Co-spectrum and mean velocity in turbulent boundary layers

TY - JOUR

T1 - Co-spectrum and mean velocity in turbulent boundary layers

AU - Katul, Gabriel G.

AU - Porporato, Amilcare

AU - Manes, Costantino

AU - Meneveau, Charles

N1 - Funding Information: G.G.K. and A.P. acknowledge support from the National Science Foundation (Grant Nos. NSF-EAR-1013339, NSF-AGS-1102227, and NSF-CBET-103347), the United States Department of Agriculture (Grant No. 2011-67003-30222), the U.S. Department of Energy (DOE) through the office of Biological and Environmental Research (BER) Terrestrial Ecosystem Science (TES) Program (Grant No. DE-SC0006967), and the Binational Agricultural Research and Development (BARD) Fund (Grant No. IS-4374-11C). C.M. and G.G.K. thank the École Polytechnique Fédérale de Lausanne (EPFL) and M.B. Parlange for all their hospitality during the summer of 2013 that facilitated this research.

PY - 2013/9/18

Y1 - 2013/9/18

N2 - Connections are explored between spectral descriptions of turbulence and the mean velocity profile in the equilibrium layer of wall-bounded flows using a modeled budget for the co-spectral density. Using a standard model for the wall normal velocity variance and a Rotta-like return-to-isotropy closure for the pressure-strain effects, the co-spectrum is derived. The approach establishes a relation between the von Kármán (κ), one-dimensional Kolmogorov (CK'), and Rotta (A) constants, namely, κ=(4A/7CK')-3/4. Depending on the choices made about small-scale intermittency corrections, the logarithmic mean velocity profile or a power-law profile with an exponent that depends on the intermittency correction are derived thereby offering a new perspective on a long standing debate.

AB - Connections are explored between spectral descriptions of turbulence and the mean velocity profile in the equilibrium layer of wall-bounded flows using a modeled budget for the co-spectral density. Using a standard model for the wall normal velocity variance and a Rotta-like return-to-isotropy closure for the pressure-strain effects, the co-spectrum is derived. The approach establishes a relation between the von Kármán (κ), one-dimensional Kolmogorov (CK'), and Rotta (A) constants, namely, κ=(4A/7CK')-3/4. Depending on the choices made about small-scale intermittency corrections, the logarithmic mean velocity profile or a power-law profile with an exponent that depends on the intermittency correction are derived thereby offering a new perspective on a long standing debate.

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U2 - 10.1063/1.4821997

DO - 10.1063/1.4821997

M3 - Letter

SN - 1070-6631

VL - 25

JO - Physics of Fluids

JF - Physics of Fluids

IS - 9

M1 - 091702

ER -