
Accession Number : AD0680761
Title : ON THE PRINCIPLE OF EXCHANGE OF STABILITIES,
Corporate Author : RAND CORP SANTA MONICA CALIF
Personal Author(s) : Davis,Stephen H.
Report Date : DEC 1968
Pagination or Media Count : 57
Abstract : Proof is given of a perturbation theorem: A class of real, bounded (nonselfajoint) perturbations of norm epsilon to real selfadjoint operators preserves the reality of the simple eigenvalues for epsilon sufficiently small. A bound is obtained on epsilon. Application is made to Benard convection with constant heat sources, radiation, particular timedependent profiles, variable fluid properties, and nonlinear equations of state, and to instability of circular Couette flow for a range of gap widths. In each case the growth rate is the eigenvalue, and hence if epsilon is less than the critical value, traveling waveswhether growing or decaying are forbidden. (Author)
Descriptors : (*PARTIAL DIFFERENTIAL EQUATIONS, *PERTURBATION THEORY), (*ATMOSPHERIC MOTION, HEAT TRANSFER), (*COUETTE FLOW, STABILITY), NAVIER STOKES EQUATIONS, EQUATIONS OF STATE, MATRICES(MATHEMATICS), NUMERICAL ANALYSIS, CONVECTION(HEAT TRANSFER), THERMAL RADIATION, THEOREMS
Subject Categories : Meteorology
Theoretical Mathematics
Fluid Mechanics
Distribution Statement : APPROVED FOR PUBLIC RELEASE