Shocklet statistics in compressible isotropic turbulence

Shocklet statistics in compressible isotropic turbulence are studied by using numerical simulations with solenoidal forcing, at the turbulent Mach number Mt ranging from 0.5 up to 1.0 and at the Taylor Reynolds number Re. ranging from 110 to 250. A power-law region of the probability density function (PDF) of the shocklet strength M-n - 1 (Mn is the normal shock Mach number) is observed. The magnitude of the power-law exponent is found to decrease with the increase of Mt. We show that the most probable shocklet strength is proportional to M-t(3), and the shocklet thickness corresponding to the most probable shock Mach number is proportional to M-t(-2) in our numerical simulations. The PDFs of the jumps of the velocity and thermodynamic variables across a shocklet exhibit a similar power-law scaling. The statistics of the jumps of the velocity and thermodynamic variables are further investigated by conditioned average. Nonlinear models for the conditional average of the jumps of the velocity and thermodynamic variables are developed and verified.