Nonlinear interaction of thermogravitational waves and thermomagnetic rolls in a vertical layer of ferrofluid placed in a normal magnetic field

Abstract

The interacting thermogravitational and thermomagnetic instabilities arising in a vertical layer of non-isothermal ferrofluid placed in a horizontal magnetic field are investigated by means of a weakly nonlinear analysis. An expansion in disturbance amplitude leads to the reduction of a full problem to a system of coupled cubic Landau amplitude equations. Their solutions are analyzed and interpreted from a physical point of view. The details of an intricate competition between gravitational and magnetic buoyancy mechanisms are highlighted. The spatial structure of the resulting flow patterns is discussed. It is shown that the parametric existence regions determined for finite amplitude disturbances differ drastically from those predicted based on the analysis of infinitesimal perturbations. Subsequently, the cross-layer heat flux characteristics are discussed. It is shown that the co-existence of two physical mechanisms of convection can lead to a suppression of heat transfer rather than to its enhancement.