Period stabilization in the Busse-Heikes model of the Kuppers-Lortz instability

Abstract

The Busse-Heikes dynamical model is described in terms of relaxational and non-relaxational dynamics. Within this dynamical picture a diverging alternating period is calculated in a reduced dynamics given by a time-dependent Hamiltonian with decreasing energy. A mean period is calculated which results from noise stabilization of a mean energy. The consideration of spatial-dependent amplitudes leads to vertex formation. The competition of front motion around the vertices and the Kuppers-Lortz instability in determining an alternating period is discussed.