On the Origins of Vorticity in a Simulated Tornado-Like Vortex

Johannes M. L. Dahl aDepartment of Geosciences, Texas Tech University, Lubbock, Texas

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Jannick Fischer aDepartment of Geosciences, Texas Tech University, Lubbock, Texas

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Abstract

The authors explore the dynamical origins of rotation of a mature tornado-like vortex (TLV) using an idealized numerical simulation of a supercell thunderstorm. Using 30-min forward parcel trajectories that terminate at the base of the TLV, the vorticity dynamics are analyzed for n = 7 parcels. Aside from the integration of the individual terms of the traditional vorticity equation, an alternative formulation of the vorticity equation and its integral, here referred to as vorticity source decomposition, is employed. This formulation is derived on the basis of Truesdell’s “basic vorticity formula,” which is obtained by first formulating the vorticity in material (Lagrangian) coordinates, and then obtaining the components relative to the fixed spatial (Eulerian) basis by applying the vector transformation rule. The analysis highlights surface drag as the most reliable vorticity source for the rotation at the base of the vortex for the analyzed parcels. Moreover, the vorticity source decomposition exposes the importance of small amounts of vorticity produced baroclinically, which may become significant after sufficient stretching occurs. Further, it is shown that ambient vorticity, upon being rearranged as the trajectories pass through the storm, may for some parcels directly contribute to the rotation of the TLV. Finally, the role of diffusion is addressed using analytical solutions of the steady Burgers–Rott vortex, suggesting that diffusion cannot aid in maintaining the vortex core.

Fischer’s current affiliation: Karlsruher Institut für Technologie, Karlsruhe, Germany.

© 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Johannes Dahl, johannes.dahl@ttu.edu

Abstract

The authors explore the dynamical origins of rotation of a mature tornado-like vortex (TLV) using an idealized numerical simulation of a supercell thunderstorm. Using 30-min forward parcel trajectories that terminate at the base of the TLV, the vorticity dynamics are analyzed for n = 7 parcels. Aside from the integration of the individual terms of the traditional vorticity equation, an alternative formulation of the vorticity equation and its integral, here referred to as vorticity source decomposition, is employed. This formulation is derived on the basis of Truesdell’s “basic vorticity formula,” which is obtained by first formulating the vorticity in material (Lagrangian) coordinates, and then obtaining the components relative to the fixed spatial (Eulerian) basis by applying the vector transformation rule. The analysis highlights surface drag as the most reliable vorticity source for the rotation at the base of the vortex for the analyzed parcels. Moreover, the vorticity source decomposition exposes the importance of small amounts of vorticity produced baroclinically, which may become significant after sufficient stretching occurs. Further, it is shown that ambient vorticity, upon being rearranged as the trajectories pass through the storm, may for some parcels directly contribute to the rotation of the TLV. Finally, the role of diffusion is addressed using analytical solutions of the steady Burgers–Rott vortex, suggesting that diffusion cannot aid in maintaining the vortex core.

Fischer’s current affiliation: Karlsruher Institut für Technologie, Karlsruhe, Germany.

© 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Johannes Dahl, johannes.dahl@ttu.edu
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  • Aris, R., 1962: Vectors, Tensors, and the Basic Equations of Fluid Mechanics. Dover Publications, 286 pp.

  • Boyer, C. H., and J. M. L. Dahl, 2020: The mechanisms responsible for large near-surface surface vertical vorticity within simulated supercellular and quasi-linear storm modes. Mon. Wea. Rev., 148, 42814297, https://doi.org/10.1175/MWR-D-20-0082.1.

    • Search Google Scholar
    • Export Citation
  • Bryan, G. H., and J. M. Fritsch, 2002: A benchmark simulation for moist nonhydrostatic numerical models. Mon. Wea. Rev., 130, 29172928, https://doi.org/10.1175/1520-0493(2002)130<2917:ABSFMN>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Coffer, B. E., and M. D. Parker, 2017: Simulated supercells in nontornadic and tornadic VORTEX2 environments. Mon. Wea. Rev., 145, 149180, https://doi.org/10.1175/MWR-D-16-0226.1.

