Longitudinal and transverse structure functions in high-Reynolds-number turbulence

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