Abstract
This chapter reviews the generic problem of the propagation of vortical waves across junctions between one wave-bearing medium and another. Two simpler examples are considered first where the waves are not vortical, namely waves across junctions in elastic tubes and those between two spring-supported elastic plates. It is assumed that the eigensolutions are known for the corresponding spatially homogeneous problems. The task is how to determine the amplitudes of the reflected and transmitted waves given the amplitude of the incident wave. In general, there may be more than one incident, reflected or transmitted wave. It is shown how this sort of problem may be solved in terms of the homogeneous eigensolutions by drawing an analogy between the junction and a wave-driver. The particular problem studied is that of a Tollmien-Schlichting wave, propagating along a rigid-walled channel flow, that is incident on a section of the channel where the walls consist of compliant panels. It is shown how the wave system over the compliant panels and the amplitude of the Tollmien-Schlichting wave leaving the compliant section may be determined in terms of the incident wave. The techniques reviewed for this problem are considered to be generic.
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Carpenter, P.W., Sen, P.K. (2003). Propagation of Waves Across Junctions Between Rigid and Compliant Walls. In: Carpenter, P.W., Pedley, T.J. (eds) Flow Past Highly Compliant Boundaries and in Collapsible Tubes. Fluid Mechanics and Its Applications, vol 72. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0415-1_7
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DOI: https://doi.org/10.1007/978-94-017-0415-1_7
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