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Title: Long ring waves in a stratified fluid over a shear flow
Authors: Khusnutdinova, Karima R.
Zhang, Xizheng
Keywords: Geophysical and geological flows
Internal waves
Stratified flows
Issue Date: 2016
Publisher: © Cambridge University Press
Citation: KHUSNUTDINOVA, K.R. and ZHANG, X., 2016. Long ring waves in a stratified fluid over a shear flow. Journal of Fluid Mechanics, 794, pp.17-44.
Abstract: Oceanic waves registered by satellite observations often have curvilinear fronts and propagate over various currents. In this paper we study long linear and weakly nonlinear ring waves in a stratified fluid in the presence of a depth-dependent horizontal shear flow. It is shown that, despite the clashing geometries of the waves and the shear flow, there exists a linear modal decomposition (different from the known decomposition in Cartesian geometry), which can be used to describe distortion of the wavefronts of surface and internal waves, and systematically derive a $2+1$2+1-dimensional cylindrical Korteweg–de Vries-type equation for the amplitudes of the waves. The general theory is applied to the case of the waves in a two-layer fluid with a piecewise-constant current, with an emphasis on the effect of the shear flow on the geometry of the wavefronts. The distortion of the wavefronts is described by the singular solution (envelope of the general solution) of the nonlinear first-order differential equation, constituting generalisation of the dispersion relation in this curvilinear geometry. There exists a striking difference in the shapes of the wavefronts of surface and interfacial waves propagating over the same shear flow.
Description: This paper was accepted for publication in the journal Journal of Fluid Mechanics and the definitive published version is available at http://dx.doi.org/10.1017/jfm.2016.147
Version: Accepted for publication
DOI: 10.1017/jfm.2016.147
URI: https://dspace.lboro.ac.uk/2134/21018
Publisher Link: http://dx.doi.org/10.1017/jfm.2016.147
ISSN: 0022-1120
Appears in Collections:Published Articles (Maths)

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