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

Citation:
Wagner, GL, Young WR.  2016.  A three-component model for the coupled evolution of near-inertial waves, quasi-geostrophic flow and the near-inertial second harmonic. Journal of Fluid Mechanics. 802:806-837.

Date Published:

2016/09

Keywords:

deep-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.

Notes:

n/a

Website

DOI:

10.1017/jfm.2016.487