Acceleration of passive tracers in compressible turbulent flow

Effect of shock waves on the statistics and scaling in compressible isotropic turbulence

The statistics and scaling of compressible isotropic turbulence in the presence of large-scale shock waves are investigated by using numerical simulations at turbulent Mach number M_{t} ranging from 0.30 to 0.65. The spectra of the compressible velocity component, density, pressure, and temperature exhibit a k^{-2} scaling at different turbulent Mach numbers. The scaling exponents for structure functions of the compressible velocity component and thermodynamic variables are close to 1 at high orders n≥3. The probability density functions of increments of the compressible velocity component and thermodynamic variables exhibit a power-law region with the exponent -2. Models for the conditional average of increments of the compressible velocity component and thermodynamic variables are developed based on the ideal shock relations and are verified by numerical simulations. The overall statistics of the compressible velocity component and thermodynamic variables are similar to one another at different turbulent Mach numbers. It is shown that the effect of shock waves on the compressible velocity spectrum and kinetic energy transfer is different from that of acoustic waves.

Influence of compressibility on the Lagrangian statistics of vorticity-strain-rate interactions

The objective of this study is to investigate the influence of compressibility on Lagrangian statistics of vorticity and strain-rate interactions. The Lagrangian statistics are extracted from "almost" time-continuous data sets of direct numerical simulations of compressible decaying isotropic turbulence by employing a cubic spline-based Lagrangian particle tracker. We study the influence of compressibility on Lagrangian statistics of alignment in terms of compressibility parameters-turbulent Mach number, normalized dilatation-rate, and flow topology. In comparison to incompressible turbulence, we observe that the presence of compressibility in a flow field weakens the alignment tendency of vorticity toward the largest strain-rate eigenvector. Based on the Lagrangian statistics of alignment conditioned on dilatation and topology, we find that the weakened tendency of alignment observed in compressible turbulence is because of a special group of fluid particles that have an initially negligible dilatation-rate and are associated with stable-focus-stretching topology.