Inertial Effects on Rotating Flow in a Porous Layer

Abstract

Inertial effects on flow instabilities in a horizontal reactive porous layer with a deformed upper boundary are studied using a linear stability analysis and under the condition that the porous layer, which is also referred to as a dendrite or mushy layer, is rotating about an inclined axis during the solidification of a binary alloy. The linear stability analysis leads to new results about the effects of the inertial force on the existence and the number of the oscillatory modes and on the preference of either left- or right-traveling longitudinal rolls, which can depend on the angle of inclination γ of the rotation axis with respect to the vertical axis. For some 0° < γ < 90° and for the rotation rate beyond some particular value, the preferred flow solution in the form of left-traveling rolls can be replaced by the one in the form of right-traveling rolls or vice versa. The preferred flow pattern, the period of oscillation of the flow solution, the critical Rayleigh number, and the shape and structure of the deformed upper boundary of the layer are found to depend on the inertial effect.