Zero-Prandtl-number convection

Abstract

The zero-Prandtl-number limit of the Oberbeck—Boussinesq equations is compared to small-Prandtl-number Rayleigh—Bénard convection through numerical simulations. Both no-slip and free-slip boundary conditions, imposed at the top and bottom of a small-aspect-ratio, horizontally periodic box are considered. A rich variety of regimes is observed as the Rayleigh number is increased: supercritical oscillatory instabilities for various values of the aspect ratios, competition between two-dimensional rolls, squares and hexagonal patterns, competition between travelling and standing waves, transition to chaos, and scalings laws for the first Rayleigh-number decade. This multiplicity of regimes can be attributed to the close interaction between the stationary and oscillatory instabilities at zero Prandtl number.