Study of the Geometry of Flow Patterns in a Compressible Wake

Abstract

Direct numerical simulations of turbulence provide better understanding of fine scale motions and indicate that the dissipation motion in incompressible turbulence has a universal character. The fine scale motion by the evolution equation of the velocity gradient tensor A _ij in incompressible turbulence has been investigated by Vielliefosse [1] and others. In compressible turbulence, there is another kind of dissipation motion, so called dilatation dissipation due to divv ≠ 0. Maekawa [2] (1998) extended the incompressible evolution equations analyzed by Cantwell[3] (1992) for compressible flow and found that the velocity gradient tensor was governed by a linear second order system whose coefficients are expressed in terms of the invariant P and its derivatives and the invariant Q. This fact suggests that analytical feature of A _ij is characterized by the analytical features of the invariants P and Q. Maekawa and Matsuo [4](1998) applied the solutions of the evolution equations to explain the statistical robust tendency of homogenous isotropic compressible turbulence for initial high turbulent Mach numbers. In what follows, flow structures of inhomogeneous compressible flow such as a wake in the invariant space are investigated. The solutions of the evolution equations are applied to understanding the definite trends presented in the invariant space.