Oscillatory convection in a rotating layer

The stability of travelling and standing rolls in oscillatory rotating convection is considered from the point of view of equivariant bifurcation theory. To study stability with respect to oblique perturbations the problem is formulated on a rotating rhombic lattice. All primary solution branches with maximal isotropy are determined together with their stability properties using a truncation of the most general equivariant vector field at third order. In addition as many as seven branches of temporally periodic or quasiperiodic solutions with submaximal isotropy may be present. Instabilities analogous to the Küppers-Lortz instability of steady rolls in rotating convection are uncovered for both travelling rolls and for standing rolls. These instabilities are triggered by the formation of a heteroclinic orbit connecting two travelling roll states or two sets of standing rolls with different wave vectors. Conditions are given for the formation and asymptotic stability of a structurally stable heteroclinic cycle connecting four travelling roll states. The results are compared with recent studies of oscillatory patterns on a rotating square lattice and on a nonrotating rhombic lattice.