Exact solutions of Rayleigh's equation and sufficient conditions for inviscid instability of parallel, bounded shear flows
type: Item
instance of: scholarly article
title: Exact solutions of Rayleigh's equation and sufficient conditions for inviscid instability of parallel, bounded shear flows
zbMATH Open document ID: 0819.76027
DOI: 10.1007/BF00991900
author: Radhakrishnan Srinivasan
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1994-11-20T00:00:00Z
review text: The object is to specify sufficient conditions for the inviscid instability of a general class of plane parallel flows. For a given complex eigenvalue and a real wave number, and for the real part of the adjoint eigenfunction, the Rayleigh's equation is converted into a nonlinear integral equation, if the basic velocity profile \(U(y)\) is given. Then the author deduces sufficient conditions for the existence and uniqueness of solution to this integral equation (for homogeneous boundary conditions) and shows that the velocity is unstable. Again, a method is given to obtain a general class of new exact neutrally stable solutions of the Rayleigh's equation for a given complex eigenvalue, a real wave number, and a function \(U(y)\). The paper is of theoretical nature.
reviewed by: V. M. Soundalgekar
Mathematics Subject Classification ID: 76E05
zbMATH DE Number: 690942
zbMATH Keywords: complex eigenvalue
zbMATH Keywords: adjoint eigenfunction
zbMATH Keywords: nonlinear integral equation
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
MaRDI profile type: Publication
cites work: On the linear stability of inviscid incompressible plane parallel flow
cites work: Note on a paper of John W. Miles
cites work: Q3230984
cites work: Necessary and Sufficient Condition for the Stability of Plane Parallel Inviscid Flow
description: scientific article; zbMATH DE number 690942