Instability mechanism for miscible two‐fluid channel flow with wall slip

Abstract

AbstractModal analysis of the Reynolds‐Orr energy equation for a miscible viscosity stratified slippery channel flow is deliberated. The main aim is to extend the earlier work of Ghosh . (Phys. Fluid, Vol. 26, 014107 (2014)) to discusses the instability mechanism, which has not been investigated so far. The generalized equation governing the average rate of change of disturbance kinetic energy is evaluated after solving the Orr‐Sommerfeld boundary value problem. The analysis includes viscosity perturbation and slip boundary condition. Maximum growth rate curves for two‐dimensional disturbances reconfirm the existence of new unstable modes at low Reynolds numbers. Stabilizing and destabilizing effects of wall velocity slip are found depending on parameter regime. The physical mechanism responsible for the dual role of the wall slip is brought to light by estimating the alteration of kinetic energy due to the production and dissipation of energy originating from various factors inside the perturbed flow. Slip boundary condition at the wall affects the base flow as well as perturbations. Our numerical calculations here show how the wall velocity slip gives impact on each energy terms. The results ensure that, the new unstable mode is occurred due to the overlap of velocity and viscosity disturbance vortices. Stability characteristics of this overlap instability are ruled by the energy sourcing from the Reynolds stress and the viscosity perturbation gradient effect.