Theory of turbulent mixing at the interface of fluids in a gravity field

Abstract

The theory of turbulent mixing at the interface of two media in accelerated motion was constructed in [1], and an approximate solution was given for incompressible fluids. The time variation of kinetic energy was neglected in the equation of balance for the kinetic energy of the turbulent motion. In [2] the characteristic turbulent velocity is averaged over the mixing region. This allows the initial equations to be solved allowing for the time variation of kinetic energy. It turns out that the resulting density profile roughly coincides with the profile of [1] within a wide range of variation of the initial density differential. In the present paper the equations for the mixing of incompressible fluids are studied in their complete form. It is established that the solutions of [1, 2] are applicable within a limited region, valid for small density ratios. The resulting solution is analyzed qualitatively, and it is shown that the density gradient at the mixing front is discontinuous. The dependence of the solution on two empirical constants is investigated. An approximate choice of the values of these constants is made on the basis of the theoretical considerations of [2, 3], and by comparison with the solution of [1]. The mixing asymmetry is found numerically as a function of the initial density differential. Quantitative characteristics of the solution are illustrated in graphs.