Multiple Instabilities in a Triply Diffusive System

The model equations describing two‐dimensional convection in a fluid system driven by three diffusing components are studied. For such a model Griffiths found the state of pure conduction could become unstable to simultaneous steady and oscillatory convection. When the diffusing agents are temperature, salt, and angular velocity, Arneodo et al. found five instabilities of the rest state, including three multiple instabilities. In this paper we return to the model introduced by Griffiths, and, identifying his multiple instability as one of those found by Arneodo et al., we use dynamical systems theory to derive and study the evolution equations for the amplitudes of convection close to bifurcation.