Computation of Reynolds and boundary shear stress in submerged jets on rough boundaries

The results of a theoretical investigation on the Reynolds and boundary shear stresses in submerged jets on horizontal rough boundaries are presented. The decay of submerged jet and the growth of the boundary layer are formulated empirically. Then, the Reynolds and boundary shear stresses are theoretically determined integrating the Navier-Stokes equations aided by the functional relationships of the longitudinal velocity and the turbulence stresses within the boundary layer. Experiments were carried out to detect the velocity by an acoustic Doppler velocimeter (ADV) in submerged jets of different submergence ratios over rough boundaries. The theoretical results correspond reasonably with the experimental data. The Reynolds stress near the boundary is positive and diminishes sharply changing its sign to negative and forming protuberance that increases with increase in boundary roughness. However, the boundary shear stress diminishes with increase in longitudinal distance and increases with increase in boundary roughness.