Thermal instability of a heterogeneous rotating fluid layer with free boundaries (Q800177)

The authors study the thermal instability of a heterogeneous rotating fluid layer with free boundaries. The model is a viscous, incompressible, rotating and nonhomogeneous fluid layer with free boundaries with density \(\rho_ 0f(z)\), where \(\rho_ 0\) is a positive constant with the dimension of the density, and f is a monotonic function of the vertical coordinate z with \(f(0)=1\). The fluid is rotating with an angular velocity \(\Omega\) about the vertical axis. In this respect, one notes that the principle of exchange of stabilities is not valid for this problem. The present solution is shown to be characterized by a variational principle expressed in terms of certain parameters related to the Rayleigh number. Moreover, for certain values of these parameters, marginal state does not exist and non-oscillatory unstable modes exist. The paper also contains numerical computations with the assumption that the density of the fluid varies exponentially.