Accession Number : AD0253030

Title :   NONLINEAR EFFECTS IN THERMAL CONVECTION

Corporate Author : BROWN UNIV PROVIDENCE RI

Personal Author(s) : BISSHOPP, F.E.

Report Date : MAR 1961

Pagination or Media Count : 1

Abstract : The nonlinear equations governing thermally induced convective motions in a plane liquid layer are examined. Under the assumption that steady motions take place within an array of closed cells which are characterized by a single wavenumber, formal solutions of the governing equations can be generated by means of regular perturbation theory. The perturbation theory is carried to second order in a quantity A which is essentially the maximum vertical velocity of the fluid, and formal expressions, applicable for any combination of rigid and free bounding planes, for corrections to the solutions predicted by the linearized equations are given. Explicit evaluations of the corrections are carried out in the simple case where both bounding planes are free, and an investigation of the stability of the resulting solutions is made. Modes of motion described by wave-numbers in a neighborhood of the one initially assumed are excited, regardless of how the initial wave-number was chosen. The apparent contradiction indicates that a Fourier analysis of finite-amplitude convective motions should include a continuous spectrum of wavenumbers. (Author)

Descriptors :   *CONVECTION, *HEAT, FOURIER ANALYSIS, LIQUIDS, PERTURBATION THEORY.

Distribution Statement : APPROVED FOR PUBLIC RELEASE