Accession Number:

AD0680761

Title:

ON THE PRINCIPLE OF EXCHANGE OF STABILITIES,

Descriptive Note:

Corporate Author:

RAND CORP SANTA MONICA CALIF

Personal Author(s):

Report Date:

1968-12-01

Pagination or Media Count:

57.0

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

Subject Categories:

  • Meteorology
  • Theoretical Mathematics
  • Fluid Mechanics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE