Exact solutions of Rayleigh's equation and sufficient conditions for inviscid instability of parallel, bounded shear flows 13; 13;

Srinivasan, Radhakrishnan (1994) Exact solutions of Rayleigh's equation and sufficient conditions for inviscid instability of parallel, bounded shear flows 13; 13;. Zeitschrift fuer angewandte Mathematik und Physik, 45 (4). pp. 615-637. ISSN 0044-2275

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Abstract

Sufficient conditions are obtained for the inviscid instability of a general class of plane parallel shear flows. First, Rayleigh's equation is converted into a nonlinear integral equation for the basic velocity profile, and sufficient conditions are then deduced for the existence and uniqueness of solutions to this integral equation, subject to appropriate homogeneous boundary conditions on the eigenfunction theta(y). The velocity profiles U(y) so derived are guaranteed to be unstable. The paper also describes a method for obtaining a general class of new exact neutrally stable solutions of Rayleigh's equation. An example is presented of a class of neutrally stable solutions for jetlike profiles on an unbounded domain.

Item Type: Journal Article
Uncontrolled Keywords: Shear flow;Parallel flow;Flow stability;Invicid flow;Rayleigh equations;Fluid boundaries;Existence theorems;uniqueness theorem;velocity distribution
Subjects: ENGINEERING > Fluid Mechanics and Thermodynamics
Division/Department: National Trisonic Aerodynamic Facility
Depositing User: M/S ICAST NAL
Date Deposited: 05 Oct 2006
Last Modified: 24 May 2010 09:51
URI: http://nal-ir.nal.res.in/id/eprint/2872

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