TY - JOUR

T1 - Law of bounded dissipation and its consequences in turbulent wall flows

AU - Chen, Xi

AU - Sreenivasan, Katepalli R.

N1 - Funding Information:
X.C. acknowledges support from the National Natural Science Foundation of China, grant nos. 12072012, 11721202 and 91952302.
Publisher Copyright:
© The Author(s), 2021. Published by Cambridge University Press.

PY - 2022/2/25

Y1 - 2022/2/25

N2 - 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. 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, owing to the natural constraint that the dissipation rate is bounded. Specifically, where 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, and the coefficient depends on but not on. Moreover, there exists a scaling law for the maximum value in the wall-normal direction of high-order moments, of the form, where represents the streamwise or spanwise velocity fluctuation, and and are independent of. 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 -norm Gaussian', is proposed to explain the observed linear dependence of on.

AB - 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. 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, owing to the natural constraint that the dissipation rate is bounded. Specifically, where 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, and the coefficient depends on but not on. Moreover, there exists a scaling law for the maximum value in the wall-normal direction of high-order moments, of the form, where represents the streamwise or spanwise velocity fluctuation, and and are independent of. 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 -norm Gaussian', is proposed to explain the observed linear dependence of on.

KW - pipe flow boundary layer

KW - turbulence theory

KW - turbulent boundary layers

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U2 - 10.1017/jfm.2021.1052

DO - 10.1017/jfm.2021.1052

M3 - Article

AN - SCOPUS:85122805669

VL - 933

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

M1 - A20

ER -