Rapid Development of the Tropical Cyclone Warm Core

Jonathan L. Vigh Colorado State University, Fort Collins, Colorado

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Wayne H. Schubert Colorado State University, Fort Collins, Colorado

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Abstract

This paper presents a simple theoretical argument to isolate the conditions under which a tropical cyclone can rapidly develop a warm-core thermal structure and subsequently approach a steady state. The theoretical argument is based on the balanced vortex model and, in particular, on the associated transverse circulation equation and the geopotential tendency equation. These second-order partial differential equations contain the diabatic forcing and three spatially varying coefficients: the static stability A, the baroclinity B, and the inertial stability C. Thus, the transverse circulation and the temperature tendency in a tropical vortex depend not only on the diabatic forcing but also on the spatial distributions of A, B, and C. Experience shows that the large radial variations of C are typically the most important effect. Under certain simplifying assumptions as to the vertical structure of the diabatic forcing and the spatial variability of A, B, and C, the transverse circulation equation and the geopotential tendency equation can be solved via separation of variables. The resulting radial structure equations retain the dynamically important radial variation of C and can be solved in terms of Green’s functions. These analytical solutions show that the vortex response to a delta function in the diabatic heating depends critically on whether the heating occurs in the low-inertial-stability region outside the radius of maximum wind or in the high-inertial-stability region inside the radius of maximum wind. This result suggests that rapid intensification is favored for storms that have at least some of the eyewall convection inside the radius of maximum wind. The development of an eye partially removes diabatic heating from the high-inertial-stability region of the storm center; however, rapid intensification may continue if the eyewall heating continues to become more efficient. As the warm core matures and static stability increases over the inner core, conditions there become less favorable for deep upright convection and the storm tends to approach a steady state.

Corresponding author address: Jonathan L. Vigh, Department of Atmospheric Science, Colorado State University, Fort Collins, CO 80523. Email: vigh@atmos.colostate.edu

This article included in the TCSP NAMMA special collection.

Abstract

This paper presents a simple theoretical argument to isolate the conditions under which a tropical cyclone can rapidly develop a warm-core thermal structure and subsequently approach a steady state. The theoretical argument is based on the balanced vortex model and, in particular, on the associated transverse circulation equation and the geopotential tendency equation. These second-order partial differential equations contain the diabatic forcing and three spatially varying coefficients: the static stability A, the baroclinity B, and the inertial stability C. Thus, the transverse circulation and the temperature tendency in a tropical vortex depend not only on the diabatic forcing but also on the spatial distributions of A, B, and C. Experience shows that the large radial variations of C are typically the most important effect. Under certain simplifying assumptions as to the vertical structure of the diabatic forcing and the spatial variability of A, B, and C, the transverse circulation equation and the geopotential tendency equation can be solved via separation of variables. The resulting radial structure equations retain the dynamically important radial variation of C and can be solved in terms of Green’s functions. These analytical solutions show that the vortex response to a delta function in the diabatic heating depends critically on whether the heating occurs in the low-inertial-stability region outside the radius of maximum wind or in the high-inertial-stability region inside the radius of maximum wind. This result suggests that rapid intensification is favored for storms that have at least some of the eyewall convection inside the radius of maximum wind. The development of an eye partially removes diabatic heating from the high-inertial-stability region of the storm center; however, rapid intensification may continue if the eyewall heating continues to become more efficient. As the warm core matures and static stability increases over the inner core, conditions there become less favorable for deep upright convection and the storm tends to approach a steady state.

Corresponding author address: Jonathan L. Vigh, Department of Atmospheric Science, Colorado State University, Fort Collins, CO 80523. Email: vigh@atmos.colostate.edu

This article included in the TCSP NAMMA special collection.

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  • Abramowitz, M., and I. A. Stegun, 2006: Handbook of Mathematical Functions. Dover, 1046 pp.

  • Adler, R. F., and E. B. Rodgers, 1977: Satellite-observed latent heat release in a tropical cyclone. Mon. Wea. Rev., 105 , 956963.

