Non-equilibrium dissipation laws in a minimal two-scale wake model

The existence of a large-scale non-equilibrium dissipation law (Ce similar to Re-lambda(-15/14)) has been well documented through various experiments conducted on grid-generated turbulent wake flows. In our previous studies, we have successfully demonstrated the coexistence of a rapid non-equilibrium dissipation law (C-epsilon similar to Re-lambda(-2)) before the large-scale counterpart in homogeneous isotropic turbulence with inversed or perturbed initial conditions and accordingly developed the closure models. In this paper, we introduce a simplified minimal two-scale wake model, which serves as a simplification of grid-generated turbulence experiments. It is evident that both the large-scale and rapid non-equilibrium dissipation laws coexist in this flow, similar to our previous studies in homogeneous isotropic turbulence. Moreover, we show that the utilization or exclusion of spanwise averages does not significantly affect the qualitative characteristics of non-equilibrium behaviors. Furthermore, by investigating the turbulent/non-turbulent interface, we argue that the presence of coherent structures is not necessarily required to generate the scaling associated with non-equilibrium behavior.

Automated summary

The existence of a large-scale non-equilibrium dissipation law has been confirmed through experiments on grid-generated turbulent wake flows. Previous studies have shown the coexistence of a rapid non-equilibrium dissipation law before the large-scale counterpart in homogeneous isotropic turbulence. In this paper, a simplified minimal two-scale wake model is introduced, which confirms the coexistence of both dissipation laws similar to previous studies.