Understanding Instabilities of Tropical Cyclones and Their Evolution with a Moist Convective Rotating Shallow-Water Model

Noé Lahaye Laboratoire de Météorologie Dynamique, CNRS-IPSL, ENS/UPMC, Paris, France

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Vladimir Zeitlin Laboratoire de Météorologie Dynamique, CNRS-IPSL, ENS/UPMC, Paris, France

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Abstract

Instabilities of hurricane-like vortices are studied with the help of a rotating shallow-water model, including the effects of moist convection. Linear stability analysis demonstrates that dominant unstable modes are mixed Rossby–inertia–gravity waves. It is shown that, depending on fine details of the vorticity profile, a wavenumber selection of the instability may operate or not, leading in some cases to an unstable mode with a distinctively maximal growth rate and in other cases to an ensemble of unstable modes with close growth rates. Numerical simulations are performed in order to investigate nonlinear saturation of the instability and to understand the dynamical role of moisture. In agreement with previous studies, the authors confirm axisymmetrization of vorticity in the course of the development of the instability, which induces changes of intensity of the hurricane. In “dry” simulations, winds are intensified only inside the radius of maximum wind, while the maximum value of the wind decreases. “Moist precipitating” simulations (with and without evaporation) exhibit a net increase of winds, also at the radius of maximum wind, as compared to the dry simulations. Dynamical effects of moisture on the reorganization of the vortex and on the efficiency of inertia–gravity wave emission are quantified and shown to be considerable. Periodic bursts in the emission of waves related to the development of the unstable modes inside the vortex are evidenced, as well as the appearance of convectively coupled waves in the moist precipitating simulations with evaporation.

Corresponding author address: Noé Lahaye, Department of Mechanical and Aerospace Engineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0411. E-mail: nlahaye@eng.ucsd.edu

Current affiliation: Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, California.

Abstract

Instabilities of hurricane-like vortices are studied with the help of a rotating shallow-water model, including the effects of moist convection. Linear stability analysis demonstrates that dominant unstable modes are mixed Rossby–inertia–gravity waves. It is shown that, depending on fine details of the vorticity profile, a wavenumber selection of the instability may operate or not, leading in some cases to an unstable mode with a distinctively maximal growth rate and in other cases to an ensemble of unstable modes with close growth rates. Numerical simulations are performed in order to investigate nonlinear saturation of the instability and to understand the dynamical role of moisture. In agreement with previous studies, the authors confirm axisymmetrization of vorticity in the course of the development of the instability, which induces changes of intensity of the hurricane. In “dry” simulations, winds are intensified only inside the radius of maximum wind, while the maximum value of the wind decreases. “Moist precipitating” simulations (with and without evaporation) exhibit a net increase of winds, also at the radius of maximum wind, as compared to the dry simulations. Dynamical effects of moisture on the reorganization of the vortex and on the efficiency of inertia–gravity wave emission are quantified and shown to be considerable. Periodic bursts in the emission of waves related to the development of the unstable modes inside the vortex are evidenced, as well as the appearance of convectively coupled waves in the moist precipitating simulations with evaporation.

Corresponding author address: Noé Lahaye, Department of Mechanical and Aerospace Engineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0411. E-mail: nlahaye@eng.ucsd.edu

Current affiliation: Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, California.

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  • Billant, P., and S. Le Dizès, 2009: Waves on a columnar vortex in a strongly stratified fluid. Phys. Fluids, 21, 106602, doi:10.1063/1.3248366.

  • Bouchut, F., J. Lambaerts, G. Lapeyre, and V. Zeitlin, 2009: Fronts and nonlinear waves in a simplified shallow-water model of the atmosphere with moisture and convection. Phys. Fluids, 21, 116604, doi:10.1063/1.3265970.

    • Search Google Scholar
    • Export Citation
  • Boyd, J. P., 1987: Orthogonal rational functions on a semi-infinite interval. J. Comput. Phys., 70, 6388, doi:10.1016/0021-9991(87)90002-7.

    • Search Google Scholar
    • Export Citation
  • Bui, H. H., R. K. Smith, M. T. Montgomery, and J. Peng, 2009: Balanced and unbalanced aspects of tropical cyclone intensification. Quart. J. Roy. Meteor. Soc., 135, 17151731, doi:10.1002/qj.502.

