On the finite-amplitude steady convection in rotating mushy layers (Q2745727)

This paper presents a theoretical study of a mushy layer in a state of uniform rotation about the vertical, a problem which has been studied before for non-rotating systems. Of particular interest is to determine how the rotation of the system controls the bifurcating convection with both the oblique-roll planform and the planform of hexagonal symmetry when the Rayleigh number is slightly in excess of its critical value. In particular, the author considers the case of two-dimensional convection in the form of oblique rolls, and the case of three-dimensional convection with hexagonal symmetry. After the governing equations along with boundary conditions are presented in non-dimensional form, these equations are solved analytically using the perturbation method for small amplitude parameters and for small Rayleigh number. Conditions for the existence of solutions of these equations are also established.NEWLINENEWLINETwo nice results are found. First, it is shown that the increase in Taylor number \(T\), which is proportional to the uniform angular velocity of the system, tends to increase the linear critical Rayleigh number, which causes the system to be more stable. Second, the presence of the rotational constraint can be accompanied by a qualitative change in physical effects which are intrinsic to the mushy layer and which are included in the analysis as perturbations to the near-eutectic approximation of the system. In particular, by analyzing the first-order correction to the linear critical Rayleigh number, the author finds that the stabilizing effect of increasing the linear measure of permeability variations, \(K_1\) (measures how the permeability linearly varies with the local solid fraction, \(C_s\)), is constrained to the range \(0\leq T<3\) of Taylor numbers.