A new model for mixing and fluctuations in a turbulent wake

Abstract

A new model for turbulent wake mixing is proposed. The entrainment of surrounding fluid by the growth of the turbulent core in a high-speed wake is pictured as introducing into the core fluid elements that retain for some time properties characteristic of their state prior to entrainment. This leads to a two-component wake structure, consisting of well mixed fluid on the one hand, and unassimilated fluid on the other. The delay in complete assimilation is represented in the model by a mixing lag. A straightforward set of equations describing the proposed (one-dimensional) model is derived. The two-component model leads to a prediction of mean-mass and electron-density fluctuations in the wake. The fluctuations are assumed to arise from random convection of inhomogeneous fluid elements, rather than by compressibility effects or dissipation associated with the turbulent velocity field, which are shown to be small by comparison. Simple approximate expressions for the relative-mass and electron-density fluctuations are derived which show that the two are not generally equal, as has often been assumed in computations of radar backscatter from wakes. Numerical predictions for the magnitude and variation of mass density fluctuations in a relatively lowspeed wake are obtained by solving a simplified set of equations, in which the lag is represented by an effective mixing boundary, and are in encouraging agreement with the general magnitude and trend observed experimentally, although firm experimental measurements are lacking at this time.