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

Abstract

The existence of a large-scale non-equilibrium dissipation law (Cε∼Reλ−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 (Cε∼Reλ−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.

Unsteady and Inhomogeneous Turbulent Fluctuations around Isotropic Equilibrium

“…Again, these approaches extend the results for inertial range quantities to integral lengths and timescales. A recent extension where the small scales are perturbed instead of the large ones is proposed [93] and numerically verified [94], yielding an expression similar to Equation ( 27), but with an exponent close to −2 instead of −15/14.…”