Instability threshold of a model for deep convection with depth-dependent viscosity

The effect of depth-dependent viscosity on the onset of convection in deep horizontal layers heated from below is investigated. In the Zeytounian deep convection model (1989), the depth-dependent viscosity is introduced. The instability threshold of the thermal conduction rest state, is evaluated (in the free-free case). It is obtained that: (1) the strong principle of exchange of stability holds; (2) the instability threshold depends - via a simple closed form (1.1) - on the viscosity law; (3) a fall in the instability threshold is driven by the depth-dependent viscosity. The action of (quadratic) polynomial and exponential depth-dependent viscosity on the instability threshold is evaluated. Although needs to be verified by experiments, the results obtained appear to be of interest not only for theoreticians but also for experimentalists.