Supergradient Winds in Simulated Tropical Cyclones

Richard Rotunno aNCAR, Boulder, Colorado

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Abstract

In a previous paper a formula was derived for the maximum potential intensity of the tangential wind in a tropical cyclone called PI+. The formula, PI+2 = EPI2 + αrmwmηm, where EPI is the maximum potential intensity of the gradient wind and αrmwmηm represents the supergradient winds. The latter term is the product of the radius rm, the vertical velocity wm, the azimuthal vorticity ηm at the radius and height of the maximum tangential wind (rm, zm), and the (nearly constant) α. Examination of a series of simulations of idealized tropical cyclones indicate an increasing contribution from the supergradient-wind term to PI+ as the radius of maximum wind increases. In the present paper, the physical content of the supergradient-wind term is developed showing how it is directly related to tropical cyclone boundary layer dynamics. It is found that rmwmηmumin2zm(rm)/lυ(zm)rm, where −umin is the maximum boundary layer radial inflow velocity and lυ(z) is the vertical mixing length.

© 2022 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: Richard Rotunno, rotunno@ucar.edu

Abstract

In a previous paper a formula was derived for the maximum potential intensity of the tangential wind in a tropical cyclone called PI+. The formula, PI+2 = EPI2 + αrmwmηm, where EPI is the maximum potential intensity of the gradient wind and αrmwmηm represents the supergradient winds. The latter term is the product of the radius rm, the vertical velocity wm, the azimuthal vorticity ηm at the radius and height of the maximum tangential wind (rm, zm), and the (nearly constant) α. Examination of a series of simulations of idealized tropical cyclones indicate an increasing contribution from the supergradient-wind term to PI+ as the radius of maximum wind increases. In the present paper, the physical content of the supergradient-wind term is developed showing how it is directly related to tropical cyclone boundary layer dynamics. It is found that rmwmηmumin2zm(rm)/lυ(zm)rm, where −umin is the maximum boundary layer radial inflow velocity and lυ(z) is the vertical mixing length.

© 2022 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: Richard Rotunno, rotunno@ucar.edu
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  • Bell, M. M., and M. T. Montgomery, 2008: Observed structure, evolution, and potential intensity of category 5 Hurricane Isabel (2003) from 12 to 14 September. Mon. Wea. Rev., 136, 20232046, https://doi.org/10.1175/2007MWR1858.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bell, M. M., M. T. Montgomery, and K. A. Emanuel, 2012: Air–sea enthalpy and momentum exchange at major hurricane wind speeds observed during CBLAST. J. Atmos. Sci., 69, 31973222, https://doi.org/10.1175/JAS-D-11-0276.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bödewadt, U. T., 1940: Die Drehströmung über festem Grunde. Z. Angew. Math. Mech., 20, 241253, https://doi.org/10.1002/zamm.19400200502.

