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 (non-self-ajoint) perturbations of norm epsilon to real self-adjoint 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 time-dependent 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 waves--whether 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