Self-Stratification of Tropical Cyclone Outflow. Part I: Implications for Storm Structure

Kerry Emanuel Program in Atmospheres, Oceans, and Climate, Massachusetts Institute of Technology, Cambridge, Massachusetts

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Richard Rotunno National Center for Atmospheric Research, Boulder, Colorado

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Abstract

Extant theoretical work on the steady-state structure and intensity of idealized axisymmetric tropical cyclones relies on the assumption that isentropic surfaces in the storm outflow match those of the unperturbed environment at large distances from the storm’s core. These isentropic surfaces generally lie just above the tropopause, where the vertical temperature structure is approximately isothermal, so it has been assumed that the absolute temperature of the outflow is nearly constant. Here it is shown that this assumption is not justified, at least when applied to storms simulated by a convection-resolving axisymmetric numerical model in which much of the outflow occurs below the ambient tropopause and develops its own stratification, unrelated to that of the unperturbed environment. The authors propose that this stratification is set in the storm’s core by the requirement that the Richardson number remain near its critical value for the onset of small-scale turbulence. This ansatz is tested by calculating the Richardson number in numerically simulated storms, and then showing that the assumption of constant Richardson number determines the variation of the outflow temperature with angular momentum or entropy and thereby sets the low-level radial structure of the storm outside its radius of maximum surface winds. Part II will show that allowing the outflow temperature to vary also allows one to discard an empirical factor that was introduced in previous work on the intensification of tropical cyclones.

The National Center for Atmospheric Research is sponsored by the National Science Foundation.

Corresponding author address: Kerry Emanuel, Rm. 54-1814, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139. E-mail: emanuel@mit.edu

Abstract

Extant theoretical work on the steady-state structure and intensity of idealized axisymmetric tropical cyclones relies on the assumption that isentropic surfaces in the storm outflow match those of the unperturbed environment at large distances from the storm’s core. These isentropic surfaces generally lie just above the tropopause, where the vertical temperature structure is approximately isothermal, so it has been assumed that the absolute temperature of the outflow is nearly constant. Here it is shown that this assumption is not justified, at least when applied to storms simulated by a convection-resolving axisymmetric numerical model in which much of the outflow occurs below the ambient tropopause and develops its own stratification, unrelated to that of the unperturbed environment. The authors propose that this stratification is set in the storm’s core by the requirement that the Richardson number remain near its critical value for the onset of small-scale turbulence. This ansatz is tested by calculating the Richardson number in numerically simulated storms, and then showing that the assumption of constant Richardson number determines the variation of the outflow temperature with angular momentum or entropy and thereby sets the low-level radial structure of the storm outside its radius of maximum surface winds. Part II will show that allowing the outflow temperature to vary also allows one to discard an empirical factor that was introduced in previous work on the intensification of tropical cyclones.

The National Center for Atmospheric Research is sponsored by the National Science Foundation.

Corresponding author address: Kerry Emanuel, Rm. 54-1814, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139. E-mail: emanuel@mit.edu
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  • Bister, M., and K. A. Emanuel, 1998: Dissipative heating and hurricane intensity. Meteor. Atmos. Phys., 65, 233240.

  • Bister, M., and K. A. Emanuel, 2002: Low frequency variability of tropical cyclone potential intensity. 1. Interannual to interdecadal variability. J. Geophys. Res., 107, 4801, doi:10.1029/2001JD000776.

    • 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.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Chavas, D. R., and K. A. Emanuel, 2010: A QuickSCAT climatology of tropical cyclone size. Geophys. Res. Lett., 37, L18816, doi:10.1029/2010GL044558.

    • Search Google Scholar
    • Export Citation
  • Emanuel, K. A., 1983: On assessing local conditional symmetric instability from atmospheric soundings. Mon. Wea. Rev., 111, 20162033.

    • Search Google Scholar
    • Export Citation
  • Emanuel, K. A., 1986: An air–sea interaction theory for tropical cyclones. Part I. J. Atmos. Sci., 43, 585605.

  • Emanuel, K. A., 1997: Some aspects of hurricane inner-core dynamics and energetics. J. Atmos. Sci., 54, 10141026.

  • Emanuel, K. A., 2004: Tropical cyclone energetics and structure. Atmospheric Turbulence and Mesoscale Meteorology, E. Federovich, R. Rotunno, and B. Stevens, Eds., Cambridge University Press, 240 pp.

    • Search Google Scholar
    • Export Citation
  • Hakim, G. J., 2011: The mean state of axisymmetric hurricanes in statistical equilibrium. J. Atmos. Sci., 68, 13641376.

  • Kepert, J. D., 2010: Slab- and height-resolving models of the tropical cyclone boundary layer. Part I: Comparing the simulations. Quart. J. Roy. Meteor. Soc., 136, 16861699.

    • Search Google Scholar
    • Export Citation
  • Kleinschmidt, E., Jr., 1951: Gundlagen einer Theorie des tropischen Zyklonen. Arch. Meteor. Geophys. Bioklimatol., 4A, 5372.

  • Mrowiec, A. A., S. T. Garner, and O. M. Pauluis, 2011: Axisymmetric hurricane in a dry atmosphere: Theoretical framework and numerical experiments. J. Atmos. Sci., 68, 16071619.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Shutts, G. J., 1981: Hurricane structure and the zero potential vorticity approximation. Mon. Wea. Rev., 109, 324329.

  • 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.

    • Search Google Scholar
    • Export Citation
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