• Antkowiak, A., and P. Brancher, 2004: Transient energy growth for the Lamb-Oseen vortex. Phys. Fluids, 16 , L1L4. doi:10.1063/1.1626123.

    • Search Google Scholar
    • Export Citation
  • Bachman, D. A., 1998: Nonlinear phenomena in a pure electron plasma studied with a 2D fluid code. Ph.D. dissertation, California Institute of Technology, 143 pp.

  • Balmforth, N. J., S. G. Llewellyn Smith, and W. R. Young, 2001: Disturbing vortices. J. Fluid Mech., 426 , 95133.

  • Bassom, A. P., and A. D. Gilbert, 1998: The spiral wind-up of vorticity in an inviscid planar vortex. J. Fluid Mech., 371 , 109140.

  • Benilov, E. S., 2005: The effect of ageostrophy on the stability of thin oceanic vortices. Dyn. Atmos. Oceans, 39 , 211226.

  • Black, P. G., and Coauthors, 2007: Air–sea exchange in hurricanes: Synthesis of observations from the Coupled Boundary Layer Air–Sea Transfer Experiment. Bull. Amer. Meteor. Soc., 88 , 357374.

    • Search Google Scholar
    • Export Citation
  • Briggs, R. J., J. D. Daugherty, and R. H. Levy, 1970: Role of Landau damping in crossed-field electron beams and inviscid shear flow. Phys. Fluids, 13 , 421432.

    • Search Google Scholar
    • Export Citation
  • Broadbent, E. G., and D. W. Moore, 1979: Acoustic destabilization of vortices. Philos. Trans. Roy. Soc. London, A290 , 353371.

  • Brunet, G., and M. T. Montgomery, 2002: Vortex Rossby waves on smooth circular vortices: I. Theory. Dyn. Atmos. Oceans, 35 , 153177.

  • Cass, A. C., 1998: Experiments on vortex symmetrization in magnetized electron columns. Ph.D. dissertation, University of California, San Diego, 64 pp.

  • Chan, W. M., K. Shariff, and T. H. Pulliam, 1993: Instabilities of two-dimensional inviscid compressible vortices. J. Fluid Mech., 253 , 173209.

    • Search Google Scholar
    • Export Citation
  • Charney, J. G., 1948: On the scale of atmospheric motions. Geophys. Publ., 17 , 117.

  • Chen, Y., and M. K. Yau, 2001: Spiral bands in a simulated hurricane. Part I: Vortex Rossby wave verification. J. Atmos. Sci., 58 , 21282145.

    • Search Google Scholar
    • Export Citation
  • Chen, Y., G. Brunet, and M. K. Yau, 2003: Spiral bands in a simulated hurricane. Part II: Wave activity diagnostics. J. Atmos. Sci., 60 , 12391256.

    • Search Google Scholar
    • Export Citation
  • Chimonas, G., and H. M. Hauser, 1997: The transfer of angular momentum from vortices to gravity swirl waves. J. Atmos. Sci., 54 , 17011711.

    • 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.

  • Chow, K. C., K. L. Chan, and A. K. H. Lau, 2002: Generation of moving spiral bands in tropical cyclones. J. Atmos. Sci., 59 , 29302950.

    • Search Google Scholar
    • Export Citation
  • Corngold, N. R., 1995: Linear response of the two-dimensional pure electron plasma: Quasi-modes for some model profiles. Phys. Plasmas, 2 , 620628.

    • Search Google Scholar
    • Export Citation
  • Davidson, R. C., 1990: Physics of Nonneutral Plasmas. Addison-Wesley, 733 pp.

  • Dutton, J. A., 1976: The Ceaseless Wind: An Introduction to the Theory of Atmospheric Motion. McGraw-Hill, 579 pp.

  • Emanuel, K. A., 1986: An air-sea interaction theory for tropical cyclones. Part I: Steady state maintenance. J. Atmos. Sci., 43 , 585604.

    • Search Google Scholar
    • Export Citation
  • Emanuel, K. A., 1995: Sensitivity of tropical cyclones to surface exchange coefficients and a revised steady state model incorporating eye dynamics. J. Atmos. Sci., 52 , 39693976.

