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

TitleAn asymptotic model for the propagation of oceanic internal tides through quasi-geostrophic flow
Publication TypeJournal Article
Year of Publication2017
AuthorsWagner G.L, Ferrando G., Young W.R
JournalJournal of Fluid Mechanics
Volume828
Pagination779-811
Date Published2017/10
Type of ArticleArticle
ISBN Number0022-1120
Accession NumberWOS:000410524800006
Keywordsdissipation; gravity-waves; hawaiian ridge; internal waves; mean flow; near-inertial waves; ocean processes; Potential vorticity; tidal energy; turbulence; water; Wave scattering
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.

DOI10.1017/jfm.2017.509
Short TitleJ. Fluid Mech.
Student Publication: 
No