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A three-component model for the coupled evolution of near-inertial waves, quasi-geostrophic flow and the near-inertial second harmonic

Published online by Cambridge University Press:  10 August 2016

G. L. Wagner Open the ORCID record for G. L. Wagner [Opens in a new window]  and
W. R. Young
G. L. Wagner*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA 90293-0411, USA
W. R. Young
Affiliation:
Scripps Institution of Oceanography, University of California San Diego, La Jolla, CA 90293-0213, USA
*
†Email address for correspondence: glwagner@ucsd.edu
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Abstract

We derive an asymptotic model that describes the nonlinear coupled evolution of (i) near-inertial waves (NIWs), (ii) balanced quasi-geostrophic flow and (iii) near-inertial second harmonic waves with frequency near $2f_{0}$ , where $f_{0}$ is the local inertial frequency. This ‘three-component’ model extends the two-component model derived by Xie & Vanneste (J. Fluid Mech., vol. 774, 2015, pp. 143–169) to include interactions between near-inertial and $2f_{0}$ waves. Both models possess two conservation laws which together imply that oceanic NIWs forced by winds, tides or flow over bathymetry can extract energy from quasi-geostrophic flows. A second and separate implication of the three-component model is that quasi-geostrophic flow catalyses a loss of NIW energy to freely propagating waves with near- $2f_{0}$ frequency that propagate rapidly to depth and transfer energy back to the NIW field at very small vertical scales. The upshot of near- $2f_{0}$ generation is a two-step mechanism whereby quasi-geostrophic flow catalyses a nonlinear transfer of near-inertial energy to the small scales of wave breaking and diapycnal mixing. A comparison of numerical solutions with both Boussinesq and three-component models for a two-dimensional initial value problem reveals strengths and weaknesses of the model while demonstrating the extraction of quasi-geostrophic energy and production of small vertical scales.

JFM classification

Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Ocean processes Geophysical and Geological Flows: Quasi-geostrophic flows

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Papers
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Journal of Fluid Mechanics , Volume 802 , 10 September 2016 , pp. 806 - 837
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© 2016 Cambridge University Press 

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