Wavy stripes and squares in zero-Prandtl-number convection

A simple model to explain the numerically observed behavior of chaotically varying stripes and square patterns in zero-Prandtl-number convection in Boussinesq fluid is presented. The nonlinear interaction of mutually perpendicular sets of wavy rolls, via higher-order modes, may lead to a competition between the two sets of rolls. The appearance of square patterns is due to a secondary forward bifurcation from a set of wavy rolls. The statistics of the spatially averaged energy signal shows a power-law behavior.