Abstract
We investigate the Rayleigh-Bénard convection under sinusoidally varying temperatures of the horizontal rigid planes bounding a laterally infinite fluid layer for the bicritical states. The problem is analogous to the well studied Faraday instability and Rayleigh-Bénard convection under gravity modulation. Under modulation, the neutral instability curve is found to alternate between the conventional harmonic and subharmonic tongues in the space of the dimensionless wave number of disturbance and the control parameter. The transition between harmonic and subharmonic critical instability responses is found to occur via a bicritical state, where the two instability responses coexist with different wave numbers. These bicritical states are found to depend upon the modulation parameters and the Prandtl number.
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