Stability of an oscillatory shear flow in a differentially heated vertical channel

The linear stability of an oscillatory shear flow in a differentially heated vertical channel was investigated numerically for Re = 1000 and Pr = 0.7. The Galerkin method is used to solve the disturbance momentum and energy equations. The results show that the least stable disturbance could be three-dimensional for higher flow oscillation frequency and larger flow oscillation amplitude, while it is two-dimensional in the isothermal oscillatory and heated steady channel flows. The flow oscillation acts to stabilize the flow at moderate and high oscillation frequencies, where the degree of stabilization increases with the oscillation amplitude; but, it acts to destabilize the flow and the amount of destabilization increases with the oscillation amplitude at low oscillation frequency. It is shown from the balance of disturbance kinetic energy budget that shear production is responsible for the flow instability. For the 2-D wave initiated instability, almost all the shear production is generated during a very short time interval at low oscillation frequency, while it is generated during most of the time of a cycle for the 3-D disturbance.