Bounded dissipation law and profiles of turbulent velocity moments in wall flows

Understanding the effects of solid boundaries on turbulent fluctuations remains a long-standing challenge. Available data on mean-square fluctuations in these flows show apparent contradiction with classical scaling. We had earlier proposed an alternative model based on the principle of bounded dissipation. Despite its putative success, a conclusive outcome requires much higher Reynolds numbers than are available at present, or can be expected to be available in the near future. However, the model can be validated satisfactorily even within the Reynolds number range already available by considering high-order moments and their distributions in the wall-normal direction. Expressions for high-order moments of streamwise velocity fluctuation [Formula: see text] are derived in the form [Formula: see text], where the superscript [Formula: see text] indicates the wall unit normalization, and brackets stand for averages over time and the homogeneous plane normal to the wall, [Formula: see text] is an integer, [Formula: see text] and [Formula: see text] are constants independent of the friction Reynolds number [Formula: see text], and [Formula: see text] is the distance away from the wall, normalized by the flow thickness [Formula: see text]. In particular, [Formula: see text] according to the "linear q-norm Gaussian" process, where [Formula: see text] and [Formula: see text] are flow-independent constants. Excellent agreement is found between this formula and the available data in boundary layers, pipes, and channels for [Formula: see text]. For fixed [Formula: see text], the present formulation leads to the bounded state [Formula: see text] as [Formula: see text]. This work demonstrates the success of the present model in describing the behavior of fluctuations in wall flows.