    • Search Google Scholar
    • Export Citation
  • Enagonio, J., and M. T. Montgomery, 2001: Tropical cyclogenesis via convectively forced vortex Rossby waves in a shallow-water primitive equation model. J. Atmos. Sci., 58 , 685706.

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

    • Search Google Scholar
    • Export Citation
  • Ford, R., 1994b: The response of a rotating ellipse of uniform potential vorticity to gravity wave radiation. Phys. Fluids, 6 , 36943704.

    • Search Google Scholar
    • Export Citation
  • Ford, R., M. E. McIntyre, and W. A. Norton, 2000: Balance and the slow quasi-manifold: Some explicit results. J. Atmos. Sci., 57 , 12361254.

    • Search Google Scholar
    • Export Citation
  • Ford, R., M. E. McIntyre, and W. A. Norton, 2002: Reply. J. Atmos. Sci., 59 , 28782882.

  • Griffiths, M., and M. J. Reeder, 1996: Stratospheric inertia-gravity waves generated in a numerical model of frontogenesis. I: Model solutions. Quart. J. Roy. Meteor. Soc., 122 , 11531174.

    • Search Google Scholar
    • Export Citation
  • Guinn, T. A., and W. H. Schubert, 1993: Hurricane spiral bands. J. Atmos. Sci., 50 , 33803403.

  • Haynes, P. H., 1988: Forced, dissipative generalizations of finite amplitude wave-activity conservation relations for zonal and nonzonal basic flows. J. Atmos. Sci., 45 , 2352.

    • Search Google Scholar
    • Export Citation
  • Hoskins, B. J., and F. P. Bretherton, 1972: Atmospheric frontogenesis models: Mathematical formulation and solution. J. Atmos. Sci., 29 , 1137.

    • Search Google Scholar
    • Export Citation
  • Hoskins, B. J., 1975: The geostrophic momentum approximation and the semigeostrophic equations. J. Atmos. Sci., 32 , 233242.

  • Hoskins, B. J., M. E. McIntyre, and A. W. Robertson, 1985: On the use and significance of isentropic potential vorticity maps. Quart. J. Roy. Meteor. Soc., 111 , 877946.

    • Search Google Scholar
    • Export Citation
  • Howe, M. S., 2003: The Theory of Vortex Sound. Cambridge University Press, 216 pp.

  • Jones, S. C., 1995: The evolution of vortices in vertical shear. I: Initially barotropic vortices. Quart. J. Roy. Meteor. Soc., 121 , 821851.

    • Search Google Scholar
    • Export Citation
  • Kelvin, Lord, 1880: On the vibrations of a columnar vortex. Philos. Mag., 10 , 155168.

  • Killworth, P. D., and M. E. McIntyre, 1985: Do Rossby-wave critical layers absorb, reflect, or over-reflect? J. Fluid Mech., 161 , 449492.

    • Search Google Scholar
    • Export Citation
  • Kop’ev, V. F., and E. A. Leont’ev, 1983: Acoustic instability of an axial vortex. Sov. Phys. Acoust., 29 , 111115.

  • Kop’ev, V. F., and E. A. Leont’ev, 1985: Energy aspect of the acoustic instability of certain steady-state vortices. Sov. Phys. Acoust., 31 , 205207.

    • Search Google Scholar
    • Export Citation
  • Kop’ev, V. F., and E. A. Leont’ev, 1988: Acoustic instability of planar vortex flows with circular streamlines. Sov. Phys. Acoust., 34 , 276278.

    • Search Google Scholar
    • Export Citation
  • Landau, L., 1946: On the vibration of the electronic plasma. J. Phys. U.S.S.R., 10 , 25.

  • Lansky, I. M., T. M. O’Neil, and D. A. Schecter, 1997: A theory of vortex merger. Phys. Rev. Lett., 79 , 14791482.

  • Le Dizes, S., 2000: Non-axisymmetric vortices in two-dimensional flows. J. Fluid Mech., 406 , 175198.

