| Abstrakt: |
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 Reτ. 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 Reτ, owing to the natural constraint that the dissipation rate is bounded. Specifically, Φ∞ - Φ = CΦ Re-1/4τ, 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 CΦ depends on Φ but not on Reτ. Moreover, there exists a scaling law for the maximum value in the wall-normal direction of high-order moments, of the form (ϕ2q)1/q max = αq - βq Re-1/4τ, where ϕ represents the streamwise or spanwise velocity fluctuation, and αq and βq are independent of Reτ. 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 αq on q. [ABSTRACT FROM AUTHOR] |
