Extended self-similarity in moment-generating-functions in wall-bounded turbulence at high Reynolds number

In wall-bounded turbulence, the moment generating functions (MGFs) of the streamwise velocity fluctuations < exp(qu(z)(+))> develop power-law scaling as a function of the wall normal distance z/delta Here u is the streamwise velocity fluctuation, + indicates normalization in wall units (averaged friction velocity), z is the distance from the wall, q is an independent variable, and delta is the boundary layer thickness. Previous work has shown that this power-law scaling exists in the log-region 3Re(tau)(0.5) less than or similar to z(+), z less than or similar to 0.15 delta where Re-tau is the friction velocity-based Reynolds number. Here we present empirical evidence that this self-similar scaling can be extended, including bulk and viscosity-affected regions 30 < z(+), z < delta, provided the data are interpreted with the Extended-Self-Similarity (ESS), i.e., self-scaling of the MGFs as a function of one reference value, q(o). ESS also improves the scaling properties, leading to more precise measurements of the scaling exponents. The analysis is based on hot-wire measurements from boundary layers at Re-tau ranging from 2700 to 13 000 from the Melbourne High-Reynolds-Number-Turbulent-Boundary-Layer-Wind-Tunnel. Furthermore, we investigate the scalings of the filtered, large-scale velocity fluctuations u(z)(L) and of the remaining small-scale component, u(z)(S) = u(z) - u(z)(L). The scaling of u(z)(L) falls within the conventionally defined log region and depends on a scale that is proportional to l(+) similar to Re-tau(1/2); the scaling of u(z)(S) extends over a much wider range from z(+) approximate to 30 to z approximate to 0.5 delta. Last, we present a theoretical construction of two multiplicative processes for u(z)(L) and U-z(L) that reproduce the empirical findings concerning the scalings properties as functions of z(+) and in the ESS sense.