    • Search Google Scholar
    • Export Citation
  • Chane Ming, F., Z. Chen, and F. Roux, 2010: Analysis of gravity-waves produced by intense tropical cyclones. Ann. Geophys., 28, 531547, doi:10.5194/angeo-28-531-2010.

    • Search Google Scholar
    • Export Citation
  • Chen, Y., and M. K. Yau, 2001: Spiral bands in a simulated hurricane. Part I: Vortex Rossby wave verification. J. Atmos. Sci., 58, 21282145, doi:10.1175/1520-0469(2001)058<2128:SBIASH>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Chow, K. C., and K. L. Chan, 2003: Angular momentum transports by moving spiral waves. J. Atmos. Sci., 60, 20042009, doi:10.1175/1520-0469(2003)060<2004:AMTBMS>2.0.CO;2.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Emanuel, K., 1997: Some aspects of hurricane inner-core dynamics and energetics. J. Atmos. Sci., 54, 10141026, doi:10.1175/1520-0469(1997)054<1014:SAOHIC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Ford, R., 1994: The instability of an axisymmetric vortex with monotonic potential vorticity in rotating shallow water. J. Fluid Mech., 280, 303334, doi:10.1017/S0022112094002946.

    • Search Google Scholar
    • Export Citation
  • Frierson, D., A. J. Majda, and O. M. Pauluis, 2004: Large scale dynamics of precipitation fronts in the tropical atmosphere: A novel relaxation limit. Commun. Math. Sci., 2, 591626, doi:10.4310/CMS.2004.v2.n4.a3.

    • Search Google Scholar
    • Export Citation
  • Gill, A., 1982: Atmosphere-Ocean Dynamics. Academic Press, 662 pp.

  • Goswami, P., and B. N. Goswami, 1991: Modification of n = 0 equatorial waves due to interaction between convection and dynamics. J. Atmos. Sci., 48, 22312244, doi:10.1175/1520-0469(1991)048<2231:MOEWDT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Hausman, S., K. Ooyama, and W. Schubert, 2006: Potential vorticity structure of simulated hurricanes. J. Atmos. Sci., 63, 87108, doi:10.1175/JAS3601.1.

    • Search Google Scholar
    • Export Citation
  • Heifetz, E., C. H. Bishop, and P. Alpert, 1999: Counter-propagating Rossby waves in the barotropic Rayleigh model of shear instability. Quart. J. Roy. Meteor. Soc., 125, 28352853, doi:10.1256/smsqj.56003.

    • Search Google Scholar
    • Export Citation
  • Hendricks, E. A., W. H. Schubert, R. K. Taft, H. Wang, and J. P. Kossin, 2009: Life cycles of hurricane-like vorticity rings. J. Atmos. Sci., 66, 705722, doi:10.1175/2008JAS2820.1.

    • Search Google Scholar
    • Export Citation
  • Hendricks, E. A., B. D. McNoldy, and W. H. Schubert, 2012: Observed inner-core structural variability in Hurricane Dolly (2008). Mon. Wea. Rev., 140, 40664077, doi:10.1175/MWR-D-12-00018.1.

    • Search Google Scholar
    • Export Citation
  • Hendricks, E. A., W. H. Schubert, Y.-H. Chen, H.-C. Kuo, and M. S. Peng, 2014: Hurricane eyewall evolution in a forced shallow-water model. J. Atmos. Sci., 71, 16231643, doi:10.1175/JAS-D-13-0303.1.

    • Search Google Scholar
    • Export Citation
  • Hodyss, D., and D. Nolan, 2008: The Rossby-inertia-buoyancy instability in baroclinic vortices. Phys. Fluids, 20, 096602, doi:10.1063/1.2980354.

  • Kossin, J., and M. Eastin, 2001: Two distinct regimes in the kinematic and thermodynamic structure of the hurricane eye and eyewall. J. Atmos. Sci., 58, 10791090, doi:10.1175/1520-0469(2001)058<1079:TDRITK>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kossin, J., and W. Schubert, 2001: Mesovortices, polygonal flow patterns, and rapid pressure falls in hurricane-like vortices. J. Atmos. Sci., 58, 21962209, doi:10.1175/1520-0469(2001)058<2196:MPFPAR>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kossin, J., and W. Schubert, 2004: Mesovortices in Hurricane Isabel. Bull. Amer. Meteor. Soc., 85, 151153, doi:10.1175/BAMS-85-2-151.

