The dynamics of triple convection

A numerical analysis of the dynamics of triple convection is presented. It is shown that in the parameter space of a fluid subject to triple convection, there is a critical hypersurface on which three linear growth rates vanish, and all the remaining rates are negative. Parameter values chosen to place a triply unstable system near the critical condition in the hypersurface may lead to complicated temporal behavior, and in some cases, chaotic behavior. The problem is illustrated using the example of Arenodo (1982) from geophysical fluid dynamics: a two-dimensional, Boussinesq thermohaline convection in a plane parallel layer. In the example, it is assumed that the parallel layer is in rotation around a vertical axis, and is subject to convenient boundary conditions. The theoretical calculations from the example are applied to other types of triply unstable systems, and the possibility of chaotic temporal behavior is exmined.