Mechanisms for Spontaneous Gravity Wave Generation within a Dipole Vortex

Chris Snyder National Center for Atmospheric Research,* Boulder, Colorado

Search for other papers by Chris Snyder in
Current site
Google Scholar
PubMed
Close
,
Riwal Plougonven Laboratoire de Météorologie Dynamique, IPSL, Ecole Normale Supérieure, Paris, France

Search for other papers by Riwal Plougonven in
Current site
Google Scholar
PubMed
Close
, and
David J. Muraki Department of Mathematics, Simon Fraser University, Vancouver, British Columbia, Canada

Search for other papers by David J. Muraki in
Current site
Google Scholar
PubMed
Close
Restricted access

We are aware of a technical issue preventing figures and tables from showing in some newly published articles in the full-text HTML view.
While we are resolving the problem, please use the online PDF version of these articles to view figures and tables.

Abstract

Previous simulations of dipole vortices propagating through rotating, stratified fluid have revealed small-scale inertia–gravity waves that are embedded within the dipole near its leading edge and are approximately stationary relative to the dipole. The mechanism by which these waves are generated is investigated, beginning from the observation that the dipole can be reasonably approximated by a balanced quasigeostrophic (QG) solution. The deviations from the QG solution (including the waves) then satisfy linear equations that come from linearization of the governing equations about the QG dipole and are forced by the residual tendency of the QG dipole (i.e., the difference between the time tendency of the QG solution and that of the full primitive equations initialized with the QG fields). The waves do not appear to be generated by an instability of the balanced dipole, as homogeneous solutions of the linear equations amplify little over the time scale for which the linear equations are valid. Linear solutions forced by the residual tendency capture the scale, location, and pattern of the inertia–gravity waves, although they overpredict the wave amplitude by a factor of 2. There is thus strong evidence that the waves are generated as a forced linear response to the balanced flow. The relation to and differences from other theories for wave generation by balanced flows, including those of Lighthill and Ford et al., are discussed.

Corresponding author address: C. Snyder, NCAR, P.O. Box 3000, Boulder, CO 80307–3000. Email: chriss@ucar.edu

Abstract

Previous simulations of dipole vortices propagating through rotating, stratified fluid have revealed small-scale inertia–gravity waves that are embedded within the dipole near its leading edge and are approximately stationary relative to the dipole. The mechanism by which these waves are generated is investigated, beginning from the observation that the dipole can be reasonably approximated by a balanced quasigeostrophic (QG) solution. The deviations from the QG solution (including the waves) then satisfy linear equations that come from linearization of the governing equations about the QG dipole and are forced by the residual tendency of the QG dipole (i.e., the difference between the time tendency of the QG solution and that of the full primitive equations initialized with the QG fields). The waves do not appear to be generated by an instability of the balanced dipole, as homogeneous solutions of the linear equations amplify little over the time scale for which the linear equations are valid. Linear solutions forced by the residual tendency capture the scale, location, and pattern of the inertia–gravity waves, although they overpredict the wave amplitude by a factor of 2. There is thus strong evidence that the waves are generated as a forced linear response to the balanced flow. The relation to and differences from other theories for wave generation by balanced flows, including those of Lighthill and Ford et al., are discussed.

Corresponding author address: C. Snyder, NCAR, P.O. Box 3000, Boulder, CO 80307–3000. Email: chriss@ucar.edu

Save
  • Errico, R. M., 1982: Normal mode initialization and the generation of gravity waves by quasigeostrophic forcing. J. Atmos. Sci., 39 , 573586.

    • 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, 6A , 36943704.

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

    • Search Google Scholar
    • Export Citation
  • Guest, F. M., M. J. Reeder, C. J. Marks, and D. J. Karoly, 2000: Inertia–gravity waves observed in the lower stratosphere over Macquarie Island. J. Atmos. Sci., 57 , 737752.

    • Search Google Scholar
    • Export Citation
  • Kizner, Z., G. Reznik, B. Fridman, R. Khvoles, and J. McWilliams, 2008: Shallow-water modons on the f-plane. J. Fluid Mech., 603 , 305329.

