Spontaneous Surface Generation and Interior Amplification of Internal Waves in a Regional-Scale Ocean Model

Callum J. Shakespeare Research School of Earth Sciences, and ARC Centre of Excellence in Climate System Science, Australian National University, Canberra, Australian Capital Territory, Australia

Search for other papers by Callum J. Shakespeare in
Current site
Google Scholar
PubMed
Close
and
Andrew McC. Hogg Research School of Earth Sciences, and ARC Centre of Excellence in Climate System Science, Australian National University, Canberra, Australian Capital Territory, Australia

Search for other papers by Andrew McC. Hogg in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

Recent theories, models, and observations have suggested the presence of significant spontaneous internal wave generation at density fronts near the ocean surface. Spontaneous generation is the emission of waves by unbalanced, large Rossby number flows in the absence of direct forcing. Here, spontaneous generation is investigated in a zonally reentrant channel model using parameter values typical of the Southern Ocean. The model is carefully equilibrated to obtain a steady-state wave field for which a closed energy budget is formulated. There are two main results: First, waves are spontaneously generated at sharp fronts in the top 50 m of the model. The magnitude of the energy flux to the wave field at these fronts is comparable to that from other mechanisms of wave generation. Second, the surface-generated wave field is amplified in the model interior through interaction with horizontal density gradients within the main zonal current. The magnitude of the mean-to-wave conversion in the model interior is comparable to recent observational estimates and is the dominant source of wave energy in the model, exceeding the initial spontaneous generation. This second result suggests that internal amplification of the wave field may contribute to the ocean’s internal wave energy budget at a rate commensurate with known generation mechanisms.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author e-mail: Callum J. Shakespeare, callum.shakespeare@anu.edu.au

Abstract

Recent theories, models, and observations have suggested the presence of significant spontaneous internal wave generation at density fronts near the ocean surface. Spontaneous generation is the emission of waves by unbalanced, large Rossby number flows in the absence of direct forcing. Here, spontaneous generation is investigated in a zonally reentrant channel model using parameter values typical of the Southern Ocean. The model is carefully equilibrated to obtain a steady-state wave field for which a closed energy budget is formulated. There are two main results: First, waves are spontaneously generated at sharp fronts in the top 50 m of the model. The magnitude of the energy flux to the wave field at these fronts is comparable to that from other mechanisms of wave generation. Second, the surface-generated wave field is amplified in the model interior through interaction with horizontal density gradients within the main zonal current. The magnitude of the mean-to-wave conversion in the model interior is comparable to recent observational estimates and is the dominant source of wave energy in the model, exceeding the initial spontaneous generation. This second result suggests that internal amplification of the wave field may contribute to the ocean’s internal wave energy budget at a rate commensurate with known generation mechanisms.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author e-mail: Callum J. Shakespeare, callum.shakespeare@anu.edu.au
Save
  • Bell, T., 1975: Topographically generated internal waves in the open ocean. J. Geophys. Res., 80, 320327, doi:10.1029/JC080i003p00320.

  • Blumen, W., 1972: Geostrophic adjustment. Rev. Geophys. Space Phys., 10, 485528, doi:10.1029/RG010i002p00485.

  • Booker, J. R., and F. P. Bretherton, 1967: The critical layer for internal gravity waves in a shear flow. J. Fluid Mech., 27, 513539, doi:10.1017/S0022112067000515.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Danioux, E., J. Vanneste, P. Klein, and H. Sasaki, 2012: Spontaneous inertia-gravity-wave generation by surface-intensified turbulence. J. Fluid Mech., 699, 153173, doi:10.1017/jfm.2012.90.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Grisouard, N., M. B. Fox, and J. Nijjer, 2016: Radiation of internal waves by symmetrically unstable fronts. Eighth Int. Symp. on Stratified Flows, San Diego, CA, University of California, San Diego, 1–8. [Available online at http://escholarship.org/uc/item/2b59h10g#page-1.]

