The study of stability mechanism for multi-layer fluids flowing onto an inclined plane

In this study we have performed the computation of eigenfunctions for determining various disturbance quantities in the inclined plane flow system. These disturbance quantities are subsequently inserted into disturbance energy equations to evaluate the amount of energy transfer at the interface and the free surface, and provide an insight into understanding instability mechanisms of multi-layer fluids onto an inclined plane. In energy analysis it is demonstrated that the dominant mechanisms occurring in the interlaces and the free surface are active in these instabilities, Specifically, it is suggested that the stability mechanism for the interface is associated with the coupling between the disturbance quantities and the base state velocity gradient.