Falsaperla, Paolo - Giacobbe, Andrea (2010) Marginal conditions for the solute BĂ©nard problem with many types of bounday conditions. [Preprint]
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A large number of variants of the BĂ©nard problem (with a solute, rotating, subject to magnetic field, etc) have been extensively studied. Despite this, some new interesting results can be obtained when non--standard boundary conditions are taken into consideration. In this work we investigate an infinite layer of fluid heated and salted from below, subject to a variety of boundary conditions: finite slip on velocities and Robin conditions on temperature and solute concentration. We write analytical conditions for the onset of stationary convection, we obtain simplified formulas for particularly symmetric cases, we draw marginal regions in some significant cases, and we perform an asymptotic analysis for small wave numbers.
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