    • Search Google Scholar
    • Export Citation
  • Kossin, J., B. McNoldy, and W. Schubert, 2002: Vortical swirls in hurricane eye clouds. Mon. Wea. Rev., 130, 31443149, doi:10.1175/1520-0493(2002)130<3144:VSIHEC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kwon, Y., and W. Frank, 2005: Dynamic instabilities of simulated hurricane-like vortices and their impact on the core structure of hurricanes. Part I: Dry experiments. J. Atmos. Sci., 62, 39553973, doi:10.1175/JAS3575.1.

    • Search Google Scholar
    • Export Citation
  • Kwon, Y., and W. Frank, 2008: Dynamic instabilities of simulated hurricane-like vortices and their impact on the core structure of hurricanes. Part II: Moist experiments. J. Atmos. Sci., 65, 106122, doi:10.1175/2007JAS2132.1.

    • Search Google Scholar
    • Export Citation
  • Lahaye, N., and V. Zeitlin, 2015: Centrifugal, barotropic and baroclinic instabilities of isolated ageostrophic anticyclones in the two-layer rotating shallow water model and their nonlinear saturation. J. Fluid Mech., 762, 534, doi:10.1017/jfm.2014.631.

    • Search Google Scholar
    • Export Citation
  • Lambaerts, J., G. Lapeyre, and V. Zeitlin, 2011: Moist versus dry barotropic instability in a shallow-water model of the atmosphere with moist convection. J. Atmos. Sci., 68, 12341252, doi:10.1175/2011JAS3540.1.

    • Search Google Scholar
    • Export Citation
  • Lambaerts, J., G. Lapeyre, and V. Zeitlin, 2012: Moist versus dry baroclinic instability in a simplified two-layer atmospheric model with condensation and latent heat release. J. Atmos. Sci., 69, 14051426, doi:10.1175/JAS-D-11-0205.1.

    • Search Google Scholar
    • Export Citation
  • Le Dizès, S., and P. Billant, 2009: Radiative instability in stratified vortices. Phys. Fluids, 21, 096602, doi:10.1063/1.3241995.

  • Lewis, B. M., and H. F. Hawkins, 1982: Polygonal eye walls and rainbands in hurricanes. Bull. Amer. Meteor. Soc., 63, 12941301, doi:10.1175/1520-0477(1982)063<1294:PEWARI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Menelaou, K., M. K. Yau, and Y. Martinez, 2013a: Impact of asymmetric dynamical processes on the structure and intensity change of two-dimensional hurricane-like annular vortices. J. Atmos. Sci., 70, 559582, doi:10.1175/JAS-D-12-0192.1.

    • Search Google Scholar
    • Export Citation
  • Menelaou, K., M. K. Yau, and Y. Martinez, 2013b: On the origin and impact of a polygonal eyewall in the rapid intensification of Hurricane Wilma (2005). J. Atmos. Sci., 70, 38393858, doi:10.1175/JAS-D-13-091.1.

    • Search Google Scholar
    • Export Citation
  • Möller, J. D., and R. K. Smith, 1994: The development of potential vorticity in a hurricane-like vortex. Quart. J. Roy. Meteor. Soc., 120, 12551265, doi:10.1002/qj.49712051907.

    • Search Google Scholar
    • Export Citation
  • Montgomery, M. T., and L. J. Shapiro, 1995: Generalized Charney–Stern and Fjortoft theorems for rapidly rotating vortices. J. Atmos. Sci., 52, 18291833, doi:10.1175/1520-0469(1995)052<1829:GCAFTF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Muramatsu, T., 1986: The structure of polygonal eye of a typhoon. J. Meteor. Soc. Japan, 64, 913921.

  • Naylor, J., and D. Schecter, 2014: Evaluation of the impact of moist convection on the development of asymmetric inner core instabilities in simulated tropical cyclones. J. Adv. Model. Earth Syst., 6, 10271048, doi:10.1002/2014MS000366.

