Two-point description of two-fluid turbulent mixing—I. Model formulation

Abstract

We describe a two-point spectral transport approach to the investigation of fluid instability, generalized turbulence, and the interpenetration of fluids across an interface. The technique also applies to a single fluid with large variations in density. Departures of fluctuating velocity components from the local mean are far subsonic, but the mean Mach number can be large. This work is focused on flows with large variations in fluid density (e.g. two-field fluid interpenetration). The starting point for analysis is the set of Navier–Stokes equations, for which we assume relevance in our investigations, even in the presence of sharp density variations between fluids. Models for two-field analysis with drag representations for momentum exchange can also be used and are discussed previously. In this work departures from mean flow are included in the stochastic concept of turbulence. Reynolds decomposition into mean and fluctuating parts is carried out in the spirit of this generalized concept, which is meaningful despite arbitrariness as to which scales are identified as mean flow and which are identified as fluctuations. This spectral formulation motivates a novel description of the global effects of pressure due to incompressibility. We discuss its derivation and the modifications this ‘nonlocal’ formulation has on the turbulence spectra. We also discuss the consequences of spectral self-similarity exhibited by this model. This identification of spectral self-similarity in a circumstance of inhomogeneous, variable density turbulence is novel.