    • Search Google Scholar
    • Export Citation
  • Ley, B., and W. R. Peltier, 1978: Wave generation and frontal collapse. J. Atmos. Sci., 35 , 317.

  • Lighthill, M. J., 1952: On sound generated aerodynamically. I. General theory. Proc. Roy. Soc. London, 211A , 564587.

  • McIntyre, M., 2009: Spontaneous imbalance and hybrid vortex-gravity structures. J. Atmos. Sci., 66 , 13151326.

  • Medvedev, A. S., and N. M. Gavrilov, 1995: The nonlinear mechanism of gravity wave generation by meteorological motions in the atmosphere. J. Atmos. Terr. Phys., 57 , 12211231.

    • Search Google Scholar
    • Export Citation
  • Muraki, D. M., and C. Snyder, 2007: Vortex dipoles for surface quasigeostrophic models. J. Atmos. Sci., 64 , 29612967.

  • 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
  • Plougonven, R., and C. Snyder, 2007: Inertia–gravity waves spontaneously generated by jets and fronts. Part I: Different baroclinic life cycles. J. Atmos. Sci., 64 , 25022520.

    • Search Google Scholar
    • Export Citation
  • Plougonven, R., and F. Zhang, 2007: On the forcing of inertia–gravity waves by synoptic-scale flows. J. Atmos. Sci., 64 , 17371742.

  • Plougonven, R., H. Teitelbaum, and V. Zeitlin, 2003: Inertia gravity wave generation by the tropospheric midlatitude jet as given by the Fronts and Atlantic Storm-Track Experiment radio soundings. J. Geophys. Res., 108 , 4686. doi:10.1029/2003JD003535.

    • Search Google Scholar
    • Export Citation
  • Plougonven, R., D. J. Muraki, and C. Snyder, 2005: A baroclinic instability that couples balanced motions and gravity waves. J. Atmos. Sci., 62 , 15451559.

    • 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
  • Sakai, S., 1989: Rossby–Kelvin instability: A new type of ageostrophic instability caused by a resonance between Rossby waves and gravity waves. J. Fluid Mech., 202 , 149176.

    • 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
  • Snyder, C., 1999: Error growth in flows with finite-amplitude waves or other coherent structures. J. Atmos. Sci., 56 , 500506.

  • Snyder, C., W. Skamarock, and R. Rotunno, 1993: Frontal dynamics near and following frontal collapse. J. Atmos. Sci., 50 , 31943212.

  • Snyder, C., T. M. Hamill, and S. Trier, 2003: Linear evolution of forecast error covariances in a quasigeostrophic model. Mon. Wea. Rev., 131 , 189205.

    • Search Google Scholar
    • Export Citation
  • Snyder, C., D. J. Muraki, R. Plougonven, and F. Zhang, 2007: Inertia–gravity waves generated within a dipole vortex. J. Atmos. Sci., 64 , 44174431.

    • Search Google Scholar
    • Export Citation
  • Vanneste, J., 2008: Exponential smallness of inertia–gravity wave generation at small Rossby number. J. Atmos. Sci., 65 , 16221637.

  • 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
  • Viúdez, A., 2007: The origin of the stationary frontal wave packet spontaneously generated in rotating stratified vortex dipoles. J. Fluid Mech., 593 , 359383.

    • Search Google Scholar
    • Export Citation
  • Viúdez, A., 2008: The stationary frontal wave packet spontaneously generated in mesoscale dipoles. J. Phys. Oceanogr., 38 , 243256.

  • Wang, S., F. Zhang, and C. Snyder, 2009: Generation and propagation of inertia–gravity waves from vortex dipoles and jets. J. Atmos. Sci., 66 , 12941314.

    • Search Google Scholar
    • Export Citation
  • Warn, T., 1997: Nonlinear balance and quasi-geostrophic sets. Atmos.–Ocean, 35 , 135145.

  • Warn, T., O. Bokhove, T. G. Shepherd, and G. K. Vallis, 1995: Rossby number expansions, slaving principles, and balance dynamics. Quart. J. Roy. Meteor. Soc., 121 , 723739.

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

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 477 264 89
PDF Downloads 196 34 3