Numerical Simulation of Two-Dimensional Shear Flow

Abstract

Numerical experiments on finite difference solutions of time dependent two-dimensional Navier-Stokes equations are used to study the transition triggering off in a mixing layer of initial tanh(y) profile. The inflow is excited by sinusoidal waves resulting from the linear theory of hydrodynamic instability. Numerical realizations are compared, through stream wise growth of momentum thickness and vorticity plots, with Winant and Browand experiments.

The transition control and triggering off are studied through the finite difference solution of the two-dimensional time dependant Navier-Stokes equations.  In a shear flow, the transition results from hydrodynamic amplification of unstable disturbances stimulated by perturbations of diverse origin.  In a unidirectional flow, the most unstable disturbances are two-dimensional transverse waves {2, 3} and experiments have shown the area where small disturbances grow exponentially {5,8,9,10}.  Thus, a two dimensional numerical simulation is well suited to the study of transition triggering off.