Prediction of plane‐wise turbulent events to the Reynolds stress in a flow over scour‐bed

Abstract

In this paper, we intend to quantify the contribution of turbulent events to the total Reynolds shear stresses , , and from the four different quadrants of three different planes (xy, xz, yz); and to make a comparative study among the planes in the scour geometry developed by short circular cylinder of fixed length with a fixed diameter placed over the sand bed transverse to the flow. We also intend to predict the magnitude of covariance terms , , and and their contributions in the four quadrants by making use of the conditional probability distribution of the Reynolds shear stresses , , and , which can be derived by applying the cumulant‐discard method to the Gram‐Charlier probability distribution of the two variables. This consideration motivates the work on the flow over the obstacle marks generated on sand bed using different short cylinders. The contributions of burst‐sweep cycles to the Reynolds shear stresses from the planes over and within the scour around the obstacle are computed using the quadrant analysis to identify the leading shear stress plane, which are responsible to form the scour geometry. It is discovered that the yz and xy‐ planes are much more important in the scouring regions, whereas xz‐ plane is important for the smooth surface. Using cumulant‐discard method (taking into account the cumulants of less than fourth order), it is shown that the qualitative behaviours of turbulent events agree well with experimental data. Thus, it is confirmed that even the third‐order probability distribution of the Reynolds stresses can describe the experimental results very well.