    • Search Google Scholar
    • Export Citation
  • Nolan, D., and M. Montgomery, 2002: Nonhydrostatic, three-dimensional perturbations to balanced hurricane-like vortices. Part I: Linearized formulation, stability, and evolution. J. Atmos. Sci., 59, 29893020, doi:10.1175/1520-0469(2002)059<2989:NTDPTB>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Plougonven, R., and V. Zeitlin, 2002: Internal gravity wave emission from a pancake vortex: An example of wave-vortex interaction in strongly stratified flows. Phys. Fluids, 14, 12591268, doi:10.1063/1.1448297.

    • Search Google Scholar
    • Export Citation
  • Plougonven, R., and F. Zhang, 2014: Internal gravity waves from atmospheric jets and fronts. Rev. Geophys., 52, 3376, doi:10.1002/2012RG000419.

    • Search Google Scholar
    • Export Citation
  • Reasor, P., M. Eastin, and J. Gamache, 2009: Rapidly intensifying Hurricane Guillermo (1997). Part I: Low-wavenumber structure and evolution. Mon. Wea. Rev., 137, 603631, doi:10.1175/2008MWR2487.1.

    • Search Google Scholar
    • Export Citation
  • Rozoff, C. M., J. P. Kossin, W. H. Schubert, and P. J. Mulero, 2009: Internal control of hurricane intensity variability: The dual nature of potential vorticity mixing. J. Atmos. Sci., 66, 133147, doi:10.1175/2008JAS2717.1.

    • Search Google Scholar
    • Export Citation
  • Schecter, D. A., 2008: The spontaneous imbalance of an atmospheric vortex at high Rossby number. J. Atmos. Sci., 65, 24982521, doi:10.1175/2007JAS2490.1.

    • Search Google Scholar
    • Export Citation
  • Schecter, D. A., and M. T. Montgomery, 2004: Damping and pumping of a vortex Rossby wave in a monotonic cyclone: Critical layer stirring versus inertia-buoyancy wave emission. Phys. Fluids, 16, 13341348, doi:10.1063/1.1651485.

    • Search Google Scholar
    • Export Citation
  • Schecter, D. A., and M. T. Montgomery, 2006: Conditions that inhibit the spontaneous radiation of spiral inertia-gravity waves from an intense mesoscale cyclone. J. Atmos. Sci., 63, 435456, doi:10.1175/JAS3641.1.

    • Search Google Scholar
    • Export Citation
  • Schecter, D. A., and M. T. Montgomery, 2007: Waves in a cloudy vortex. J. Atmos. Sci., 64, 314337, doi:10.1175/JAS3849.1.

  • Schubert, W. H., M. T. Montgomery, R. K. Taft, T. A. Guinn, S. R. Fulton, J. P. Kossin, and J. P. Edwards, 1999: Polygonale eyewalls, asymmetric eye contraction, and potential vorticity mixing in hurricanes. J. Atmos. Sci., 56, 11971223, doi:10.1175/1520-0469(1999)056<1197:PEAECA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Spiga, A., H. Teitelbaum, and V. Zeitlin, 2008: Identification of the sources of inertia-gravity waves in the Andes Cordillera region. Ann. Geophys., 26, 25512568, doi:10.5194/angeo-26-2551-2008.

    • Search Google Scholar
    • Export Citation
  • Wang, Y., 2002: Vortex Rossby waves in a numerically simulated tropical cyclone. Part II: The role in tropical cyclone structure and intensity changes. J. Atmos. Sci., 59, 12391262, doi:10.1175/1520-0469(2002)059<1239:VRWIAN>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Wang, Y., and C. C. Wu, 2004: Current understanding of tropical cyclone structure and intensity changes—A review. Meteor. Atmos. Phys., 87, 257278, doi:10.1007/s00703-003-0055-6.

    • Search Google Scholar
    • Export Citation
  • Willoughby, H., R. Darling, and M. Rahn, 2006: Parametric representation of the primary hurricane vortex. Part II: A new family of sectionally continuous profiles. Mon. Wea. Rev., 134, 11021120, doi:10.1175/MWR3106.1.

    • Search Google Scholar
    • Export Citation
  • Yang, B., Y. Wang, and B. Wang, 2007: The effect of internally generated inner-core asymmetries on tropical cyclone potential intensity. J. Atmos. Sci., 64, 11651188, doi:10.1175/JAS3971.1.

    • Search Google Scholar
    • Export Citation
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