Self-similarity in turbulent wall-wake flow downstream of a wall-mounted vertical cylinder

The time-averaged turbulent flow characteristics in a wall-wake flow downstream of a wall-mounted vertical cylinder (free-surface piercing) are analyzed from the viewpoint of self-similarity in their vertical profiles. In a wall-wake flow, the deficits (differences between upstream and downstream values at a given elevation) in streamwise velocity, Reynolds shear stress, turbulence intensities, and third-order moments exhibit a certain degree of self-similarity in their vertical profiles when they are scaled by their respective maximum deficit values. For scaling the vertical distance to achieve the self-similarity, the velocity deficit profiles are scaled by the half-thickness of maximum velocity deficit, whereas the profiles of all other aforementioned turbulence quantities are scaled by the half-thickness of Reynolds shear stress deficit. The values of the maximum deficit of all the quantities diminish with the downstream distance, signifying the recovery of their uninterrupted upstream profiles. The deficits in mixing length and turbulent length (the Taylor microscale) scale also exhibit a certain degree of similarity in their profiles, when they are appropriately scale.