Longitudinal and Transverse structure functions in high Reynolds-number turbulence

2010/12/18 by Rainer Grauer, Grauer, Rainer, Holger Homann +3 · 2 citations
Engineering · Environmental Science · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Hydrology and Drought Analysis #Wind and Air Flow Studies

paper · doi:10.48550/arxiv.1012.4070

openalex publication_date 2010/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using exact relations between velocity structure functions (Hill, Hill and Boratav, and Yakhot) and neglecting pressure contributions in a first approximation, we obtain a closed system and derive simple order-dependent rescaling relationships between longitudinal and transverse structure functions. By means of numerical data with turbulent Reynolds numbers ranging from \Re_λ=320 to \Re_λ=730, we establish a clear correspondence between their respective scaling range, while confirming that their scaling exponents do differ. This difference does not seem to depend on Reynolds number. Making use of the Mellin transform, we further map longitudinal to (rescaled) transverse probability density functions.

Cited by

• Synthetic Turbulence via an Instanton Gas Approximation
• Predicting any small-scale statistics of high-Reynolds-number turbulence using ensemble simulations

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