Convective Patterns in Horizontal Flow

PACS. 47.25Q- Convection and heat transfer. PACS. 47.60- Flows in ducts, channels, and conduits. Abstract.- Rayleigh-BBnard convection in the presence of a horizontal throughflow perpen-dicular to the convective roll chain is investigated with a Id amplitude equation and with a 2d numerical simulation of the basic hydrodynamic equations. Results agree very well with each other. The flow leads to propagating convective patterns in the form of travelling wave states which for increasing flow are localized further and further downstream. Unique wave number selection is observed. Related experiments are discussed. An interesting pattern forming nonlinear system is the Rayleigh-B6nard problem subject to a lateral throughflow [l]. Here we report how the stationary convective roll chain in this system is changed when a lateral flow is imposed perpendicular to the roll axes, say in a long narrow channel heated from below. Then the onset of convection is delayed [l] and, more importantly, it becomes oscillatory with a forward Hopf bifurcation to a stable travelling wave (TW) state where the roll pattern propagates downstream. Hopf frequency, phase velocity, and group velocity grow for small flow rates linearly with the associated Reynolds