Spiral vortices in compressible turbulent flows

We extend the spiral vortex solution of Lundgren [Phys. Fluids 25, 2193 (19 82)] to compressible turbulent flows with a perfect gas. This model links t he dynamical and the spectral properties of incompressible flows, providing a k(-5/3) Kolmogorov energy spectrum. In so doing, a compressible spatiote mporal transformation is derived, reducing the dynamics of three-dimensiona l vortices, stretched by an axisymmetric incompressible strain, into a two- dimensional compressible vortex dynamics. It enables us to write the three- dimensional spectra of the incompressible and compressible square velocitie s in terms of, respectively, the two-dimensional spectra of the enstrophy a nd of the square velocity divergence, by the use of a temporal integration. Numerical results are presented from decaying direct simulations performed with 512(2) grid points; initially, the rms Mach number is 0.23, with loca l values up to 0.9, the Reynolds number is 700, and the ratio between compr essible and incompressible square velocities is 0.1. A k(-5/3) inertial beh avior is seen to result from the dynamical evolution for both the compressi ble and incompressible three-dimensional spectra. (C) 2001 American Institu te of Physics.