Nonlinear oscillatory convection in rotating mushy layers

We consider the problem of nonlinear oscillatory convection in a horizontal mushy layer rotating about a vertical axis. We analyze the standing and traveling modes of oscillatory convection in the form of two-dimensional oblique rolls and three-dimensional distorted patterns. Under a near-eutectic approximation and the limit of large far-field temperature, we determine the two- and three-dimensional oscillatory solutions to the weakly nonlinear problem by using a perturbation technique, and the stability of these oscillatory solutions are investigated with respect to arbitrary three-dimensional disturbances. The results of the analyses indicate, in particular, that depending on the range of the values of the parameters, convection in the form of supercritical traveling hexagons can be stable and preferred, provided the value of the rotation parameter T (square root of a Taylor number) is not too small and is below some value, which can depend on the other parameter values. [More ...]published or submitted for publicationis peer reviewe