Anisotropy Properties of Turbulence in Flow Over Seepage Bed

Abstract

Abstract This present study analyzes the Reynolds stress anisotropy in the nonuniform sediment beds under the condition of no seepage and downward seepage flow. The results show the estimation of the deviation measure from the isotropic turbulence in view of Reynolds stress tensor for turbulent flow in the presence of seepage through the channel bed. The investigation presents the Lumley triangle for flow turbulence, Eigen values, and the invariant functions for the whole flow depth subjected to no seepage and seepage beds. The longitudinal profile of anisotropy tensor within the near-bed zone for seepage flow provides the higher anisotropic stream than those of no seepage flow, while the remaining (transverse and vertical) profiles of anisotropy tensor in the vicinity of bed for seepage flows provide lower anisotropic stream. The anisotropic invariant maps show the near bed anisotropy inclining to be a two-component isotropy subjected to no seepage and seepage flow. With the increase in vertical distance from bed surface that is close to the water surface, the data sets of anisotropic invariant maps for no seepage and seepage flows show a trend of one-component isotropy, while it has an affinity to develop a three-component isotropy in the vicinity of midzone of the flow depth. Invariant function data sets present a well two-component isotropy in the near bed region of flow and a quasi-three component isotropy in the outer region of flow for seepage flows as compared to no seepage flow.