Influence of the thermoelectric effect on the Rayleigh-Bénard instability inside a magnetic field

We investigate the influence of thermoelectric effect on the onset of thermal instability in the Rayleigh-Bénard system with vertical magnetic field. An electrically conducting fluid is confined in an infinite horizontal layer between thick thermally and electrically conducting walls. A horizontal temperature variation resulting from convective instability leads to horizontal temperature gradients along the liquid-solid interface acting as a source of thermoelectric currents. Through interaction with the applied magnetic field, the Lorentz force is created modifying the instability. We find that the critical Rayleigh number for onset of convection is not changed by the thermoelectric effect. However, the thermal gradient on the liquid-solid boundary leads to a change of the shape of the unstable mode creating helical flow in the evolving convection rolls because of the Lorentz force parallel to their axis. The created kinetic helicity depends linearly on the dimensionless parameter K(TE) characterizing the strength of the thermoelectric effect.