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

We describe a two-point spectral transport approach to the investigation of fluid instability, generalized turbulence, and the interpenetration of flu ids 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 inves tigations, even in the presence of sharp density variations between fluids. Models for two-field analysis with drag representations for momentum excha nge can also be used and are discussed previously. In this work departures from mean flow are included in the stochastic concept of turbulence. Reynol ds decomposition into mean and fluctuating parts is carried out in the spir it of this generalized concept, which is meaningful despite arbitrariness a s to which scales are identified as mean flow and which are identified as f luctuations. This spectral formulation motivates a novel description of the global effects of pressure due to incompressibility. We discuss its deriva tion and the modifications this 'nonlocal' formulation has on the turbulenc e spectra. We also discuss the consequences of spectral self-similarity exh ibited by this model. This identification of spectral selfsimilarity in a c ircumstance of inhomogeneous, variable density turbulence is novel. (C) 199 9 Elsevier Science Ltd. All rights reserved.