## Abstract

We present results from 128^{3} and 256^{3} direct numerical simulations (DNS) of decaying compressible, isotropic turbulence at fluctuation Mach numbers of M_{t} ˜0.1-0.5 and at Taylor Reynolds numbers Re_{λ} = O(50-100). The presence or absence of fluctuations of thermodynamic quantities as well as velocity divergence in the initial conditions are found to have a negligible effect on the decay of turbulent kinetic energy. The decay of the turbulent kinetic energy shows no significant effect of M_{t} and power laws fitted to the timewise decay exhibit exponents n = 1.3-1.7 that are similar to those found for decaying incompressible turbulence. The main new phenomenon produced by compressibility is the appearance of random shocklets which form during the main part of the decay. An algorithm is developed to extract and quantify the shocklet statistics from the DNS fields. A model for the probability density function (PDF) of the shocklet strength M_{n} - I (M_{n} is the normal shock Mach number) is derived based on combining weak-shock theory with a model of the PDF of longitudinal velocity differences in the turbulence. This shows reasonable agreement with PDFs obtained from the shocklet extraction algorithm. The model predicts that at moderate M_{t} the most probable shocklet strength is proportional to M_{t}/Re_{λ}^{1/}1^{2} and also that the PDF for the shock thicknesses has an inverse cubic tail. The shock thickness statistics are found to scale on the Kolmogorov length rather than the mean free path in the gas.

Original language | English (US) |
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Pages (from-to) | 1415-1430 |

Number of pages | 16 |

Journal | Physics of Fluids |

Volume | 13 |

Issue number | 5 |

DOIs | |

State | Published - May 2001 |

Externally published | Yes |

## ASJC Scopus subject areas

- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Fluid Flow and Transfer Processes
- Computational Mechanics