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A wave driver theory for vortical waves propagating across junctions with application to those between rigid and compliant walls

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Sen, P. K., Ph.D., Carpenter, P. W. (Peter William), 1942-, Hedge, S. R. and Davies, Christopher. (2009) A wave driver theory for vortical waves propagating across junctions with application to those between rigid and compliant walls. Journal of Fluid Mechanics, Vol.625 . pp. 1-46. ISSN 0022-1120

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Official URL: http://dx.doi.org/10.1017/S0022112008005545

Abstract

A theory is described for propagation of vortical waves across alternate rigid and compliant panels. The structure in the fluid side at the junction of panels is a highly vortical narrow viscous structure which is idealized as a wave driver. The wave driver is modelled as a ‘half source cum half sink’. The incoming wave terminates into this structure and the outgoing wave emanates from it. The model is described by half Fourier–Laplace transforms respectively for the upstream and downstream sides of the junction. The cases below cutoff and above cutoff frequencies are studied. The theory completely reproduces the direct numerical simulation results of Davies & Carpenter (J. Fluid Mech., vol. 335, 1997, p. 361). Particularly, the jumps across the junction in the kinetic energy integral, the vorticity integral and other related quantities as obtained in the work of Davies & Carpenter are completely reproduced. Also, some important new concepts emerge, notable amongst which is the concept of the pseudo group velocity.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Divisions:	Faculty of Science > Engineering
Library of Congress Subject Headings (LCSH):	Vortex-motion -- Research, Wave-motion, Theory of, Laplace transformation, Fourier transformations, Fluid dynamics
Journal or Publication Title:	Journal of Fluid Mechanics
Publisher:	Cambridge University Press
ISSN:	0022-1120
Date:	April 2009
Volume:	Vol.625
Page Range:	pp. 1-46
Identification Number:	10.1017/S0022112008005545
Status:	Peer Reviewed
Access rights to Published version:	Restricted or Subscription Access
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URI:	http://wrap.warwick.ac.uk/id/eprint/2576