Travelling wave convection in a rotating layer

Small amplitude twodimensional Boussinesq convection in a plane layer with stress-free boundaries rotating uniformly about the vertical is studied. A horizontally unbounded layer is modelled by periodic boundary conditions. When the centrifugal force is balanced by an appropriate pressure gradient the resulting equations are translation invariant, and overstable convection can take the form of travelling waves. In the Prandtl number regime 0.53 < σ < 0.68 such solutions are preferred over the more usual standing waves. For σ<0.53, travelling waves are stable provided the Taylor number is sufficiently large.