. dynamics using a laboratory model. J. Atmos. Sci., 29, 1194± Rusak, Z., S. Wang, and C. H. Whiting, 1998: The evolution of a 1204. perturbed vortex in a pipe to axisymmetric vortex breakdown. Wicker, L. J., and R. B. Wilhelmson, 1995: Simulation and analysis J. Fluid Mech., 366, 211±237. of tornado development and decay within a three-dimensional Schlichting, H., 1979: Boundary-Layer Theory. McGraw-Hill, 817 supercell thunderstorm. J. Atmos. Sci., 52, 2675±2703. pp. Wurman, J., J. Straka, E. Rasmussen, M. Randall, and A. Zahrai, Snow, J. T., 1982: A review of recent advances in tornado vortex 1997: Design and deployment of a portable, pencil-beam, pulsed, dynamics. Rev. Geophys. Space Phys., 20, 953±964. 3-cm Doppler radar. J. Atmos. Oceanic Technol., 6, 1502±1512.

Unauthenticated | Downloaded 09/24/21 07:11 PM UTC