    • Search Google Scholar
    • Export Citation
  • Coriton, B., and J. H. Frank, 2016: Experimental study of vorticity-strain rate interaction in turbulent partially premixed jet flames using tomographic particle image velocimetry. Phys. Fluids, 28, 025109, https://doi.org/10.1063/1.4941528.

    • Search Google Scholar
    • Export Citation
  • Dahl, J. M. L., 2015: Near-ground rotation in simulated supercells: On the robustness of the baroclinic mechanism. Mon. Wea. Rev., 143, 49294942, https://doi.org/10.1175/MWR-D-15-0115.1.

    • Search Google Scholar
    • Export Citation
  • Dahl, J. M. L., 2017: Tilting of horizontal shear vorticity and the development of updraft rotation in supercell thunderstorms. J. Atmos. Sci., 74, 29973020, https://doi.org/10.1175/JAS-D-17-0091.1.

    • Search Google Scholar
    • Export Citation
  • Dahl, J. M. L., 2020: Near-surface vortex formation in supercells from the perspective of vortex patch dynamics. Mon. Wea. Rev., 148, 35333547, https://doi.org/10.1175/MWR-D-20-0080.1.

    • Search Google Scholar
    • Export Citation
  • Dahl, J. M. L., M. D. Parker, and L. J. Wicker, 2014: Imported and storm-generated near-ground vertical vorticity in a simulated supercell. J. Atmos. Sci., 71, 30273051, https://doi.org/10.1175/JAS-D-13-0123.1.

    • Search Google Scholar
    • Export Citation
  • Davies-Jones, R., 1991: The frontogenetical forcing of secondary circulations. Part I: The duality and generalization of the Q vector. J. Atmos. Sci., 48, 497509, https://doi.org/10.1175/1520-0469(1991)048<0497:TFFOSC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Davies-Jones, R., 2000: A Lagrangian model for baroclinic genesis of mesoscale vortices. Part I: Theory. J. Atmos. Sci., 57, 715736, https://doi.org/10.1175/1520-0469(2000)057<0715:ALMFBG>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Davies-Jones, R., 2006: Integrals of the vorticity equation. Part I: General three- and two-dimensional flows. J. Atmos. Sci., 63, 598610, https://doi.org/10.1175/JAS3646.1.

    • Search Google Scholar
    • Export Citation
  • Davies-Jones, R., 2008: Can a descending rain curtain in a supercell instigate tornadogenesis barotropically? J. Atmos. Sci., 65, 24692497, https://doi.org/10.1175/2007JAS2516.1.

    • Search Google Scholar
    • Export Citation
  • Davies-Jones, R., 2015: Formulas for parcel velocity and vorticity in a rotating coordinate system. J. Atmos. Sci., 72, 39083922, https://doi.org/10.1175/JAS-D-15-0015.1.

    • Search Google Scholar
    • Export Citation
  • Davies-Jones, R., 2021: Invented forces in supercell models. J. Atmos. Sci., 78, 29272939, https://doi.org/10.1175/JAS-D-21-0082.1.

  • Davies-Jones, R., 2022: Theory of parcel vorticity evolution in supercell-like flows. J. Atmos. Sci., 79, 12531270, https://doi.org/10.1175/JAS-D-21-0178.1.

    • Search Google Scholar
    • Export Citation
  • Davies-Jones, R., and H. E. Brooks, 1993: Mesocyclogenesis from a theoretical perspective. The Tornado: Its Structure, Dynamics, Prediction, and Hazards, Geophys. Monogr., Vol. 79, Amer. Geophys. Union, 105–114, https://doi.org/10.1029/GM079p0105.

