LOW-DIMENSIONAL MODELS FOR FLOWS WITH DENSITY-FLUCTUATIONS

A low-dimensional model, using the proper orthogonal, or Karhunen-Loev e decomposition, has been remarkably successful in representing the be havior of the wall region of a turbulent boundary layer. We briefly su mmarize this work. We may hope for similar success in other flows in w hich coherent structures play an important role, in particular flows w ith density fluctuations. We sketch an approach to such a decompositio n for flows with density fluctuations, suggesting various alternatives which weigh the available information differently. In such a low-dime nsional model, obtaining the empirical eigenfunctions poses a problem, since they can usually be determined only from extensive measurements or direct numerical simulations. However, recent work with energy met hod stability theory (modified by use of an anisotropic eddy viscosity and feedback to the mean profile) has been remarkably successful in p redicting the form of the empirical eigenfunctions in the isothermal b oundary layer. We present here preliminary results for sheared Rayleig h-Benard convection; these results do not include anisotropic eddy vis cosities and feedback, and do not predict directly the form of the POD eigenfunctions; however, a very satisfactory comparison can be made w ith the second order moments obtained from a DNS. (C) 1997 American In stitute of Physics.