  • 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
  • Maslowe, S. A., 1986: Critical layers in shear flow. Annu. Rev. Fluid. Mech., 18 , 405432.

  • McDonald, N. J., 1968: The evidence for the existence of Rossby-like waves in the hurricane vortex. Tellus, 20 , 138150.

  • McIntyre, M. E., 1981: On the ‘wave-momentum’ myth. J. Fluid Mech., 106 , 331347.

  • McWilliams, J. C., 1985: A uniformly valid model spanning the regimes of geostrophic and isotropic, stratified turbulence: Balanced turbulence. J. Atmos. Sci., 42 , 17731774.

    • Search Google Scholar
    • Export Citation
  • McWilliams, J. C., L. P. Graves, and M. T. Montgomery, 2003: A formal theory for vortex Rossby waves and vortex evolution. Geophys. Astrophys. Fluid Dyn., 97 , 275309.

    • Search Google Scholar
    • Export Citation
  • Möller, J. D., and M. T. Montgomery, 1999: Vortex Rossby waves and hurricane intensification in a barotropic model. J. Atmos. Sci., 56 , 16741687.

    • Search Google Scholar
    • Export Citation
  • Möller, J. D., and M. T. Montgomery, 2000: Tropical cyclone evolution via potential vorticity anomalies in a three-dimensional balance model. J. Atmos. Sci., 57 , 33663387.

    • Search Google Scholar
    • Export Citation
  • Möller, J. D., and L. J. Shapiro, 2002: Balanced contributions to the intensification of Hurricane Opal as diagnosed from a GFDL model forecast. Mon. Wea. Rev., 130 , 18661881.

    • Search Google Scholar
    • Export Citation
  • Montgomery, M. T., and R. J. Kallenbach, 1997: A theory of vortex Rossby-waves and its application to spiral bands and intensity changes in hurricanes. Quart. J. Roy. Meteor. Soc., 123 , 435465.

    • Search Google Scholar
    • Export Citation
  • Montgomery, M. T., and C. Lu, 1997: Free waves in barotropic vortices. Part I: Eigenmode structure. J. Atmos. Sci., 54 , 18681885.

  • Montgomery, M. T., and J. L. Franklin, 1998: An assessment of the balance approximation in hurricanes. J. Atmos. Sci., 55 , 21932200.

  • Montgomery, M. T., and L. J. Shapiro, 1995: Generalized Charney–Stern and Fjortoft theorems for rapidly rotating vortices. J. Atmos. Sci., 52 , 18291833.

    • Search Google Scholar
    • Export Citation
  • Muraki, D. J., C. Snyder, and R. Rotunno, 1999: The next-order corrections to quasigeostrophic theory. J. Atmos. Sci., 56 , 15471560.

  • Nolan, D. S., and B. F. Farrell, 1999: Generalized stability analyses of asymmetric disturbances in one- and two-celled vortices maintained by radial inflow. J. Atmos. Sci., 56 , 12821307.

    • Search Google Scholar
    • Export Citation
  • O’Neil, T. M., 1965: Collisionless damping of nonlinear plasma oscillations. Phys. Fluids, 8 , 22552262.

  • O’Sullivan, D., and T. J. Dunkerton, 1995: Generation of inertia–gravity waves in a simulated life cycle of baroclinic instability. J. Atmos. Sci., 52 , 36953705.

    • Search Google Scholar
    • Export Citation
  • Papaloizou, J. C. B., and J. E. Pringle, 1987: The dynamic stability of differentially rotating discs—III. Mon. Not. Roy. Astron. Soc., 225 , 267283.

    • Search Google Scholar
    • Export Citation
  • Pillai, S., and R. W. Gould, 1994: Damping and trapping in 2D inviscid fluids. Phys. Rev. Lett., 73 , 28492852.

  • 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.

    • Search Google Scholar
    • Export Citation
  • Plougonven, R., and C. Snyder, 2005: Gravity waves excited by jets: Propagation versus generation. Geophys. Res. Lett., 32 .L18802, doi:10.1029/2005GL023730.

