Abstract
We here analyse two models of double-diffusive convection in fluid layer when viscosity depends on temperature quadratically. However, to a linearized instability analysis, conditional and global (unconditional) nonlinear stability theories are applied. For the first model, we establish an unconditional nonlinear energy stability. Moreover, in the second model the standard energy method does not yield unconditional stability so a conditional energy analysis is employed to achieve nonlinear results. In addition, the nonlinear stability bounds is found to be independent of the salt field and a presentation of the region of possible subcritical instabilities is given.
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