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

TitleA three-component model for the coupled evolution of near-inertial waves, quasi-geostrophic flow and the near-inertial second harmonic
Publication TypeJournal Article
Year of Publication2016
AuthorsWagner G.L, Young W.R
JournalJournal of Fluid Mechanics
Volume802
Pagination806-837
Date Published2016/09
Type of ArticleArticle
ISBN Number0022-1120
Accession NumberWOS:000390097200006
Keywordsdeep-ocean; dispersion; energy; internal waves; layer; mesoscale eddy field; ocean processes; oscillations; propagation; quasi-geostrophic flows
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 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.

DOI10.1017/jfm.2016.487
Short TitleJ. Fluid Mech.
Student Publication: 
No
Research Topics: 
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