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 the 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. Floquet analysis of the underlying system reveals that under modulation, the instability sets in as a convective-roll pattern executing harmonic or subharmonic temporal oscillations, depending upon the modulation, the angle of inclination, and the Prandtl number of the fluid. Under modulation, the onset of the instability is in the form of one of two spatial modes: the longitudinal mode and the transverse mode. The value of the angle of inclination for the codimension-2 point is found to be a function of the amplitude and the frequency of modulation. Furthermore, the temporal response is harmonic, or subharmonic, or bicritical depending upon the modulation. The temperature modulation offers good control of time-periodic heat and mass transfer in the inclined layer convection.