THE NONLINEAR INTERACTION OF TWO DISTURBANCES IN THE THERMAL CONVECTION PROBLEM

Abstract

In the thermal convection problem with free boundaries, the interaction of two roll disturbances is considered. The problem is reduced to a pair of nonlinear ordinary differential equations, which should also provide a model for the interaction of two disturbances in more general situations than that for which these equations have been derived. The equations contain several parameters which necessitates a discussion of several possible types of solution. Under certain circumstances, an equilibrium state may be composed of a mixture of a linearly stable disturbance and a linearly unstable disturbance. For the thermal convection problem, when the Rayleigh number is slightly above the minimum critical value, the equilibrium state will contain only one of two linearly unstable disturbances. Results are compared with experimental observations. (Author)

Document Details

Document Type
Technical Report
Publication Date
Feb 20, 1962
Accession Number
AD0274779

Entities

People

  • Lee A. Segel

Organizations

  • Rensselaer Polytechnic Institute

Tags

DTIC Thesaurus Topics

  • Arrhenius Equation
  • Boundaries
  • Convection
  • Differential Equations
  • Equations
  • Mathematics
  • Observation

Fields of Study

  • Mathematics

Readers

  • Control Systems Engineering.
  • Fluid Dynamics.