Skip to main content Accessibility help
×
Home

Variational treatment of inertia–gravity waves interacting with a quasi-geostrophic mean flow

  • Rick Salmon (a1)

Abstract

The equations for three-dimensional hydrostatic Boussinesq dynamics are equivalent to a variational principle that is closely analogous to the variational principle for classical electrodynamics. Inertia–gravity waves are analogous to electromagnetic waves, and available potential vorticity (i.e. the amount by which the potential vorticity exceeds the potential vorticity of the rest state) is analogous to electric charge. The Lagrangian can be expressed as the sum of three parts. The first part corresponds to quasi-geostrophic dynamics in the absence of inertia–gravity waves. The second part corresponds to inertia–gravity waves in the absence of quasi-geostrophic flow. The third part represents a coupling between the inertia–gravity waves and quasi-geostrophic motion. This formulation provides the basis for a general theory of inertia–gravity waves interacting with a quasi-geostrophic mean flow.

Copyright

Corresponding author

Email address for correspondence: rsalmon@ucsd.edu

References

Hide All
Bretherton, F. P. 1969 On the mean motion induced by internal gravity waves. J. Fluid Mech. 36, 785803.
Bühler, O. & McIntyre, M. E. 1998 On non-dissipative wave–mean interactions in the atmosphere or oceans. J. Fluid Mech. 354, 301343.
Bühler, O. & McIntyre, M. E. 2003 Remote recoil: a new wave–mean interaction effect. J. Fluid Mech. 492, 207230.
Bühler, O. & McIntyre, M. E. 2005 Wave capture and wave–vortex duality. J. Fluid Mech. 534, 6795.
Landau, L. D. & Lifshitz, E. M. 1975 The Classical Theory of Fields. Pergamon.
McIntyre, M. E. & Norton, W. A. 2000 Potential vorticity inversion on a hemisphere. J. Atmos. Sci. 57, 12141235.
Salmon, R. 1998 Lectures on Geophysical Fluid Dynamics. Oxford University Press.
Salmon, R. 2014 Analogous formulation of electrodynamics and two-dimensional fluid dynamics. J. Fluid Mech. 761, R2, 1–12.
Wagner, G. L. & Young, W. R. 2015 Available potential vorticity and wave-averaged quasi-geostrophic flow. J. Fluid Mech. 785, 401424.
Wheeler, J. A. & Feynman, R. P. 1949 Classical electrodynamics in terms of direct interparticle action. Rev. Mod. Phys. 21 (3), 425433.
Whitham, G. B. 1965 A general approach to linear and nonlinear waves using a Lagrangian. J. Fluid Mech. 22, 273283.
Whitham, G. B. 1974 Linear and Nonlinear Waves. Wiley.
Xie, J.-H. & Vanneste, J. 2015 A generalized-Lagrangian-mean model of the interactions between near-inertial waves and mean flow. J. Fluid Mech. 774, 143169.
Young, W. R. 2012 An exact thickness-weighted average formulation of the Boussinesq equations. J. Phys. Oceanogr. 42, 692707.
Young, W. R. & Ben Jelloul, M. 1997 Propagation of near-inertial oscillations through a geostrophic flow. J. Mar. Res. 55, 735766.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Related content

Powered by UNSILO

Variational treatment of inertia–gravity waves interacting with a quasi-geostrophic mean flow

  • Rick Salmon (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.