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Kelvin-Helmholtz creeping flow at the interface between two viscous fluids


Forbes, LK and Paul, RA and Chen, MJ and Horsley, DE, Kelvin-Helmholtz creeping flow at the interface between two viscous fluids, The ANZIAM Journal, 56, (4) pp. 317-358. ISSN 1446-1811 (2015) [Refereed Article]

Copyright Statement

Copyright 2015 Australian Mathematical Society

DOI: doi:10.1017/S1446181115000085


The Kelvin–Helmholtz flow is a shearing instability that occurs at the interface between two fluids moving with different speeds. Here, the two fluids are each of finite depth, but are highly viscous. Consequently, their motion is caused by the horizontal speeds of the two walls above and below each fluid layer. The motion of the fluids is assumed to be governed by the Stokes approximation for slow viscous flow, and the fluid motion is thus responsible for movement of the interface between them. A linearized solution is presented, from which the decay rate and the group speed of the wave system may be obtained. The nonlinear equations are solved using a novel spectral representation for the streamfunctions in each of the two fluid layers, and the exact boundary conditions are applied at the unknown interface location. Results are presented for the wave profiles, and the behaviour of the curvature of the interface is discussed. These results are compared to the Boussinesq–Stokes approximation which is also solved by a novel spectral technique, and agreement between the results supports the numerical calculations.

Item Details

Item Type:Refereed Article
Keywords:interfacial flow, viscous fluids, curvature singularity, Kelvin-Helmholtz instability, interface, spectral representation, Stokes flow
Research Division:Mathematical Sciences
Research Group:Applied mathematics
Research Field:Theoretical and applied mechanics
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Forbes, LK (Professor Larry Forbes)
UTAS Author:Paul, RA (Dr Rhys Paul)
UTAS Author:Chen, MJ (Mr Michael Chen)
UTAS Author:Horsley, DE (Dr David Horsley)
ID Code:106703
Year Published:2015
Funding Support:Australian Research Council (DP140100094)
Web of Science® Times Cited:6
Deposited By:Mathematics and Physics
Deposited On:2016-02-17
Last Modified:2017-11-01

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