Instability of rotating convection

Convection rolls in a rotating layer can become unstable to the Kuppers-Lor tz instability. When the horizontal boundaries are stress free and the Pran dtl number is finite, this instability diverges in the limit where the pert urbation rolls make a small angle with the original rolls. This divergence is resolved by taking full account of the resonant mode interactions that o ccur in this limit: it is necessary to include two roll modes and a large-s cale mean flow in the perturbation. It is found that rolls of critical wave length whose amplitude is of order epsilon are always unstable to rolls ori ented at an angle of order E-2/5. However, these rolls are unstable to pert urbations at an infinitesimal angle if the Taylor number is greater than 4 pi(4). Unlike the Kuppers-Lortz instability, this new instability at infini tesimal angles does not depend on the direction of rotation; it is driven b y the flow along the axes of the rolls. It is this instability that dominat es in the limit of rapid rotation. Numerical simulations confirm the analyt ical results and indicate that the instability is subcritical, leading to a n attracting heteroclinic cycle. We show that the small-angle instability g rows more rapidly than the skew-varicose instability.