    • Search Google Scholar
    • Export Citation
  • Polvani, L. M., J. C. McWilliams, M. A. Spall, and R. Ford, 1994: The coherent structures of shallow-water turbulence: Deformation-radius effects, cyclone/anticyclone asymmetry and gravity-wave generation. Chaos, 4 , 177186.

    • Search Google Scholar
    • Export Citation
  • Reasor, P. D., and M. T. Montgomery, 2001: Three-dimensional alignment and co-rotation of weak, TC-like vortices via linear vortex-Rossby-waves. J. Atmos. Sci., 58 , 23062330.

    • Search Google Scholar
    • Export Citation
  • Reasor, P. D., M. T. Montgomery, and L. D. Grasso, 2004: A new look at the problem of tropical cyclones in shear flow: Vortex resiliency. J. Atmos. Sci., 61 , 322.

    • Search Google Scholar
    • Export Citation
  • Reeder, M. J., and M. Griffiths, 1996: Stratospheric inertia-gravity waves generated in a numerical model of frontogenesis. II: Wave sources, generation mechanisms and momentum fluxes. Quart. J. Roy. Meteor. Soc., 122 , 11751195.

    • Search Google Scholar
    • Export Citation
  • Ren, S., 1999: Further results on the stability of rapidly rotating vortices in the asymmetric balance formulation. J. Atmos. Sci., 56 , 475482.

    • Search Google Scholar
    • Export Citation
  • Rossi, L. F., J. F. Lingevitch, and A. J. Bernoff, 1997: Quasi-steady monopole and tripole attractors for relaxing vortices. Phys. Fluids, 9 , 23292338.

    • Search Google Scholar
    • Export Citation
  • Saujani, S., and T. G. Shepherd, 2002: Comments on “Balance and the slow quasimanifold: Some explicit results”. J. Atmos. Sci., 59 , 28742877.

    • Search Google Scholar
    • Export Citation
  • Schecter, D. A., D. H. E. Dubin, A. C. Cass, C. F. Driscoll, I. M. Lansky, and T. M. O’Neil, 2000: Inviscid damping of asymmetries on a two-dimensional vortex. Phys. Fluids, 12 , 23972412.

    • Search Google Scholar
    • Export Citation
  • Schecter, D. A., and M. T. Montgomery, 2003: On the symmetrization rate of an intense geophysical vortex. Dyn. Atmos. Oceans, 37 , 5587.

    • 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.

    • 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.

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

  • Schecter, D. A., M. T. Montgomery, and P. D. Reasor, 2002: A theory for the vertical alignment of a quasigeostrophic vortex. J. Atmos. Sci., 59 , 150168.

    • Search Google Scholar
    • Export Citation
  • Schecter, D. A., M. E. Nicholls, J. Persing, A. J. Bedard Jr., and R. A. Pielke Sr., 2008: Infrasound emitted by tornado-like vortices: Basic theory and a numerical comparison to the acoustic radiation of a single-cell thunderstorm. J. Atmos. Sci., 65 , 685713.

    • Search Google Scholar
    • Export Citation
  • Shapiro, L. J., and M. T. Montgomery, 1993: A three-dimensional balance theory for rapidly rotating vortices. J. Atmos. Sci., 50 , 33223335.

    • Search Google Scholar
    • Export Citation
  • Shepherd, T. G., 2003: Hamiltonian dynamics. Encyclopedia of Atmospheric Sciences, J. R. Holton, J. A. Curry, and J. A. Pyle, Eds., Academic Press, 929–938.

    • Search Google Scholar
    • Export Citation
  • Shukhman, I. G., 1991: Nonlinear evolution of spiral density waves generated by the instability of the shear layer in a rotating compressible fluid. J. Fluid Mech., 233 , 587612.

    • Search Google Scholar
    • Export Citation
  • Snyder, C., W. C. Skamarock, and R. Rotunno, 1993: Frontal dynamics near and following frontal collapse. J. Atmos. Sci., 50 , 31493212.