  • Bryan, G. H., 2012: Effects of surface exchange coefficients and turbulence length scales on the intensity and structure of numerically simulated hurricanes. Mon. Wea. Rev., 140, 11251143, https://doi.org/10.1175/MWR-D-11-00231.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bryan, G. H., and R. Rotunno, 2009a: Evaluation of an analytical model for the maximum intensity of tropical cyclones. J. Atmos. Sci., 66, 30423060, https://doi.org/10.1175/2009JAS3038.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bryan, G. H., and R. Rotunno, 2009b: The maximum intensity of tropical cyclones in axisymmetric numerical model simulations. Mon. Wea. Rev., 137, 17701789, https://doi.org/10.1175/2008MWR2709.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bryan, G. H., R. P. Worsnop, J. K. Lundquist, and J. Zhang, 2017: A simple method for simulating wind profiles in the boundary layer of tropical cyclones. Bound.-Layer Meteor., 162, 475502, https://doi.org/10.1007/s10546-016-0207-0.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Burggraf, O. R., K. Stewartson, and R. Belcher, 1971: Boundary induced by a potential vortex. Phys. Fluids, 14, 18211833, https://doi.org/10.1063/1.1693691.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Emanuel, K. A., 1986: An air–sea interaction theory for tropical cyclones. Part I: Steady-state maintenance. J. Atmos. Sci., 43, 585605, https://doi.org/10.1175/1520-0469(1986)043<0585:AASITF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Frisius, T., D. Schönemann, and J. Vigh, 2013: The impact of gradient wind imbalance on potential intensity of tropical cyclones in an unbalanced slab boundary layer model. J. Atmos. Sci., 70, 10741890, https://doi.org/10.1175/JAS-D-12-0160.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kepert, J. D., 2001: The dynamics of boundary layer jets within the tropical cyclone core. Part I: Linear theory. J. Atmos. Sci., 58, 24692484, https://doi.org/10.1175/1520-0469(2001)058<2469:TDOBLJ>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kepert, J. D., 2006a: Observed boundary layer wind structure and balance in the hurricane core. Part I: Hurricane Georges. J. Atmos. Sci., 63, 21692193, https://doi.org/10.1175/JAS3745.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kepert, J. D., 2006b: Observed boundary layer wind structure and balance in the hurricane core. Part II: Hurricane Mitch. J. Atmos. Sci., 63, 21942211, https://doi.org/10.1175/JAS3746.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kepert, J. D., 2012: Choosing a boundary layer parameterization for tropical cyclone modeling. Mon. Wea. Rev., 140, 14271445, https://doi.org/10.1175/MWR-D-11-00217.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kepert, J. D., 2017: Time and space scales in the tropical cyclone boundary layer, and the location of the eyewall updraft. J. Atmos. Sci., 74, 33053323, https://doi.org/10.1175/JAS-D-17-0077.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kepert, J. D., and Y. Wang, 2001: The dynamics of boundary layer jets within the tropical cyclone core. Part II: Nonlinear enhancement. J. Atmos. Sci., 58, 24852501, https://doi.org/10.1175/1520-0469(2001)058<2485:TDOBLJ>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kuo, H. L., 1971: Axisymmetric flows in the boundary layer of a maintained vortex. J. Atmos. Sci., 28, 2041, https://doi.org/10.1175/1520-0469(1971)028<0020:AFITBL>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mallen, K. J., M. T. Montgomery, and B. Wang, 2005: Reexamining the near-core radial structure of the tropical cyclone primary circulation: Implications for vortex resiliency. J. Atmos. Sci., 62, 408425, https://doi.org/10.1175/JAS-3377.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Miyamoto, Y., M. Satoh, and H. Tomita, 2014: Gradient wind balance in tropical cyclones in high-resolution global experiments. Mon. Wea. Rev., 142, 19081926, https://doi.org/10.1175/MWR-D-13-00115.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Montgomery, M. T., and R. K. Smith, 2017: Recent developments in the fluid dynamics of tropical cyclones. Annu. Rev. Fluid Mech., 49, 541574, https://doi.org/10.1146/annurev-fluid-010816-060022.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Peng, K., R. Rotunno, and G. H. Bryan, 2018: Evaluation of a time-dependent model for the intensification of tropical cyclones. J. Atmos. Sci., 75, 21252138, https://doi.org/10.1175/JAS-D-17-0382.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Peng, K., R. Rotunno, G. H. Bryan, and J. Fang, 2019: Evolution of an axisymmetric tropical cyclone before reaching slantwise moist neutrality. J. Atmos. Sci., 76, 18651884, https://doi.org/10.1175/JAS-D-18-0264.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Powell, M. D., 1980: Evaluations of diagnostic marine boundary-layer models applied to hurricanes. Mon. Wea. Rev., 108, 757766, https://doi.org/10.1175/1520-0493(1980)108<0757:EODMBL>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rotunno, R., 2014: Secondary circulations in rotating-flow boundary layers. Aust. Meteor. Oceanogr. J., 64, 2735, https://doi.org/10.22499/2.6401.004.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rotunno, R., and K. A. Emanuel, 1987: An air–sea interaction theory for tropical cyclones. Part II: Evolutionary study using a nonhydrostatic axisymmetric numerical model. J. Atmos. Sci., 44, 542561, https://doi.org/10.1175/1520-0469(1987)044<0542:AAITFT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rotunno, R., and G. H. Bryan, 2012: Effects of parameterized diffusion on simulated hurricanes. J. Atmos. Sci., 69, 22842299, https://doi.org/10.1175/JAS-D-11-0204.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Smith, R. K., and M. T. Montgomery, 2020: The generalized Ekman model for the tropical cyclone boundary layer revisited: The myth of inertial stability as a restoring force. Quart. J. Roy. Meteor. Soc., 146, 34353449, https://doi.org/10.1002/qj.3854.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Smith, R. K., M. T. Montgomery, and S. Vogl, 2008: A critique of Emanuel’s hurricane model and potential intensity theory. Quart. J. Roy. Meteor. Soc., 134, 551561, https://doi.org/10.1002/qj.241.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Smith, R. K., M. T. Montgomery, and N. V. Sang, 2009: Tropical cyclone spin-up revisited. Quart. J. Roy. Meteor. Soc., 135, 13211335, https://doi.org/10.1002/qj.428.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stern, D. P., and G. H. Bryan, 2018: Using simulated dropsondes to understand extreme updrafts and wind speeds in tropical cyclones. Mon. Wea. Rev., 146, 39013925, https://doi.org/10.1175/MWR-D-18-0041.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stern, D. P., J. D. Kepert, G. H. Bryan, and J. D. Doyle, 2020: Understanding atypical midlevel wind speed maxima in hurricane eyewalls. J. Atmos. Sci., 77, 15311557, https://doi.org/10.1175/JAS-D-19-0191.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tao, D., M. Bell, R. Rotunno, and P. J. van Leewen, 2020a: Why do the maximum intensities in modeled tropical cyclones vary under the same environmental conditions? Geophys. Res. Lett., 47, e2019GL085980, https://doi.org/10.1029/2019GL085980.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tao, D., R. Rotunno, and M. Bell, 2020b: Lilly’s model for steady-state tropical cyclone intensity and structure. J. Atmos. Sci., 77, 37013720, https://doi.org/10.1175/JAS-D-20-0057.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Xu, J., and Y. Wang, 2018: Effect of the initial vortex structure on intensification of a numerically simulated tropical cyclone. J. Meteor. Soc. Japan, 96, 111126, https://doi.org/10.2151/jmsj.2018-014.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, J. A., and E. W. Uhlhorn, 2012: Hurricane sea surface inflow angle and an observation-based parametric model. Mon. Wea. Rev., 140, 35873605, https://doi.org/10.1175/MWR-D-11-00339.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, J. A., R. F. Rogers, D. S. Nolan, and F. D. Marks Jr., 2011: On the characteristic height scales of the hurricane boundary layer. Mon. Wea. Rev., 139, 25232535, https://doi.org/10.1175/MWR-D-10-05017.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
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