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The vibrating ribbon problem revisited

Published online by Cambridge University Press:  26 April 2006

David E. Ashpis  and
Eli Reshotko
David E. Ashpis
Affiliation:
NASA Lewis Research Center, Cleveland, OH 44135. USA
Eli Reshotko
Affiliation:
Department of Mechanical and Aerospace Engineering, Case Western Reserve University, Cleveland, OH 44106, USA
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Abstract

A revised formal solution of the vibrating ribbon problem of hydrodynamic stability is presented. The initial formulation of Gaster (1965) is modified by application of the Briggs method and a careful treatment of the complex double Fourier transform inversions. Expressions are obtained in a natural way for the discrete spectrum as well as for the four branches of the continuous spectra. These correspond to discrete and branch-cut singularities in the complex wavenumber plane. The solutions from the continuous spectra decay both upstream and downstream of the ribbon, with the decay in the upstream direction being much more rapid than that in the downstream direction. Comments and clarification of related prior work are made.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 213 , April 1990 , pp. 531 - 547
Copyright
© 1990 Cambridge University Press

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