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Interfacial progressive gravity waves in a two-layer shear flow

Pullin, D. I. and Grimshaw, R. H. J. (1983) Interfacial progressive gravity waves in a two-layer shear flow. Physics of Fluids, 26 (7). pp. 1731-1739. ISSN 0031-9171. doi:10.1063/1.864372.

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Nonlinear interfacial gravity waves in a two-layer Boussinesq fluid are studied. In a previous paper, nonlinear waves on a vortex sheet separating two layers, each of constant density and velocity were considered. In the present paper the basic flow model consists of a constant vorticity upper layer bounded by a rigid surface and an irrotational lower layer of infinite depth with continuity of the unperturbed velocity at the density interface. Numerical solutions obtained from an exact formulation in terms of a complex-valued integral equation for the shape and local vortex-sheet strength of the wave profile are compared with results from a second-order Stokes expansion. It is found that the wave of maximum amplitude displays different geometrical features depending on the unperturbed flow parameters. These include waves containing an S-shaped section, waves with cusped crests and surface-constrained waves with long flat crests. Wave integral properties calculated, including the flux of momentum and energy in the wave propagation direction, showed monotonic variation with increasing wave amplitude.

Item Type:Article
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Additional Information:Copyright © 1983 American Institute of Physics (Received 15 November 1982; accepted 23 March 1983)
Subject Keywords:interfaces; gravity waves; nonlinear problems; boussinesq equations; fluids; layers; shear; vortices; density; velocity; fluid flow; numerical solution; integral equations; shape; stratification; flow models
Issue or Number:7
Record Number:CaltechAUTHORS:PULpof83b
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4673
Deposited By: Archive Administrator
Deposited On:02 Sep 2006
Last Modified:08 Nov 2021 20:19

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