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Nonlinear dynamics of forced baroclinic critical layers

Published online by Cambridge University Press:  25 November 2019

Chen Wang Open the ORCID record for Chen Wang [Opens in a new window]  and
Neil J. Balmforth Open the ORCID record for Neil J. Balmforth [Opens in a new window]
Chen Wang*
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada
Neil J. Balmforth
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada
*
†Email address for correspondence: chenwang@math.ubc.ca
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Abstract

In this paper, we study the forcing of baroclinic critical levels, which arise in stratified fluids with horizontal shear flow along the surfaces where the phase speed of a wave relative to the mean flow matches a natural internal wave speed. Linear theory predicts the baroclinic critical-layer dynamics is similar to that of a classical critical layer, characterized by the secular growth of flow perturbations over a region of decreasing width. By using matched asymptotic expansions, we construct a nonlinear baroclinic critical layer theory to study how the flow perturbations evolve once they enter the nonlinear regime. A key feature of the theory is that, because the location of the baroclinic critical layer is determined by the streamwise wavenumber, the nonlinear dynamics filters out harmonics and the modification to the mean flow controls the evolution. At late times, we show that the vorticity begins to focus into yet smaller regions whose width decreases exponentially with time, and that the addition of dissipative effects can arrest this focussing to create a drifting coherent structure. Jet-like defects in the mean horizontal velocity are the main outcome of the critical-layer dynamics.

JFM classification

Waves/Free-surface Flows: Critical layers Geophysical and Geological Flows: Stratified flows Geophysical and Geological Flows: Internal waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 883 , 25 January 2020 , A12
Copyright
© 2019 Cambridge University Press

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