Moment generating functions and scaling laws in the inertial layer of turbulent wall-bounded flows

Abstract

Properties of single- and two-point moment generating functions (MGFs) are examined in the inertial region of wall-bounded flows. Empirical evidence for power-law scaling of the single-point MGF 〈exp(qu+)〉 (where u+ is the normalized streamwise velocity fluctuation and q a real parameter) with respect to the wall-normal distance is presented, based on hot-wire data from a Reτ = 13 000 boundary-layer experiment. The parameter q serves as a 'dial' to emphasize different parts of the signal such as high- and low-speed regions, for positive and negative values of q, respectively. Power-law scaling 〈exp(qu+)〉 ∼ (z/δ)-τ(q) can be related to the generalized logarithmic laws previously observed in h..