ON THE PRINCIPLE OF EXCHANGE OF STABILITIES,

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)

Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1968
Accession Number
AD0680761

Entities

People

  • Stephen H. Davis

Organizations

  • RAND Corporation

Tags

DTIC Thesaurus Topics

  • Convection
  • Couette Flow
  • Eigenvalues
  • Equations
  • Equations Of State
  • Flow
  • Instability
  • Mathematics
  • Perturbations
  • Radiation
  • Traveling Waves
  • Waves

Fields of Study

  • Mathematics

Readers

  • Fluid Dynamics.
  • Linear Algebra