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_τ. This paradigm faces challenges when applied to fluctuations but has received serious attention only recently. Here, 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_τ, owing to the natural constraint that the dissipation rate is bounded. Specifically, Φ_∞-Φ =C_ΦRe_τ^-1/4, where Φ 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 ∞ denotes the bounded asymptotic value of Φ and the coefficient C_Φ depends on Φ but not on Re_τ. Moreover, there exists a scaling law for the maximum value in the wall-normal direction of high-order moments, of the form 〈ϕ^2q〉^1/q_max = α_q-β_qRe_τ^-1/4, where ϕ represents the streamwise or spanwise velocity fluctuation and α_q and β_q are independent on Re_τ. 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 α_q on q.