Hopf-Hopf and Hopf-Steady mode interactions with O(2) symmetry in Langmuir circulations

摘要

In this paper the nonlinear stability of two-dimensional Langmuir circulations in a fluid layer, stratified by vertical thermal and salinity gradients, is investigated when two distinct wavenumbers become simultaneously unstable. These instabilities take the form of O(2) symmetric Hopf-Hopf and Hopf-Steady bifurcations when the lateral boundary conditions are assumed to be periodic. In the analysis of the Hopf-Hopf bifurcation a disagreement with the group theoretic work of Chossatet al.(1986) is found. This difference is resolved by correcting the lattice of Isotropy subgroups presented by Chossatet al.(1986) and by considering the effects of the higher order terms in the amplitude evolution equations.