  • Lott, F., R. Plougonven, and J. Vanneste, 2010: Gravity waves generated by sheared potential vorticity anomalies. J. Atmos. Sci., 67, 157170, doi:10.1175/2009JAS3134.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Marshall, J., A. Adcroft, C. Hill, L. Perelman, and C. Heisey, 1997: A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers. J. Geophys. Res., 102, 57535766, doi:10.1029/96JC02775.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Miller, J. E., 1948: On the concept of frontogenesis. J. Meteor., 5, 169171, doi:10.1175/1520-0469(1948)005<0169:OTCOF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Muller, P., 1976: On the diffusion of momentum and mass by internal gravity waves. J. Fluid Mech., 77, 789823, doi:10.1017/S0022112076002899.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Munk, W., 1981: Internal waves and small-scale processes. Evolution of Physical Oceanography, B. A. Warren and C. Wunsch, Eds., MIT Press, 264–291.

  • Nagai, T., A. Tandon, E. Kunze, and A. Mahadevan, 2015: Spontaneous generation of near-inertial waves by the Kuroshio Front. J. Phys. Oceanogr., 45, 23812406, doi:10.1175/JPO-D-14-0086.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Nikurashin, M., and R. Ferrari, 2011: Global energy conversion rate from geostrophic flows into internal lee waves in the deep ocean. Geophys. Res. Lett., 38, L08610, doi:10.1029/2011GL046576.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Nikurashin, M., R. Ferrari, N. Grisouard, and K. Polzin, 2014: The impact of finite-amplitude bottom topography on internal wave generation in the Southern Ocean. J. Phys. Oceanogr., 44, 29382950, doi:10.1175/JPO-D-13-0201.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Plougonven, R., and V. Zeitlin, 2009: Nonlinear development of inertial instability in a barotropic shear. Phys. Fluids, 21, 106601, doi:10.1063/1.3242283.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Polzin, K. L., 2010: Mesoscale eddy–internal wave coupling. Part II: Energetics and results from PolyMode. J. Phys. Oceanogr., 40, 789801, doi:10.1175/2009JPO4039.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Polzin, K. L., and Y. V. Lvov, 2011: Toward regional characterizations of the oceanic internal wavefield. Rev. Geophys., 49, RG4003, doi:10.1029/2010RG000329.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ribstein, B., R. Plougonven, and V. Zeitlin, 2014: Inertial versus baroclinic instability of the Bickley jet in continuously stratified rotating fluid. J. Fluid Mech., 743, 131, doi:10.1017/jfm.2014.26.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Shakespeare, C. J., 2015: On the generation of waves during frontogenesis. Ph.D. thesis, University of Cambridge, 221 pp.

  • Shakespeare, C. J., and J. R. Taylor, 2014: The spontaneous generation of inertia–gravity waves during frontogenesis forced by large strain: Theory. J. Fluid Mech., 757, 817853, doi:10.1017/jfm.2014.514.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Shakespeare, C. J., and J. R. Taylor, 2016: Spontaneous wave generation at strongly strained density fronts. J. Phys. Oceanogr., 46, 20632081, doi:10.1175/JPO-D-15-0043.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Shakespeare, C. J., and A. M. Hogg, 2017: The viscous lee wave problem and its implications for ocean modelling. Ocean Modell., 113, 2229, doi:10.1016/j.ocemod.2017.03.006.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thomas, L. N., 2012: On the effects of frontogenetic strain on symmetric instability and inertia–gravity waves. J. Fluid Mech., 711, 620640, doi:10.1017/jfm.2012.416.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Whitt, D. B., and L. N. Thomas, 2015: Resonant generation and energetics of wind-forced near-inertial motions in a geostrophic flow. J. Phys. Oceanogr., 45, 181208, doi:10.1175/JPO-D-14-0168.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Winters, K. B., P. N. Lombard, J. J. Riley, and E. A. D’Asaro, 1995: Available potential energy and mixing in density-stratified fluids. J. Fluid Mech., 289, 115128, doi:10.1017/S002211209500125X.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wunsch, C., and R. Ferrari, 2004: Vertical mixing, energy and the general circulation of the oceans. Annu. Rev. Fluid Mech., 36, 281314, doi:10.1146/annurev.fluid.36.050802.122121.

    • Crossref
    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 899 264 23
PDF Downloads 725 168 7