Stability of hydrothermal-wave states

The half-zone model is investigated for unit aspect ratio, zero gravity and Prandtl numbers Pr = 1.5 to 7 by numerical simulations. For Reynolds numbers Re > Re c, the axisymmetric stationary flow is unstable to three-dimensional travelling waves. In the simulations, standing waves can be generated slightly above Re c. For the Prandtl numbers investigated it is found that these states are unstable and decay either into a clockwise or a counter-clockwise propagating wave. Amplitude equations are used to quantitatively describe the instability of the standing-wave states in the weakly nonlinear regime and to estimate the range of Pr within which only travelling waves are stable. For half-zones under terrestial conditions, buoyancy forces are shown to stabilize travelling waves.