Lab Home  Phone  Search  


Seventy years have passed since Kolmogorov's successful theory of incompressible turbulence, yet there is a stark absence of an analogous theory to describe compressible flows. I will briefly discuss the key notions of an inertialrange and the cascade in turbulence. I will present the relevant background and some of the difficulties that have prevented an extension of these concepts to compressible flows. I will then go over some recent developments in this regard. Some of my main conclusions which emerge from this work are: (1) any scaledecomposition aimed at probing inertialrange dynamics must satisfy an “inviscid criterion,” i.e. it must guarantee that viscous effects on the dynamics of largescale flow are negligible. (2) The inviscid criterion naturally leads to a densityweighted coarsegraining of the velocity field. Such a coarsegraining method is already known in the literature as Favre filtering; however its use has been primarily motivated by appealing modelling properties rather than underlying physical considerations. (3) The nonlinear transfer of kinetic energy to small scales is dominated by scalelocal interactions. In particular, the results preclude transfer of kinetic energy from largescales directly to dissipation scales, such as into shocks, in high Reynolds number turbulence as is commonly believed. (4) If the pressure dilatation cospectrum decays fast enough, I will show that mean kinetic and internal energy budgets statistically decouple beyond a transitional ``conversion'' range. (5) In collaboration with Shengtai Li, Hui Li, and Hao Xu at LANL, we use highresolution numerical simulations of forced and decaying compressible turbulence to compute, for the first time, pressure dilatation cospectrum and verify statistical decoupling. (6) The analysis establishes the existence of an ensuing inertial range over which mean subgridscale (SGS) kinetic energy flux becomes constant, independent of scale. Over this inertial range, mean kinetic energy cascades locally and in a conservative fashion, despite not being an invariant. Time permitting, I will then discuss rigorous constraints on the scaling of density, velocity, and pressure spectra and structure functions. Host: Peter Loxley, loxley@lanl.gov 