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Description
A vertical magnetic field delays the onset of Rayleigh-Bénard convection in a conducting liquid in agreement with Lenz' law. An insulating sidewall impedes the spreading of induced eddy currents, whereby the suppression of convection becomes less effective there. This mechanism causes convection to appear near the walls of the container while it remains suppressed in the bulk. Busse developed an asymptotic theory for the critical Rayleigh number of wall-attached convection near a straight wall using a separation ansatz with sine/cosine-dependence on the vertical coordinate, i.e. free-slip boundary conditions. Busse's model can be extended to the case of a closed rectangular box. A 2d numerical stability analysis shows that the blocking effect of a corner on the currents is more effective than that of a straight wall. The analysis is based on the quasistatic approximation and assumes that the primary instability is non-oscillatory. The results will be compared with those for a straight wall.
