A random sweeping decorrelation hypothesis explains the high-order moments of the longitudinal velocity in turbulent boundary layers

Abstract:

In his 1880 acceptance letter of the Rumford Prize, Gibbs declared that “One of the principal objects of theoretical research is to find the point of view from which the subject appears in the greatest simplicity". Guided by Gibb’s maxim, the ‘thorny’ topic of scaling laws for the normalized high-order turbulent longitudinal velocity with distance from the ground is considered. Expressions for their logarithmic variations with normalized distance from the boundary in the intermediate region of wall bounded flows are derived. This region is also where the von Kármán-Prandtl logarithmic law describes variations in the mean velocity with distance from the boundary. The ansatz is that these variations originate from a compound effect of random sweeping events and a -1 power-law scaling in the longitudinal velocity energy spectrum. Using longitudinal velocity time series sampled above a uniform ice sheet, the existence of a -1 power-law at production wavenumbers is first confirmed for near-neutral conditions. The data are then used to analyze assumptions required for the utility of the random sweeping decorrelation (RSD) hypothesis connecting the -1 power-law with log-scaling of the high-order moments of the normalized longitudinal velocity. It was found that while the RSD hypothesis is operationally applicable to scales associated with attached eddies, significant interactions among high-order turbulent velocity and velocity increments lead to the conclusion that the RSD hypothesis cannot be exactly valid. Its operational utility stems from the empirical finding that some of the interaction terms among the high-order velocity and velocity increments act in opposite directions thereby canceling their additive effects in RSD. The usage of Taylor’s frozen turbulence hypothesis on these findings are assessed using two scale-wise measures that sense Taylor’s hypothesis differently. The implications of using RSD to stratified atmospheric surface layer flows is briefly covered.