Classification of Linear Bifurcations of Double-Diffusive Micropolar Convection in Two Dimension

This paper is devoted to classifying linear bifurcations and the stability of the double -di ff usive convective micropolar fluid in a two-dimensional horizontal domain at a rest state. We prove that the linear part of the operator is sectorial; and in the plane of thermal and saline Rayleigh numbers, for any fixed values of other parameters, the boundary of the region of stability comprises infinitely many segments of lines followed by finitely many segments of hyperbolas, patched together. Indeed, for any length scale, there is an infinite sequence of critical wave vectors, in which saddle -node bifurcations occur, and there is a finite sequence of critical wave vectors, in which Hopf bifurcations occur. The region of the stability and sequences of critical wave vectors is sensitive to length scale. It is shown that considering microinertia increases the marginal instability range in both fingering and double -di ff usive convections.