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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., Carpenter, P. W., 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. doi:10.1017/S0022112008005545 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 |
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| Divisions: | Faculty of Science, Engineering and Medicine > Engineering > 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 | ||||
| Official Date: | April 2009 | ||||
| Dates: |
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| Volume: | Vol.625 | ||||
| Page Range: | pp. 1-46 | ||||
| DOI: | 10.1017/S0022112008005545 | ||||
| Status: | Peer Reviewed | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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