Excitation of Continuous and Discrete Modes in Incompressible Boundary Layers

  • David E. Ashpis


This report documents the full details of the condensed journal article by Ashpis & l_eshotko (JFM, 1990) entitled "The Vibrating Ribbon Problem Revisited". A revised formal solution of the vibrating ribbon problem of hydrodynamic stability is presented. The initial formulation of Gaster (JFM, 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 wave-number 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. • Preface This report documents the full details of the concise article entitled "The Vibrating Ribbon Problem Revisted" by Ashpis & Reshotko which appeared in the Journal of Fluid Mechanics (1990), vol. 213, pp. 531-547. This report constitutes the full manuscript that was originally submitted for publication, but had to be shortened and condensed due to space limitations. It is based on Ashpis & Reshotko (1986), a work principally supported by the US Air Force Office of Scientific Research. The present report was written after the first author joined NASA. Some typographical errors of the prior work were corrected and comments of the journal reviewers were implemented. There has been recently renewed interest in the continuous spectrum in context of its relationship to the new concepts of transient growth in hydrodynamic stability theory and its role in receptivity to freestream disturbances. Therefore it was felt that the details and the structure of this report make its documentation in form of a NASA report a valuable complement to the journal article and an accessible text to non-specialists.

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Cite this paper

@inproceedings{AshpisExcitationOC, title={Excitation of Continuous and Discrete Modes in Incompressible Boundary Layers}, author={David E. Ashpis} }