Longitudinal and Transverse structure functions in high Reynolds-number turbulence

Details Longitudinal and Transverse structure functions in high Reynolds-number turbulence Longitudinal and Transverse structure functions in high Reynolds-number turbulence

2010-12-18

arxiv.org/abs/1012.4070v1

Physics

Fluid Dynamics

4 pages, 3 figures

Scientific paper

Using exact relations between velocity structure functions \cite{hill:2001,hill-boratav:2001,yakhot:2001} and neglecting pressure contributions in a first approximation, we obtain a closed system and derive simple rescaling relationships between longitudinal and transverse structure functions. By means of numerical data with turbulent Reynolds numbers ranging from $\Re_\lambda=320$ to $\Re_\lambda=730$, we show that they share the same inertial range after rescaling, while having different scaling exponents. 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.

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