Wall-Wake Flows Downstream of a Sphere Placed on a Plane Rough Wall

The time-averaged characteristics of turbulent wall-wake flows downstream of a sphere placed on a rough wall are studied. The profiles of the defect of streamwise velocity, Reynolds shear stress, and turbulence intensities exhibit some degree of similarities when they are scaled by their respective peak defect values. For the velocity defect profiles, the vertical distances are scaled by the height of the location of the half-peak velocity defect. However, for the defect profiles of the Reynolds shear stress and the turbulence intensities, the vertical distances are scaled by the height of the location of the half-peak Reynolds shear stress defect. The magnitudes of the peak defect of all the quantities diminish with the distance downstream of the sphere characterizing the recovery of their undisturbed profiles. Additionally, the theoretical similarity solution for the velocity defect profiles is obtained. The third-order correlations imply that in the inner layer of wall wakes, a streamwise acceleration is prevalent and associated with a downward flux, suggesting sweeps. In contrast, in the outer layer, a streamwise deceleration exists and is associated with an upward flux, suggesting ejections. The profiles of the energy budget show that the turbulent and pressure energy diffusions oppose each other. The turbulent production has a positive peak, and the pressure energy diffusion has a negative peak, indicating a large gain in turbulence production in the wall-wake flows. The quadrant analysis confirms that in wall-wake flows, sweeps are the governing mechanism resulting from an inrush of fluid streaks. The bursting events have shorter duration, but they are more frequent than those in upstream.