We determine scaling exponents of structure functions for a computation with the Piecewise Parabolic Method  (or PPM) of a compressible flow at a r.m.s. Mach number of unity, using periodic boundary conditions and 5123 grid points, with δx the uniform grid increment. In  were analyzed similar computations with a one-dimensional shear wave forcing, resulting in a sizable departure from isotropy; hence we choose here a forcing consisting of a superposition of shear waves at k0 = 1 in three orthogonal directions. Contrary to , we maintain a constant temperature on average by adding a Stefan-like σT 4 cooling law to the energy equation appropriate for optically thin media. In the quasi-steady state, kinetic energy E K ~ 0.7 and heat energy E H ~ 1.5; the r.m.s. Mach number locally has excursions up to 4, with density contrasts of up to 30 and density fluctuations of order unity. The Taylor Reynolds number is close to 100, with however minimal dissipation in the large scales because of the nature of the PPM method. As in similar computations but for the decay problem , the flow consists of a superposition of strong planar shocks, vortex filaments and sheets as well as spirals , with on average a weak baroclinic term.
Bibliographical noteFunding Information:
This work was supported at the University oj Minnesota by the National Science Foundation, through a grand challenge grant ASC-9217394, and by the Department oj Energy's Office oj Energy Research, through grant DEFG02-87ER25035. In Nice, AP received support Jrom CNRS grant PNST.
- Compressible Flow
- Mach Number
- Structure Function
- Supersonic Flow
- Vortex Filament