Recently, it was observed that in nonequilibrium turbulent flows the normalized dissipation rate depends in a fairly universal way on the Reynolds number of the flow. To assess theoretical explanations of this observation, we consider here the nonequilibrium properties of freely decaying turbulence from initial conditions where the velocity field is reversed in every point in space. This test-case allows us to manipulate a turbulent flow differently from the usual way, where nonequilibrium is induced by modification of large-scale forcing mechanisms. It is shown that it is possible to obtain a different Reynolds-dependent scaling of the dissipation rate, which can be derived directly as a perturbation around the equilibrium state.

We derive from first principles analytic relations for the second- and third-order moments of $\boldsymbol{\mathsf{m}}$ , the spatial gradient of fluid velocity $\boldsymbol{u}$ , $\boldsymbol{\mathsf{m}} = \nabla \boldsymbol{u}$ , in compressible turbulence, which generalize known relations in incompressible flows. These relations, although derived for homogeneous flows, hold approximately for a mixing layer. We also discuss how to apply these relations to determine all the second- and third-order moments of the velocity gradient experimentally for isotropic compressible turbulence.

Non-equilibrium turbulent flows were considerably investigated in recent years, but most studies are restricted in grid-generated turbulence. In the present contribution we show by large-eddy simulation (LES), that there exists a weakly non-equilibrium turbulence region before the beginning of the full-developed turbulence. Both the dissipation coefficient and the skewness of longitudinal velocity gradient are used as characteristic non-equilibrium quantities, illustrating that the non-equilibrium turbulence region in channel flow is weakly similar to previous studies in grid-generated turbulence. The observation of non-equilibrium turbulence region in transitional channel flow is also expected to inspire future improvement of turbulence models.