Conditional Statistics of Reynolds Shear Stress over Scour-Hole Geometry

The study is devoted to quantify the near-bed turbulence parameters in open-channel flows over scour-hole geometry generated around the static short circular cylinders placed on the top of sediment-bed transverse to the flow. A reduction in near-bed velocity fluctuations due to the decrease of flow velocity relative to particle velocity of the transporting particles results in an excessive near-bed damping in Reynolds shear stress (RSS) distributions. The bed particles are associated with the momentum provided from the flow to maintain their motion overcoming the bed resistance. It leads to a reduction in RSS magnitude over the entire flow depth. The turbulent kinetic energy budget revels that for the scour region, the pressure energy diffusion rate near the bed changes sharply to a negative magnitude, implying a gain in turbulence production. According to the quadrant analysis (ejections, sweeps, inward interactions and outward interactions), sweep events are the principal mechanism of scouring process. Therefore main objective of the study is to predict the magnitude of the contribution to the Reynolds stress of bursting events: ‘ejections’, ‘sweeps’, ‘inward interactions’ and ‘outward interactions’. We shall do this by making use of the conditional probability distribution of the Reynolds stresses, which can be derived by applying the cumulant-discard method to the Gram-Charlier probability distribution of the two variables.

We shall verify that even the third-order conditional probability distribution of the Reynolds stress shows fairly good agreement with the experimental results and that the sequence of events in the bursting process, i.e. ejections, sweeps and interactions, is directly related to the turbulent energy budget in the form of turbulent diffusion.