Scalings of turbulence dissipation in space and time for turbulent channel flow

We investigate the turbulence dissipation scaling in turbulent channel flow in connection with Kolmogorov's equilibrium dissipation scaling. We determine the scalings of three different integral length scales arising from the non-isotropy of the flow, each integral scale resulting in different scalings for the dissipation coefficient. We retrieve the classical Taylor-Kolmogorov dissipation scaling when integral scales based on the wall-normal velocity are used, but we also find a new non-homogeneous dissipation scaling when the dissipation coefficient is computed from the integral scale of the spanwise velocity in the spanwise direction. We also analyse the time dynamics of the dissipation coefficient and the Taylor length-based Reynolds number and find that the two signals are anti-correlated with absolute correlation values from 0.5 to 0.9 across the channel. This translates into an inverse average power-law scaling of the fluctuating dissipation coefficient as a function of Taylor Reynolds number, with exponent between -1 and -1.7 depending on wall-normal direction and choice of integral scale. This anti-correlation must reflect a non-stationary cascade and, in fact, persists when the signals are filtered using either low- or high-pass filters.