Three-dimensional Marangoni-Benard flows in square and nearly square containers

Numerical continuation is used to follow branches of steady solutions to th e three-dimensional Marangoni-Benard problem in a zero gravity environment. The upper surface of the fluid is heated by a constant heat flux while the bottom is maintained at a constant temperature. Instability arises due to temperature-dependent surface tension effects but surface deflection is ign ored. Containers with square and nearly square cross sections and no-slip b oundary conditions are analyzed, and the results interpreted in terms of pr edictions from equivariant bifurcation theory. (C) 2001 American Institute of Physics.