We study the problem of double-diffusive convection in a horizontal plane fluid layer when there is a heat sink/source which is linear in the vertical coordinate which is in the opposite direction to gravity. The thresholds for linear instability are found and compared to those derived by a global nonlinear energy stability analysis. A region is discovered where a very sharp increase in Rayleigh number is observed. In addition to a linearized instability analysis, two global (unconditional) nonlinear stability thresholds are derived.
Harfash, A. J., & Nashmi, F. K. (2017). Triply Resonant Double Diffusive Convection in a Fluid Layer. Mathematical Modelling and Analysis, 22(6), 809-826. https://doi.org/10.3846/13926292.2017.1384765
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