Longitudinal and transverse modes of temperature modulated inclined layer convection

A parametric instability of an incompressible, viscous, and Boussinesq fluid layer bounded between two parallel planes is investigated numerically. The layer is assumed to be inclined at an angle with horizontal. The planes bounding the layer are subjected to a time-periodic heating. Above a threshold value, the temperature gradient across the layer leads to an instability of an initially quiescent state or a parallel flow, depending upon the angle of inclination. The Floquet analysis of the underlying system reveals that under modulation, the instability sets in as a convective roll pattern executing harmonic or subharmonic oscillations, depending upon the modulation, the angle of inclination, and Prandtl number of the fluid. Under modulation, the value of the angle of inclination for the codimension-2 point is found to be a nonconstant function of the amplitude and the frequency of modulation. Further, the instability response in the fluid layer as a longitudinal mode is always harmonic whereas the instability response as a transverse mode is harmonic, or subharmonic, or bicritical depending upon the modulation. The temperature modulation offers a good control of time-periodic heat and mass transfer in the inclined layer convection.