A selection principle in Benardtype convection
Abstract
In a Benardtype convection problem, the stationary flows of an infinite layer of fluid lying between two rigid horizontal walls and heated uniformly from below are determined. As the temperature difference across the layer increases beyond a certain value, other convective motions appear. These motions areoften cellular in character in that their streamlines are confined to certain welldefined cells having, for example, the shape of rolls or hexagons. A selection principle that explains why hexagonal cells seem to be preferred for certain ranges of the parameters is formulated. An operatortheoretical formulation of one generalized Bernard problem is given. The infinite dimensional problem is reduced to one of solving a finite dimensional system of equations, namely, the selection equations. These equations are solved and a linearized stability analysis of the resultant stationary flows is presented.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 1983
 Bibcode:
 1983STIN...8431559K
 Keywords:

 Benard Cells;
 Computational Fluid Dynamics;
 Convection;
 Laminar Flow;
 Boussinesq Approximation;
 Liapunov Functions;
 Temperature Gradients;
 Theorems;
 Fluid Mechanics and Heat Transfer