Exact time scale of energy exchange in triad interactions of homogeneous isotropic turbulence

Abstract

We solve analytically the period of a single triad interaction of homogeneous isotropic turbulence. Comparing with the traditional concept of the timescale of energy transfer, we found that this period is a timescale of energy exchange among the three wave vectors of a triad. Quantitatively, the timescale of energy exchange is usually longer if the equilibrium dissipation law is satisfied; however, when energy transfer is suppressed, the energy exchange becomes dominant. We extract the periods in typical numerical experiments of triad interactions and show that they are in good agreement with theoretical predictions. This picture implies that energy exchange corresponds to oscillation, while energy transfer corresponds to damping, and the damping rate is correlated with the oscillation. The present results of the timescale of energy transfer are expected to be applied in nonequilibrium turbulent flows.

Existence of positive skewness of velocity gradient in early transition

“…In particular, a triad phase, φ 1 ( p) + φ 1 ( q) − φ 1 ( k), is explicitly represented on the right-hand side, indicating the link between S k and the phase of velocities (see Refs. [11,[38][39][40] for more discussions). This expression explicitly illustrates that both the amplitudes and the phases can affect the evolution of S k .…”