  • Corbosiero, K. L., J. Molinari, and M. L. Black, 2005: The structure and evolution of Hurricane Elena (1985). Part I: Symmetric intensification. Mon. Wea. Rev., 133 , 29052921.

    • Search Google Scholar
    • Export Citation
  • Dunkerton, T. J., 1989: Body force circulations in a compressible atmosphere: Key concepts. Pure Appl. Geophys., 130 , 243262.

  • Eliassen, A., 1951: Slow thermally or frictionally controlled meridional circulation in a circular vortex. Astrophys. Norv., 5 , 1960.

    • Search Google Scholar
    • Export Citation
  • Eliassen, A., and M. Lystad, 1977: The Ekman layer of a circular vortex: A numerical and theoretical study. Geophys. Norv., 31 , 116.

  • Gill, A. E., 1982: Atmosphere–Ocean Dynamics. International Geophysics Series, Vol. 30, Academic Press, 662 pp.

  • Hack, J. J., and W. H. Schubert, 1986: Nonlinear response of atmospheric vortices to heating by organized cumulus convection. J. Atmos. Sci., 43 , 15591573.

    • Search Google Scholar
    • Export Citation
  • Hausman, S. A., K. V. Ooyama, and W. H. Schubert, 2006: Potential vorticity structure of simulated hurricanes. J. Atmos. Sci., 63 , 87108.

    • Search Google Scholar
    • Export Citation
  • Haynes, P. H., and T. G. Shepherd, 1989: The importance of surface pressure changes in the response of the atmosphere to zonally-symmetric thermal and mechanical forcing. Quart. J. Roy. Meteor. Soc., 115 , 11811208.

    • Search Google Scholar
    • Export Citation
  • Holland, G. J., and R. T. Merrill, 1984: On the dynamics of tropical cyclone structural changes. Quart. J. Roy. Meteor. Soc., 110 , 723745.

    • Search Google Scholar
    • Export Citation
  • Jorgensen, D. P., 1984: Mesoscale and convective-scale characteristics of mature hurricanes. Part I: General observations by research aircraft. J. Atmos. Sci., 41 , 12681286.

    • Search Google Scholar
    • Export Citation
  • Knaff, J. A., J. P. Kossin, and M. DeMaria, 2003: Annular hurricanes. Wea. Forecasting, 18 , 204223.

  • Lonfat, M., F. D. Marks Jr., and S. S. Chen, 2004: Precipitation distribution in tropical cyclones using the Tropical Rainfall Measuring Mission TRMM microwave imager: A global perspective. Mon. Wea. Rev., 132 , 16451660.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Marks Jr., F. D., 1985: Evolution of the structure of precipitation in Hurricane Allen. Mon. Wea. Rev., 113 , 909930.

  • Matsuno, T., and K. Nakamura, 1979: The Eulerian- and Lagrangian-mean meridional circulations in the stratosphere at the time of a sudden warming. J. Atmos. Sci., 36 , 640654.

    • Search Google Scholar
    • Export Citation
  • Mundell, D. B., 1990: Prediction of tropical cyclone rapid intensification. M.S. thesis, Dept. of Atmospheric Science, Colorado State University, 186 pp.

  • Nolan, D. S., Y. Moon, and D. P. Stern, 2007: Tropical cyclone intensification from asymmetric convection: Energetics and efficiency. J. Atmos. Sci., 64 , 33773405.

    • Search Google Scholar
    • Export Citation
  • Ooyama, K., 1969: Numerical simulation of the life cycle of tropical cyclones. J. Atmos. Sci., 26 , 340.

  • Pendergrass, A. G., and H. E. Willoughby, 2009: Diabatically induced secondary flows in tropical cyclones. Part I: Quasi-steady forcing. Mon. Wea. Rev., 137 , 805821.

    • Search Google Scholar
    • Export Citation
  • Rao, G. V., and P. D. MacArthur, 1994: The SSM/I estimated rainfall amounts of tropical cyclones and their potential in predicting the cyclone intensity changes. Mon. Wea. Rev., 122 , 15681574.

    • Search Google Scholar
    • Export Citation
  • Rodgers, E. B., and R. F. Adler, 1981: Tropical cyclone rainfall characteristics as determined from a satellite passive microwave radiometer. Mon. Wea. Rev., 109 , 506521.

