Turbulent Shear Stress in Heterogeneous Sediment-laden Flows

Current knowledge of the mechanics of alluvial channels depends very largely on calculations of turbulent shear stresses; typical examples are the beginning of motion of sediment particles and sediment transport in alluvial channels. If shear stress can be well defined in clear-water flows, comparatively little is known about shear stresses in sediment-laden flows. Einstein and Chien (1955) proposed a turbulent shear stress relationship that does not depend on the fall velocity of uniform sediment particles. Opposite results were later proposed by Zagustin (1969) and Willis (1972). This study briefly reviews existing relationships for turbulent shear stress in homogeneous sediment-laden flows, and proposes a derivation of turbulent shear stress in heterogeneous sediment-laden flows. The analysis of turbulent shear stress for steady-uniform flows carrying heterogeneous sediment mixtures provides additional insight on the role played by sediment size gradation and fall velocity by size fraction.