M. J. McCready, B. D. Woods and M. R. King

University of Notre Dame

The big question that arises in gas-liquid and liquid-liquid flows is not if waves will form, but if the waves will remain of small amplitude and thus not lead to atomization or a transition from stratified flow. At the present time, flow regime transition prediction procedures used in industry rely on a linear stability prediction of the long wave region as a criterion for regime transitions.

Experiments in gas-liquid channel flow, liquid-liquid channel flow and liquid-liquid Couette flow have shown that there are wide ranges of parameter space where the linearly unstable waves saturate at small amplitude. Further, while a necessary condition for growth of large amplitude waves appears to be longwave instability, this is not sufficient as there is a wide range of parameters in the Couette experiment where either no visible waves or steady small amplitude waves result for depth ratios where long waves are unstable. Thus there is a need to understand nonlinear processes that must be acting to saturate waves to predict the long distance fate of an unstable stratified flow.

This talk will examine the processes of nonlinear stabilization of finite amplitude waves. Stuart-Landau theory provides possible mechanisms of stabilization, quadratic interaction with a stable overtone, cubic - self interaction and cubic interaction with the mean flow mode. Numerical simulations of the wave spectrum reveal that a positive Landau coefficient (subcritical case) does not necessarily mean that waves are not stabilized by nonlinearity above the point of neutral stability. These simulations also suggest that in Couette flow, an energy "cascade" to higher wavenumbers can stabilization waves at very small amplitudes and prevent formation of large amplitude waves even when the system is unstable to long waves.