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Vortex Lines Within Low-Level Mesocyclones Obtained From SEPTEMBER 2008 MARKOWSKI ET AL. 3513 Vortex Lines within Low-Level Mesocyclones Obtained from Pseudo-Dual-Doppler Radar Observations ϩ PAUL MARKOWSKI,* ERIK RASMUSSEN, JERRY STRAKA,# ROBERT DAVIES-JONES,@ YVETTE RICHARDSON,* AND ROBERT J. TRAPP& *Department of Meteorology, The Pennsylvania State University, University Park, Pennsylvania ϩRasmussen Systems, Mesa, Colorado #School of Meteorology, University of Oklahoma, Norman, Oklahoma @National Severe Storms Laboratory, Norman, Oklahoma &Department of Earth and Atmospheric Sciences, Purdue University, West Lafayette, Indiana (Manuscript received 24 July 2007, in final form 4 January 2008) ABSTRACT Vortex lines passing through the low-level mesocyclone regions of six supercell thunderstorms (three nontornadic, three tornadic) are computed from pseudo-dual-Doppler airborne radar observations ob- tained during the Verification of the Origins of Rotation in Tornadoes Experiment (VORTEX). In every case, at least some of the vortex lines emanating from the low-level mesocyclones form arches, that is, they extend vertically from the cyclonic vorticity maximum, then turn horizontally (usually toward the south or southwest) and descend into a broad region of anticyclonic vertical vorticity. This region of anticyclonic vorticity is the same one that has been observed almost invariably to accompany the cyclonic vorticity maximum associated with the low-level mesocyclone; the vorticity couplet straddles the hook echo of the supercell thunderstorm. The arching of the vortex lines and the orientation of the vorticity vector along the vortex line arches, compared to the orientation of the ambient (barotropic) vorticity, are strongly suggestive of baroclinic vorticity generation within the hook echo and associated rear-flank downdraft region of the supercells, and subsequent lifting of the baroclinically altered/generated vortex lines by an updraft. Dis- cussion on the generality of these findings, possible implications for tornadogenesis, and the similarity of the observed vortex lines to vortex lines in larger-scale convective systems are included as well. 1. Introduction ponent at a time. For example, the dynamics of midlevel mesocyclogenesis in supercell thunderstorms Vortex lines (also sometimes called vortex filaments) is easily demonstrated by way of vortex lines (Davies- are lines tangent to the vorticity vector, analogous to Jones 1984; Rotunno and Klemp 1985; Fig. 1). Vortex the streamline in a velocity vector field (Dutton 1986, p. line analyses in phenomena like thunderstorms are 364; Pedlosky 1987, p. 25; Kundu 1990, p. 120).1 Vortex complicated by the baroclinic generation of vorticity by lines can aid the visualization of the three-dimensional the horizontal buoyancy gradients that accompany pre- vorticity field. The three-dimensional perspective pro- cipitation regions and vertical drafts. In the presence of vided by vortex lines can expose dynamics that may not significant baroclinic vorticity generation, vortex lines be as apparent in inspections of only one vorticity com- may not even closely approximate material lines (Helmholtz’ theorem). Nonetheless, vortex line analy- ses can be enlightening in that they can suggest plau- 1 What are referred to as “vortex lines” herein are termed “vor- sible methods of vorticity generation and reorientation ticity lines” by Lugt (1996, p. 90). Lugt defines a vortex line as an (e.g., observations of vortex rings might lead one to isolated vorticity line within a wind field that is otherwise irrota- surmise that a local buoyancy extremum is present and tional. responsible for the generation of the rings). Although the vertical component of vorticity tends to be empha- Corresponding author address: Dr. Paul Markowski, 503 sized in supercell thunderstorm and tornado studies, Walker Building, University Park, PA 16802. there is some merit in systematically inspecting the dis- E-mail: [email protected] tribution and orientation of three-dimensional vortex DOI: 10.1175/2008MWR2315.1 © 2008 American Meteorological Society Unauthenticated | Downloaded 09/27/21 04:08 AM UTC MWR2315 3514 MONTHLY WEATHER REVIEW VOLUME 136 FIG. 1. (a) Effect of a localized vertical displacement “peak” (i.e., hump in an isentropic surface) on vortex lines when the mean vorticity ␻ and mean storm-relative flow v Ϫ c are perpendicular (purely crosswise vorticity). The peak draws up loops of vortex lines (shown slightly above, instead of in, the surface for clarity), giving rise to cyclonic vorticity on the right side of the peak (relative to the shear vector S) and anticyclonic vorticity on the left side. [Solenoidal effects (not included in the drawing) actually divert the vortex lines around the right (left) side of a warm (cool) peak, relative to the mean vorticity vector, but do not alter the result.] The environmental flow across the expanding peak produces maximum updraft upstream (storm-relative frame) of the peak due to the upslope component of the vertical velocity. In this case, there is no correlation between vertical velocity and vertical vorticity. (b) As in (a), but for the other extreme when vorticity is purely streamwise (i.e., ␻ is parallel to v Ϫ c). Here, the upslope (downslope) side of the peak is also the cyclonic (anticyclonic) side, and the vertical velocity and vertical vorticity are positive correlated. (From Davies-Jones 1984.) lines in observed and simulated storms. A lengthier dis- wind fields) with the exception of the recent supercell cussion on the benefits of vortex line analysis appears in thunderstorm studies by Majcen et al. (2006) and Straka et al. (2007). Straka et al. (2007). Vortex line analyses appear relatively infrequently The origins of midlevel and low-level rotation in su- within the body of severe local storms literature. In percell thunderstorms have been reviewed by Davies- addition to the previously cited theoretical and numeri- Jones and Brooks (1993), Rotunno (1993), and Davies- cal modeling studies of midlevel mesocyclogenesis by Jones et al. (2001). [Herein, “low level” refers to alti- Davies-Jones (1984) and midlevel and low-level meso- tudes nominally Յ1000 m AGL. Davies-Jones et al. cyclogenesis by Rotunno and Klemp (1985), respec- (2001) referred to these altitudes as “near ground.” The tively, Walko (1993) and Wicker and Wilhelmson distinction between low-level and midlevel mesocy- (1995) presented vortex lines in their three-dimensional clones is discussed further in section 4.] Midlevel verti- simulations of tornadogenesis. As one would expect, cal vorticity having relatively high correlation with ver- the vortex lines were nearly erect in the tornadoes, tical velocity (negative correlation, in the case of a “left- turned horizontally at the base of the tornadoes, and moving” storm)—what most would probably consider then extended horizontally several kilometers from the the defining characteristic of a supercell thunderstorm tornadoes along the surface. Weisman and Davis (1998) (i.e., a rotating updraft)—can be envisioned as arising presented vortex lines in their investigation of the gen- from the tilting of vortex lines having a significant esis of line-end vortices in mesoscale convective sys- streamwise component by an “isentropic mountain” tems. The counterrotating mesoscale vortices com- (Davies-Jones 1984; Fig. 1). The vortex lines are quasi- monly found at opposite ends of quasi-linear convective horizontal in the ambient environment owing to the line segments were joined by “arching” vortex lines that presence of large mean vertical wind shear. On the rose out of the cyclonic vortex to the north (in the case other hand, baroclinic vorticity generation is present in of westerly mean vertical shear and a north–south con- convective storms, at least somewhere, owing to the vective line orientation), turned horizontally and ex- presence of horizontal buoyancy gradients (if there tended many tens of kilometers to the south, and then were no buoyancy gradients there could be no buoyant descended into the anticyclonic vortex. More recently, updraft in the first place). In addition to the updraft, the Nolan (2004) showed that three-dimensional Lagran- evaporation of rain, the melting of graupel and hail, and gian vortex methods (Chorin 1996) could be used to even the direct contribution to negative buoyancy by simulate mesocyclogenesis as an alternative to the tra- the mass of hydrometeors themselves unavoidably lead ditional approach of simulating the dynamics with an to horizontal buoyancy gradients and baroclinic vortic- Eulerian grid. We are unaware of any attempts to con- ity generation. Given this addition of baroclinic vortic- struct vortex lines in observed convective storms (using ity (Dutton 1986, p. 390; Davies-Jones 1996; Davies- presumably dual-Doppler–derived three-dimensional Jones et al. 2001) to the barotropic vorticity (defined as Unauthenticated | Downloaded 09/27/21 04:08 AM UTC SEPTEMBER 2008 MARKOWSKI ET AL. 3515 the vorticity that has resulted from the amplification storm-scale horizontal vorticity and is crucial for the and reorientation of the initial ambient vorticity of the development of low-level mesocyclones (Klemp and vertically sheared environment over the lifetime of the Rotunno 1983; Rotunno and Klemp 1985) [although storm), particularly at low levels within the rain-cooled recent observations (e.g., Shabbott and Markowski outflow of storms where significant buoyancy gradients 2006; Beck et al. 2006; Frame et al. 2008) have raised would most likely be found [prior modeling
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