    • Search Google Scholar
    • Export Citation
  • Rodgers, E. B., S. Chang, and H. F. Pierce, 1994: A satellite observational and numerical study of precipitation characteristics in Western North Atlantic tropical cyclones. J. Appl. Meteor., 33 , 129139.

    • Search Google Scholar
    • Export Citation
  • Rodgers, E. B., W. S. Olson, V. M. Karyampudi, and H. F. Pierce, 1998: Satellite-derived latent heating distribution and environmental influences in Hurricane Opal (1995). Mon. Wea. Rev., 126 , 12291247.

    • Search Google Scholar
    • Export Citation
  • Rodgers, E. B., W. Oson, J. Halverson, J. Simpson, and H. Pierce, 2000: Environmental forcing of Supertyphoon Paka’s (1997) latent heat structure. J. Appl. Meteor., 39 , 19832006.

    • Search Google Scholar
    • Export Citation
  • Schubert, W. H., and J. J. Hack, 1982: Inertial stability and tropical cyclone development. J. Atmos. Sci., 39 , 16871697.

  • Schubert, W. H., and J. J. Hack, 1983: Transformed Eliassen balanced vortex model. J. Atmos. Sci., 40 , 15711583.

  • Schubert, W. H., J. J. Hack, P. L. Silva Dias, and S. R. Fulton, 1980: Geostrophic adjustment in an axisymmetric vortex. J. Atmos. Sci., 37 , 14641484.

    • Search Google Scholar
    • Export Citation
  • Schubert, W. H., C. M. Rozoff, J. L. Vigh, B. D. McNoldy, and J. P. Kossin, 2007: On the distribution of subsidence in the hurricane eye. Quart. J. Roy. Meteor. Soc., 133 , 595605. doi:10.1002/qj.49.

    • Search Google Scholar
    • Export Citation
  • Shapiro, L. J., and H. E. Willoughby, 1982: The response of balanced hurricanes to local sources of heat and momentum. J. Atmos. Sci., 39 , 378394.

    • Search Google Scholar
    • Export Citation
  • Shea, D. J., and W. M. Gray, 1973: The hurricane’s inner core region. I. Symmetric and asymmetric structure. J. Atmos. Sci., 30 , 15441564.

    • Search Google Scholar
    • Export Citation
  • Steranka, J., E. B. Rodgers, and R. C. Gentry, 1986: The relationship between satellite measured convective bursts and tropical cyclone intensification. Mon. Wea. Rev., 114 , 15391546.

    • Search Google Scholar
    • Export Citation
  • van Delden, A., 1989: On the deepening and filling of balanced cyclones by diabatic heating. Meteor. Atmos. Phys., 41 , 127145.

  • Wang, Y., 2008: Structure and formation of an annular hurricane simulated in a fully compressible, nonhydrostatic model—TCM4. J. Atmos. Sci., 65 , 15051527.

    • Search Google Scholar
    • Export Citation
  • Willoughby, H. E., 1979: Forced secondary circulations in hurricanes. J. Geophys. Res., 84 , 31733183.

  • Willoughby, H. E., 1990: Temporal changes of the primary circulation in tropical cyclones. J. Atmos. Sci., 47 , 242264.

  • Willoughby, H. E., J. A. Clos, and M. G. Shoreibah, 1982: Concentric eye walls, secondary wind maxima, and the evolution of the hurricane vortex. J. Atmos. Sci., 39 , 395411.

    • Search Google Scholar
    • Export Citation
  • Willoughby, H. E., H-L. Jin, S. J. Lord, and J. M. Piotrowicz, 1984: Hurricane structure and evolution as simulated by an axisymmetric, nonhydrostatic numerical model. J. Atmos. Sci., 41 , 11691186.

    • Search Google Scholar
    • Export Citation
  • Wirth, V., and T. J. Dunkerton, 2006: A unified perspective on the dynamics of axisymmetric hurricanes and monsoons. J. Atmos. Sci., 63 , 25292547.

    • Search Google Scholar
    • Export Citation
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