Pattern Selection in Rayleigh-Bénard Convection near Threshold

A correct long-wavelength theory for convection near onset with free-slip boundary conditions requires two fields and reversible couplings. The wavelengths for which stable rolls exist are dramatically modified when the generation of vertical vorticity is taken into consideration. For small Prandtl numbers and rigid boundaries, the skewedvaricose instability of Busse and Clever is recovered by a plausible but nonrigorous modification of our free-slip equations.