A numerical study of supersonic turbulence

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We report on simulations of nonstationary supersonic isotropic turbulent flow using the Piecewise-Parabolic Method on uniform grids of 20482 in two dimensions and 2563 in three dimensions. Intersecting shock waves initiate the transfer of energy from long to short wavelengths. Weak shocks survive for many acoustic times τac. In two dimensions eddies merge over many τac. In three dimensions vortex sheets break-up into short vortex filaments within two τac. Entropy fluctuations, produced by strong shocks, are stretched into filaments over several τac. These filaments persist and are mirrored in the density. We observe three temporal phases: onset, with the initial formation of shocks; quasi-supersonic, with strong density contrasts; and post-supersonic, with a slowly decaying root mean square Mach number. Compressive modes quickly establish a k-2 velocity power spectrum. In three dimensions solenoidal modes build-up during the supersonic phase delineating through time a Kolmogorov k-5/3 envelope and leaving a self-similarly decaying ∼k-0.9 spectrum at lower wave numbers.

Original languageEnglish (US)
Pages (from-to)13-49
Number of pages37
JournalTheoretical and Computational Fluid Dynamics
Issue number1
StatePublished - Nov 1 1992


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