Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-17T07:22:24.315Z Has data issue: false hasContentIssue false
  • English
  • Français

Effect of background mean flow on PSI of internal wave beams

Published online by Cambridge University Press:  23 April 2019

Boyu Fan Open the ORCID record for Boyu Fan [Opens in a new window]  and
T. R. Akylas
Boyu Fan
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
T. R. Akylas*
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

An asymptotic model is developed for the parametric subharmonic instability (PSI) of finite-width nearly monochromatic internal gravity wave beams in the presence of a background constant horizontal mean flow. The subharmonic perturbations are taken to be short-scale wavepackets that may extract energy via resonant triad interactions while in contact with the underlying beam, and the mean flow is assumed to be small so that its advection effect on the perturbations is as important as dispersion, triad nonlinearity and viscous dissipation. In this ‘distinguished limit’, the perturbation dynamics are governed by the same evolution equations as those derived in Karimi & Akylas (J. Fluid Mech., vol. 757, 2014, pp. 381–402), except for a mean flow term that affects the group velocity of the perturbations and imposes an additional necessary condition for PSI, which stabilizes very short-scale perturbations. As a result, it is possible for a small amount of mean flow to weaken PSI dramatically.

JFM classification

Geophysical and Geological Flows: Internal waves
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 869 , 25 June 2019 , R1
Copyright
© 2019 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alford, M. H., MacKinnon, J. A., Zhao, Z., Pinkel, R., Klymak, J. & Peacock, T. 2007 Internal waves across the Pacific. Geophys. Res. Lett. 34 (24), L24601.10.1029/2007GL031566Google Scholar
Bourget, B., Dauxois, T., Joubaud, S. & Odier, P. 2013 Experimental study of parametric subharmonic instability for internal plane waves. J. Fluid Mech. 723, 1–20.10.1017/jfm.2013.78Google Scholar
Bourget, B., Scolan, H., Dauxois, T., Le Bars, M., Odier, P. & Joubaud, S. 2014 Finite-size effects in parametric subharmonic instability. J. Fluid Mech. 759, 739–750.10.1017/jfm.2014.550Google Scholar
Clark, H. A. & Sutherland, B. R. 2010 Generation, propagation, and breaking of an internal wave beam. Phys. Fluids 22 (7), 076601.Google Scholar
Dauxois, T., Joubaud, S., Odier, P. & Venaille, A. 2018 Instabilities of internal gravity wave beams. Annu. Rev. Fluid Mech. 50 (1), 131–156.10.1146/annurev-fluid-122316-044539Google Scholar
Fovell, R., Durran, D. & Holton, J. R. 1992 Numerical simulations of convectively generated stratospheric gravity waves. J. Atmos. Sci. 49 (16), 1427–1442.10.1175/1520-0469(1992)049<1427:NSOCGS>2.0.CO;22.0.CO;2>Google Scholar
Hazewinkel, J. & Winters, K. B. 2011 PSI of the internal tide on a 𝛽 plane: Flux divergence and near-inertial wave propagation. J. Phys. Oceanogr. 41 (9), 1673–1682.10.1175/2011JPO4605.1Google Scholar
Hibiya, T., Nagasawa, M. & Niwa, Y. 2002 Nonlinear energy transfer within the oceanic internal wave spectrum at mid and high latitudes. J. Geophys. Res. Oceans 107 (C11), 3207.10.1029/2001JC001210Google Scholar
Johnston, T. M. S., Rudnick, D. L., Carter, G. S., Todd, R. E. & Cole, S. T. 2011 Internal tidal beams and mixing near Monterey Bay. J. Geophys. Res. 116, C03017.10.1029/2010JC006592Google Scholar
Karimi, H. H. & Akylas, T. R. 2014 Parametric subharmonic instability of internal waves: locally confined beams versus monochromatic wavetrains. J. Fluid Mech. 757, 381–402.10.1017/jfm.2014.509Google Scholar
Karimi, H. H. & Akylas, T. R. 2017 Near-inertial parametric subharmonic instability of internal wave beams. Phys. Rev. Fluids 2 (7), 074801.10.1103/PhysRevFluids.2.074801Google Scholar
Lamb, K. G. 2004 Nonlinear interaction among internal wave beams generated by tidal flow over supercritical topography. Geophys. Res. Lett. 31 (9), L09313.Google Scholar
Lighthill, M. J. 1978 Waves in Fluids. Cambridge University Press.Google Scholar
MacKinnon, J. A., Alford, M. H., Sun, O., Pinkel, R., Zhao, Z. & Klymak, J. 2013 Parametric subharmonic instability of the internal tide at 29 °N. J. Phys. Oceanogr. 43 (1), 17–28.10.1175/JPO-D-11-0108.1Google Scholar
MacKinnon, J. A. & Winters, K. B. 2005 Subtropical catastrophe: Significant loss of low-mode tidal energy at 28. 9° . Geophys. Res. Lett. 32 (15), L15605.Google Scholar
Peacock, T., Echeverri, P. & Balmforth, N. J. 2008 An experimental investigation of internal tide generation by two-dimensional topography. J. Phys. Oceanogr. 38 (1), 235–242.Google Scholar
Richet, O., Muller, C. & Chomaz, J.-M. 2017 Impact of a mean current on the internal tide energy dissipation at the critical latitude. J. Phys. Oceanogr. 47 (6), 1457–1472.10.1175/JPO-D-16-0197.1Google Scholar
Sonmor, L. J. & Klaassen, G. P. 1997 Toward a unified theory of gravity wave stability. J. Atmos. Sci. 54 (22), 2655–2680.10.1175/1520-0469(1997)054<2655:TAUTOG>2.0.CO;22.0.CO;2>Google Scholar
Staquet, C. & Sommeria, J. 2002 Internal gravity waves: from instabilities to turbulence. Annu. Rev. Fluid Mech. 34 (1), 559–593.10.1146/annurev.fluid.34.090601.130953Google Scholar
Sutherland, B. R. 2013 The wave instability pathway to turbulence. J. Fluid Mech. 724, 1–4.10.1017/jfm.2013.149Google Scholar
Tabaei, A. & Akylas, T. R. 2003 Nonlinear internal gravity wave beams. J. Fluid Mech. 482, 141–161.10.1017/S0022112003003902Google Scholar
Young, W. R., Tsang, Y.-K. & Balmforth, N. J. 2008 Near-inertial parametric subharmonic instability. J. Fluid Mech. 607, 25–49.10.1017/S0022112008001742Google Scholar