SIMPLE-MODEL FOR LINEAR AND NONLINEAR MIXING AT UNSTABLE FLUID INTERFACES WITH VARIABLE ACCELERATION

A simple model is described for predicting the time evolution of the h alf-width h of a mixing layer between two initially separated immiscib le fluids of different density subjected to an arbitrary time-dependen t variable acceleration history a(t). The model is based on a heuristi c expression for the kinetic energy per unit area of the mixing layer. This expression is based on that for the kinetic energy of a linearly perturbed interface, but with a dynamically renormalized wavelength w hich becomes proportional to h in the nonlinear regime. An equation of motion for h is then derived from Lagrange's equations. This model re produces the known linear growth rates of the Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities, as well as the nonlinear RT gro wth law h=alpha Aat(2) for constant a (where A is the Atwood number) a nd the nonlinear RM growth law h similar to t(theta) for impulsive a, when alpha and theta depend on the rate of kinetic energy dissipation. In the case of zero dissipation, theta=2/3 in agreement with elementa ry scaling arguments. A conservative numerical scheme is proposed to s olve the model equations, and is used to perform calculations that agr ee well with published experimental mixing data for four different acc eleration histories. [S1063-651X(98)13411-6].