High-order statistics and random additive model for turbulent boundary layers

Abstract eng:
A random additive process is introduced as a simplified version of the Townsend attached eddy hypothesis to describe fluctuations in the momentum cascade in wall turbulence at high Reynolds number. This formalism can provide economical predictions about scaling behaviors in single- and multiple-point turbulence statistics in the logarithmic region. New log laws for two-point quantities are identified and confirmed using experimental data. Secondly, properties of single- and two-point moment-generating- functions (⟨exp(qu)⟩ and ⟨exp[qu(x, z) + q ′ u(x + r, z)]⟩) are investigated, where q, q ′ are real-valued parameters. Empirical evidence of power law behaviors with respect to the wall normal distance in the logarithmic region in single-point moment-generating-function (MGF) is observed. Moreover, a power-law scaling transition in two-point MGF ⟨exp(qu(x, z)qu(x + r, z))⟩ is predicted in the framework of the random additive process and Townsend’s attached eddy hypothesis, and confirmed in experimental measurements.

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