Law of bounded dissipation and its consequences in turbulent wall flows

The dominant paradigm in turbulent wall flows is that the mean velocity near the wall, when scaled on wall variables, is independent of the friction Reynolds number Re-tau. This paradigm faces challenges when applied to fluctuations but has received serious attention only recently. Here, by extending our earlier work (Chen & Sreenivasan, J. Fluid Mech., vol. 908, 2021, p. R3) we present a promising perspective, and support it with data, that fluctuations displaying non-zero wall values, or near-wall peaks, are bounded for large values of Re-tau, owing to the natural constraint that the dissipation rate is bounded. Specifically, Phi(infinity) - Phi = C-Phi Re-tau(-1/4), where Phi represents the maximum value of any of the following quantities: energy dissipation rate, turbulent diffusion, fluctuations of pressure, streamwise and spanwise velocities, squares of vorticity components, and the wall values of pressure and shear stresses; the subscript infinity denotes the bounded asymptotic value of Phi, and the coefficient C-Phi depends on Phi but not on Re-tau. Moreover, there exists a scaling law for the maximum value in the wall-normal direction of high-order moments, of the form (1/q)(max) = alpha(q) - beta(q) Re-tau(-1/4), where. represents the streamwise or spanwise velocity fluctuation, and alpha(q) and beta(q) are independent of Re-tau. Excellent agreement with available data is observed. A stochastic process for which the random variable has the form just mentioned, referred to here as the 'linear q-norm Gaussian', is proposed to explain the observed linear dependence of alpha(q) on q.

Automated summary

The dominant paradigm in turbulent wall flows, stating that the mean velocity near the wall is independent of the friction Reynolds number, has been challenged in recent research. This study presents a promising perspective supported by data, suggesting that fluctuations displaying non-zero wall values or near-wall peaks are bounded for large friction Reynolds numbers due to the natural constraint of bounded dissipation rate.