Interacting steady states in thermohaline convection

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Abstract
We consider the Boussinesq theory for convection in a rectangular box with imposed constant, negative, vertical heat and salt gradients. We analyze the bifurcation of two-dimensional convection steady states near a double instability point defined by a critical value of the thermal Rayleigh number and geometrical aspect ratio. We find that for thermohaline convection the interaction of the two lowest pure-mode steady states does not produce the tertiary bifurcation of periodic solutions because the direction of bifurcation of the modes is always the same, either both supercritical or subcritical. On the other hand, we find that the interaction can produce the secondary bifurcation of mixed-mode steady states, and that jump transitions between multiple, stable, pure-mode steady states are possible. We also find that the mixed-mode steady state is always unstable in the parameter ranges considered.

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