Onset of Thermal Buoyancy Convection in a Two-Layer System with Deformable Interface and Fixed Heat Flux at the Boundaries under Terrestrial and Microgravity Conditions

Abstract

The stability of a conductive state of a system of two horizontal layers of immiscible fluids of close densities with a fixed heat flux at external boundaries is studied. The problem is solved in the framework of the generalized Boussinesq approximation, which correctly takes into account the deformations of the interface. The onset of convection at heating from above or below is investigated. Main attention is paid to the effect of layer thickness ratio and gravity level on instability. Two long-wave instability modes related the presence of a deformable interface and to a fixed heat flux at the external boundaries are found out. They are analyzed analytically. The behavior of the system with respect to monotonic and oscillatory perturbations of finite wavelength is studied numerically. The complete stability map is obtained. It is found that for very different layer thicknesses, as well as for single layers with fixed heat flux at the boundaries, a long-wavelength instability is observed. The presence of a long-wave instability domain at close thicknesses of layers is also found, which is associated with a strong stabilization of finite-wavelength instability in this parameter range. In the case of Earth gravity, the monotonic perturbations are most dangerous at any ratios of layer thicknesses, the oscillatory mode of instability is responsible for the onset of convection only in microgravity conditions.