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Critical reflection and abyssal trapping of near-inertial waves on a β-plane

Published online by Cambridge University Press:  28 September 2011

Kraig B. Winters ,
Pascale Bouruet-Aubertot  and
Theo Gerkema
Kraig B. Winters*
Affiliation:
Scripps Institution of Oceanography, Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA 92093-0209, USA
Pascale Bouruet-Aubertot
Affiliation:
Laboratoire d’océanographie et du climat: expérimentation et approches numériques, UPMC/CRNS, BP 100, 4 place Jussieu, 75252 Paris CEDEX 05, France
Theo Gerkema
Affiliation:
Royal Netherlands Institute for Sea Research, NL-1790 AB Den Burg (Texel), The Netherlands
*
†Email address for correspondence: kraig@coast.ucsd.edu
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Abstract

We consider near-inertial waves continuously excited by a localized source and their subsequent radiation and evolution on a two-dimensional -plane. Numerical simulations are used to quantify the wave propagation and the energy flux in a realistically stratified ocean basin. We focus on the dynamics near and poleward of the inertial latitude where the local value of the Coriolis parameter matches the forcing frequency , contrasting the behaviour of waves under the traditional approximation (TA), where only the component of the Earth’s rotation aligned with gravity is retained in the dynamics, with that obtained under the non-traditional approach (non-TA) in which the horizontal component of rotation is retained. Under the TA, assuming inviscid linear wave propagation in the WKB limit, all energy radiated from the source eventually propagates toward the equator, with the initially poleward propagation being internally reflected at the inertial latitude. Under the non-TA however, these waves propagate sub-inertially beyond their inertial latitude, exhibiting multiple reflections between internal turning points that lie poleward of the inertial latitude and the bottom. The numerical experiments complement and extend existing theory by relaxing the linearity and WKB approximations, and by illustrating the time development of the steadily forced flow and the spatial patterns of energy flux and flux divergence. The flux divergence of the flow at both the forcing frequency and its first harmonic reveal the spatial patterns of nonlinear energy transfer and highlight the importance of nonlinearity in the vicinity of near-critical bottom reflection at the inertial latitude of the forced waves.

JFM classification

Geophysical and Geological Flows: Ocean processes Geophysical and Geological Flows: Stratified flows Geophysical and Geological Flows: Waves in rotating fluids
Type
Papers
Information
Journal of Fluid Mechanics , Volume 684 , 10 October 2011 , pp. 111 - 136
Copyright
Copyright © Cambridge University Press 2011

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