Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-02T18:58:12.330Z Has data issue: false hasContentIssue false

On the concentration of near-inertial waves in anticyclones

Published online by Cambridge University Press:  14 May 2015

Eric Danioux*
Affiliation:
School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh, EH9 3FD, UK
Jacques Vanneste
Affiliation:
School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh, EH9 3FD, UK
Oliver Bühler
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
*
Email address for correspondence: [email protected]

Abstract

An overlooked conservation law for near-inertial waves (NIWs) propagating in a steady background flow provides a new perspective on the concentration of these waves in regions of anticyclonic vorticity. The conservation law implies that this concentration is a direct consequence of the decrease in spatial scales experienced by an initially homogeneous wave field. Scaling arguments and numerical simulations of a reduced-gravity model of mixed-layer NIWs confirm this interpretation and elucidate the influence of the strength of the background flow relative to the dispersion.

Type
Rapids
Copyright
© 2015 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

Balmforth, N. J., Llewellyn Smith, S. G. & Young, W. R. 1998 Enhanced dispersion of near-inertial waves in an idealized geostrophic flow. J. Mar. Res. 56, 140.CrossRefGoogle Scholar
Cotter, C. J. & Reich, S. 2004 Adiabatic invariance and applications: from molecular dynamics to numerical weather prediction. BIT 44, 439455.Google Scholar
Cushman-Roisin, B. 1994 Introduction to Geophysical Fluid Dynamics. Prentice-Hall.Google Scholar
Danioux, E., Klein, P. & Rivière, P. 2008 Propagation of wind energy into the deep ocean through a fully turbulent mesoscale eddy field. J. Phys. Oceanogr. 38, 22242241.Google Scholar
Elipot, S., Lumpkin, R. & Prieto, G. 2010 Modification of inertial oscillations by the mesoscale eddy field. J. Geophys. Res. 115, C09010.Google Scholar
Falkovich, G., Kuznetsov, E. & Medvedev, S. 1994 Nonlinear interaction between long inertio-gravity waves and Rossby waves. Nonlinear Process. Geophys. 1, 168171.Google Scholar
Ferrari, R. & Wunsch, C. 2009 Ocean circulation kinetic energy: reservoirs, sources, and sinks. Annu. Rev. Fluid Mech. 41, 253282.Google Scholar
Granata, T., Wiggert, J. & Dickey, T. 1995 Trapped, near-inertial waves and enhanced chlorophyll distributions. J. Geophys. Res. 100 (C10), 2079320804.Google Scholar
Joyce, T. M., Toole, J. M., Klein, P. & Thomas, L. N. 2013 A near-inertial mode observed within a Gulf Stream warm-core ring. J. Geophys. Res. 118, 17971806.CrossRefGoogle Scholar
Klein, P., Llewellyn Smith, S. G. & Lapeyre, G. 2004 Organization of near-inertial energy by an eddy field. Q. J. R. Meteorol. Soc. 130, 11531166.Google Scholar
Kunze, E. 1985 Near-inertial wave propagation in geostrophic shear. J. Phys. Oceanogr. 15, 544565.Google Scholar
Kunze, E. & Sanford, T. B. 1984 Observations of near-inertial waves in a front. J. Phys. Oceanogr. 14, 566581.Google Scholar
Lee, D.-K. & Niiler, P. P. 1998 The inertial chimney: the near-inertial energy drainage from the ocean surface to the deep layer. J. Geophys. Res. 103 (C4), 75797591.Google Scholar
Llewellyn Smith, S. G. 1999 Near-inertial oscillations of a barotropic vortex: trapped modes and time evolution. J. Phys. Oceanogr. 29, 747761.Google Scholar
Reznik, G. M., Zeitlin, V. & Ben Jelloul, M. 2001 Nonlinear theory of geostrophic adjustment. Part 1. Rotating shallow-water model. J. Fluid Mech. 445, 93120.Google Scholar
Xie, J.-H. & Vanneste, J. 2015 A generalised-Lagrangian-mean model of the interactions between near-inertial waves and mean flow. J. Fluid Mech. (in press).Google Scholar
Young, W. R. & Ben Jelloul, M. 1997 Propagation of near-inertial oscillations through a geostrophic flow. J. Mar. Res. 55, 735766.Google Scholar
Zhai, X., Greatbach, R. J. & Zhao, J. 2005 Enhanced vertical propagation of storm-induced near-inertial energy in an eddying ocean channel model. Geophys. Res. Lett. 32, L18602.Google Scholar