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An asymptotic model for the propagation of oceanic internal tides through quasi-geostrophic flow

Published online by Cambridge University Press:  12 September 2017

G. L. Wagner Open the ORCID record for G. L. Wagner [Opens in a new window] ,
G. Ferrando  and
W. R. Young Open the ORCID record for W. R. Young [Opens in a new window]
G. L. Wagner*
Affiliation:
Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139-4307, USA
G. Ferrando
Affiliation:
Département de Physique, Ecole Normale Supérieure, 24, rue Lhomond, 75005 Paris, France
W. R. Young
Affiliation:
Scripps Institution of Oceanography, University of California San Diego, La Jolla, CA 92093-0213, USA
*
†Email address for correspondence: glwagner@mit.edu
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Abstract

We derive a time-averaged ‘hydrostatic wave equation’ from the hydrostatic Boussinesq equations that describes the propagation of inertia–gravity internal waves through quasi-geostrophic flow. The derivation uses a multiple-scale asymptotic method to isolate wave field evolution over intervals much longer than a wave period, assumes the wave field has a well-defined non-inertial frequency such as that of the mid-latitude semi-diurnal lunar tide, assumes that the wave field and quasi-geostrophic flow have comparable spatial scales and neglects nonlinear wave–wave dynamics. As a result the hydrostatic wave equation is a reduced model applicable to the propagation of large-scale internal tides through the inhomogeneous and moving ocean. A numerical comparison with the linearized and hydrostatic Boussinesq equations demonstrates the validity of the hydrostatic wave equation model and illustrates how the model fails when the quasi-geostrophic flow is too strong and the wave frequency is too close to inertial. The hydrostatic wave equation provides a first step toward a coupled model for energy transfer between oceanic internal tides and quasi-geostrophic eddies and currents.

JFM classification

Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Ocean processes Waves/Free-surface Flows: Wave scattering
Type
Papers
Information
Journal of Fluid Mechanics , Volume 828 , 10 October 2017 , pp. 779 - 811
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Copyright
© 2017 Cambridge University Press 

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