Conditionally averaged turbulent structures in 2D channel flow

This paper investigates conditionally averaged turbulent structures and the underlying mechanism of the wake law in two-dimensional (2D) uniform flow. By dividing the wall-normal velocity fluctuation into upward and downward conditions, conditionally averaged momentum equations are derived. The theoretical results show that the momentum flux caused by the conditionally upward/downward velocity leads to deviation of the conditional Reynolds shear stress from the expected linear distribution and consequently the conditionally turbulent intensities are affected; however, a self-similarity between the turbulent intensities and the Reynolds shear stress exists. It is found that in 2D flows, the wake function is also caused by the additional momentum flux. As the up/down movements of fluid particles are caused by intermittent decelerating/accelerating motions in the streamwise direction, the wake function is actually the result of an accelerating/decelerating process that causes fluctuations of pressure or water level. This study reveals that the frequency and conditional features of up/down motions rely on pressure fluctuations in pipe flow and water level variation in open-channel flows.