    • Search Google Scholar
    • Export Citation
  • Spencer, R. L., and S. N. Rasband, 1997: Damped diocotron quasi-modes of nonneutral plasmas and inviscid fluids. Phys. Plasmas, 4 , 5360.

    • Search Google Scholar
    • Export Citation
  • Vanneste, J., and I. Yavneh, 2004: Exponentially small inertia–gravity waves and the breakdown of quasigeostrophic balance. J. Atmos. Sci., 61 , 211223.

    • Search Google Scholar
    • Export Citation
  • Wang, Y., 2002a: Vortex Rossby waves in a numerically simulated tropical cyclone. Part I: Overall structure, potential vorticity, and kinetic energy budgets. J. Atmos. Sci., 59 , 12131238.

    • Search Google Scholar
    • Export Citation
  • Wang, Y., 2002b: 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.

    • Search Google Scholar
    • Export Citation
  • Zeitlin, V., 1991: On the backreaction of acoustic radiation for distributed two-dimensional vortex structures. Phys. Fluids A, 3 , 16771680.

    • Search Google Scholar
    • Export Citation
  • Zhang, F., 2004: Generation of mesoscale gravity waves in upper-tropospheric jet-front systems. J. Atmos. Sci., 61 , 440457.

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The Spontaneous Imbalance of an Atmospheric Vortex at High Rossby Number

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  • 1 NorthWest Research Associates, Redmond, Washington
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Abstract

This paper discusses recent progress toward understanding the instability of a monotonic vortex at high Rossby number, due to the radiation of spiral inertia–gravity (IG) waves. The outward-propagating IG waves are excited by inner undulations of potential vorticity that consist of one or more vortex Rossby waves. An individual vortex Rossby wave and its IG wave emission have angular pseudomomenta of opposite sign, positive and negative, respectively. The Rossby wave therefore grows in response to producing radiation. Such growth is potentially suppressed by the resonant absorption of angular pseudomomentum in a critical layer, where the angular phase velocity of the Rossby wave matches the angular velocity of the mean flow. Suppression requires a sufficiently steep radial gradient of potential vorticity in the critical layer. Both linear and nonlinear steepness requirements are reviewed.

The formal theory of radiation-driven instability, or “spontaneous imbalance,” is generalized in isentropic coordinates to baroclinic vortices that possess active critical layers. Furthermore, the rate of angular momentum loss by IG wave radiation is reexamined in the hurricane parameter regime. Numerical results suggest that the negative radiation torque on a hurricane has a smaller impact than surface drag, despite recent estimates of its large magnitude.

Corresponding author address: David A. Schecter, NorthWest Research Associates, 4118 148th Ave. NE, Redmond, WA 98052. Email: schecter@nwra.com

This article included in the Spontaneous Imbalance special collection.

Abstract

This paper discusses recent progress toward understanding the instability of a monotonic vortex at high Rossby number, due to the radiation of spiral inertia–gravity (IG) waves. The outward-propagating IG waves are excited by inner undulations of potential vorticity that consist of one or more vortex Rossby waves. An individual vortex Rossby wave and its IG wave emission have angular pseudomomenta of opposite sign, positive and negative, respectively. The Rossby wave therefore grows in response to producing radiation. Such growth is potentially suppressed by the resonant absorption of angular pseudomomentum in a critical layer, where the angular phase velocity of the Rossby wave matches the angular velocity of the mean flow. Suppression requires a sufficiently steep radial gradient of potential vorticity in the critical layer. Both linear and nonlinear steepness requirements are reviewed.

The formal theory of radiation-driven instability, or “spontaneous imbalance,” is generalized in isentropic coordinates to baroclinic vortices that possess active critical layers. Furthermore, the rate of angular momentum loss by IG wave radiation is reexamined in the hurricane parameter regime. Numerical results suggest that the negative radiation torque on a hurricane has a smaller impact than surface drag, despite recent estimates of its large magnitude.

Corresponding author address: David A. Schecter, NorthWest Research Associates, 4118 148th Ave. NE, Redmond, WA 98052. Email: schecter@nwra.com

This article included in the Spontaneous Imbalance special collection.

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