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

• Published in: Journal of fluid mechanics Vol. 625; pp. 1 - 46
• Main Authors: SEN, P. K., CARPENTER, P. W., HEGDE, S., DAVIES, C.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 25.04.2009
• Subjects: Exact sciences and technology; Fluid dynamics; Fluid mechanics; Fundamental areas of phenomenology (including applications); Kinetic energy; Physics; Theory; Transition to turbulence; Turbulent flows, convection, and heat transfer; Cut off frequency; Rigid wall; Wave propagation; Compliance; Tollmien Schlichting wave; Vorticity; Theoretical study; Flexible wall; Turbulent laminar transition
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/S0022112008005545

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.