Asymmetry of velocity increments in fully developed turbulence and the scaling of low-order moments

A study is made of the scaling of the positive part (PP) and the negative part (NP) of velocity increments in turbulent pipe flow and in simulated homogeneous turbulence in a box. For moment orders above unity, the moments of NP are larger than those of PP for all separation distances, and the scaling exponents for PP are larger than those for NP. For moment orders below unity, the absolute value of the velocity increment and of NP, as well as PP, possess scaling exponents which vary linearly with the moment order q, though apparently greater than q/3.