  • Dutton, J. A., 1976: The Ceaseless Wind. McGraw-Hill, 579 pp.

  • Epifanio, C. C., and D. R. Durran, 2002: Lee-vortex formation in free-slip stratified flow over ridges. Part II: Mechanisms of vorticity and PV production in nonlinear viscous wakes. J. Atmos. Sci., 59, 11661181, https://doi.org/10.1175/1520-0469(2002)059<1166:LVFIFS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Fischer, J., and J. M. L. Dahl, 2022: Transition of near-ground vorticity dynamics during tornadogenesis. J. Atmos. Sci., 79, 467483, https://doi.org/10.1175/JAS-D-21-0181.1.

    • Search Google Scholar
    • Export Citation
  • Hamlington, P. E., J. Schumacher, and W. J. A. Dahm, 2008: Local and nonlocal strain rate fields and vorticity alignment in turbulent flows. Phys. Rev., 77E, 026303, https://doi.org/10.1103/PhysRevE.77.026303.

    • Search Google Scholar
    • Export Citation
  • Klemp, J. B., and R. Rotunno, 1983: A study of the tornadic region within a supercell thunderstorm. J. Atmos. Sci., 40, 359377, https://doi.org/10.1175/1520-0469(1983)040<0359:ASOTTR>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kundu, P. K., and I. M. Cohen, 2008: Fluid Mechanics. Academic Press, 872 pp.

  • Markowski, P. M., 2016: An idealized numerical simulation investigation of the effects of surface drag on the development of near-surface vertical vorticity in supercell thunderstorms. J. Atmos. Sci., 73, 43494385, https://doi.org/10.1175/JAS-D-16-0150.1.

    • Search Google Scholar
    • Export Citation
  • Markowski, P. M., and Y. Richardson, 2010: Mesoscale Meteorology in Midlatitudes. Wiley-Blackwell, 407 pp.

  • Markowski, P. M., and Y. Richardson, 2014: The influence of environmental low-level shear and cold pools on tornadogenesis: Insights from idealized simulations. J. Atmos. Sci., 71, 243275, https://doi.org/10.1175/JAS-D-13-0159.1.

    • Search Google Scholar
    • Export Citation
  • Markowski, P. M., and G. H. Bryan, 2016: Les of laminar flow in the PBL: A potential problem for convective storm simulations. Mon. Wea. Rev., 144, 18411850, https://doi.org/10.1175/MWR-D-15-0439.1.

    • Search Google Scholar
    • Export Citation
  • Markowski, P. M., J. M. Straka, E. N. Rasmussen, and D. O. Blanchard, 1998: Variability of storm-relative helicity during VORTEX. Mon. Wea. Rev., 126, 29592971, https://doi.org/10.1175/1520-0493(1998)126<2959:VOSRHD>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Markowski, P. M., Y. Richardson, and G. Bryan, 2014: The origins of vortex sheets in a simulated supercell thunderstorm. Mon. Wea. Rev., 142, 39443954, https://doi.org/10.1175/MWR-D-14-00162.1.

    • Search Google Scholar
    • Export Citation
  • Marsden, J. E., and T. J. R. Hughes, 1983: Mathematical Foundations of Elasticity. Prentice-Hall, 556 pp.

  • Mashiko, W., 2016: A numerical study of the 6 May 2012 Tsukuba City supercell tornado. Part II: Mechanisms of tornadogenesis. Mon. Wea. Rev., 144, 30773098, https://doi.org/10.1175/MWR-D-15-0122.1.

    • Search Google Scholar
    • Export Citation
  • Parker, M. D., 2014: Composite VORTEX2 supercell environments from near-storm soundings. Mon. Wea. Rev., 142, 508529, https://doi.org/10.1175/MWR-D-13-00167.1.

