Bicritical states in a vertical layer of fluid under two-frequency temperature modulation

In this paper, the effect of two-frequency modulation of boundary temperatures on the onset of natural convection in a layer of fluid (with Prandtl number <12.5) between two vertical parallel planes is considered. The ratio of the two forcing frequencies and the mixing angle for the amplitude of modulation provide an efficient way of controlling the underlying instability. At the onset of instability, the fluid layer executes harmonic and subharmonic oscillations. The transition between harmonic and subharmonic responses is found to occur through an intermediate bicritical state. In addition to bicritical states, the instability is found to exhibit an almost tricritical state for a particular combination of the modulation parameters. The onset of the instability depends upon the modulation parameters and Prandtl number of the fluid.