Abstract
The velocity derivative skewness and its budget equation are analysed in non-equilibrium time-reversed turbulence. We show that the positive skewness is related to the behaviors of backward energy transfer and enstrophy divergence during the non-equilibrium procedure. A dynamic equilibrium state of the turbulence corresponds to a balanced budget of the skewness, whereas the balance is destroyed when the turbulence is perturbed and with a non-equilibrium phenomenon. Production and pressure terms are dominant to the evolution of the skewness compared to the viscosity term. Furthermore, based on this budget equation, a theoretical value of the skewness is derived for sufficiently high-Reynolds turbulent flows. The budget presented here might inspire future investigations for the modeling of non-equilibrium turbulence.
Highlights
In a recent study it was observed that in the beginning stage of the RN and RR cases, the flows are non-equilibrium.43 Figure 1 shows this phenomenon by temporal evolution of the skewness of longitudinal velocity derivative Sk as well as its comparison with the NN case
We analysed the velocity derivative skewness and its budget equation since the skewness is an important parameter for describing the non-equilibrium properties
With the help of numerical results for time-reversed non-equilibrium turbulent flows, we summarize the observations as follows: 1. The positive skewness is related to the behaviors of backward energy transfer and enstrophy divergence during the non-equilibrium procedure
Summary
In a recent study it was observed that in the beginning stage of the RN and RR cases, the flows are non-equilibrium.43 Figure 1 shows this phenomenon by temporal evolution of the skewness of longitudinal velocity derivative Sk as well as its comparison with the NN case. The skewness of longitudinal velocity derivative is a key factor for represent the degree of non-equilibrium property, as the third-order statistics are tightly related to the energy transfer.
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