    • Search Google Scholar
    • Export Citation
  • Parker, M. D., and J. M. L. Dahl, 2015: Production of near-surface vertical vorticity by idealized downdrafts. Mon. Wea. Rev., 143, 27952816, https://doi.org/10.1175/MWR-D-14-00310.1.

    • Search Google Scholar
    • Export Citation
  • Rasmussen, E. N., and D. O. Blanchard, 1998: A baseline climatology of sounding-derived supercell and tornado forecast parameters. Wea. Forecasting, 13, 11481164, https://doi.org/10.1175/1520-0434(1998)013<1148:ABCOSD>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Roberts, B., and M. Xue, 2017: The role of surface drag in mesocyclone intensification leading to tornadogenesis within an idealized supercell simulation. J. Atmos. Sci., 74, 30553077, https://doi.org/10.1175/JAS-D-16-0364.1.

    • Search Google Scholar
    • Export Citation
  • Roberts, B., M. Xue, A. D. Schenkman, and D. T. Dawson, 2016: The role of surface drag in tornadogenesis within an idealized supercell simulation. J. Atmos. Sci., 73, 33713395, https://doi.org/10.1175/JAS-D-15-0332.1.

    • Search Google Scholar
    • Export Citation
  • Salmon, R., 1998: Geophysical Fluid Dynamics. Oxford University Press, 378 pp.

  • Schenkman, A. D., M. Xue, and M. Hu, 2014: Tornadogenesis in a high-resolution simulation of the 8 May 2003 Oklahoma City supercell. J. Atmos. Sci., 71, 130154, https://doi.org/10.1175/JAS-D-13-073.1.

    • Search Google Scholar
    • Export Citation
  • Schenkman, A. D., M. Xue, and D. T. Dawson, 2016: The cause of internal outflow surges in a high-resolution simulation of the 8 May 2003 Oklahoma City tornadic supercell. J. Atmos. Sci., 73, 353370, https://doi.org/10.1175/JAS-D-15-0112.1.

    • Search Google Scholar
    • Export Citation
  • Shampine, L. F., I. Gladwell, and S. Thompson, 2003: Solving ODEs with MATLAB. Cambridge University Press, 263 pp.

  • Simmonds, J. G., 1994: A Brief on Tensor Analysis. Springer, 112 pp.

  • Truesdell, C., 1954: The Kinematics of Vorticity. Indiana University Press, 232 pp.

  • Vande Guchte, A., and J. M. L. Dahl, 2018: Sensitivities of parcel trajectories beneath the lowest scalar model level of a Lorenz vertical grid. Mon. Wea. Rev., 146, 14271435, https://doi.org/10.1175/MWR-D-17-0190.1.

    • Search Google Scholar
    • Export Citation
  • Walko, R. L., 1993: Tornado spin-up beneath a convective cell: Required basic structure of the near-field boundary layer winds. The Tornado: Its Structure, Dynamics, Prediction, and Hazards, Meteor. Monogr., Vol. 79, Amer. Geophys. Union, 89–95, https://doi.org/10.1029/GM079p0089.

  • Wicker, L. J., and R. B. Wilhelmson, 1995: Simulation and analysis of tornado development and decay within a three-dimensional supercell thunderstorm. J. Atmos. Sci., 52, 26752703, https://doi.org/10.1175/1520-0469(1995)052<2675:SAAOTD>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Wicker, L. J., and W. C. Skamarock, 2002: Time-splitting methods for elastic models using forward time schemes. Mon. Wea. Rev., 130, 20882097, https://doi.org/10.1175/1520-0493(2002)130<2088:TSMFEM>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Yokoyama, A., Y. Maruyama, and J. Mizushima, 2012: Origin of the bathtub vortex and its formation mechanism. J. Phys. Soc. Japan, 81, 074401, https://doi.org/10.1143/JPSJ.81.074401.

    • Search Google Scholar
    • Export Citation
  • Zee, A., 2013: Einstein Gravity in a Nutshell. Princeton University Press, 888 pp.

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