The dynamics of triple convection

Abstract

In the parameter space of a fluid subject to triple convection, there is a critical hypersurface on which three growth rates of linear theory vanish and all the rest are distinctly negative. When parameter values are chosen to place the system very near to this polycritical condition, the temporal behavior of the system may be complicated and even chaotic. This remark, based on rather general considerations (Arneodo et al., 1984), is here illustrated by an example from GFD (Arneodo et al., 1982): two-dimensional Boussinesq thermohaline convection (or semi-convection) in a planeparallel layer rotating about a vertical axis and subject to mathematically convenient boundary conditions. The treatment is made in terms that show why the results may apply to many fluid dynamical systems or indeed to other kinds of triply unstable systems and, using both amplitude equations and mappings, we discuss the chaos that can arise.