Saltation Layer of Particles in Water Flows Related to Transport Stage

A theoretical model has been developed to determine the maximum saltation layer thickness of sediment particles in water associated with the migration velocity of particle in the bed layer. This is consistent with Owen's (1964) hypothesis for saltation of uniform grain in air. The equation for mean particle velocity at the bed is derived by balancing the horizontal forces acting on the particle in the bed. The modified expression for mean particle velocity includes the effects of drag and lift coefficients, bed shear stress, coefficient of dynamic friction, settling velocity and pivoting angle. The saltation layer model presented here extends a reasonable physical assumption by converting the average horizontal particle velocity to a vertical component of velocity due to collisions with particles resting on the bed. This explicitly shows a functional dependence of saltation height on mean particle velocity and take-off angle. The proposed model has been tested using available experimental data and the agreement with particle velocities and saltation heights is excellent. An interesting outcome is that a quadratic relationship is suggested between the higher transport stage (upper plane bed) and the take-off angle of particle. This shows that the take-off angle decreases with increase in transport stage.