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Study of unsteady nonequilibrium stratified suspended sediment distribution in open-channel turbulent flows using shifted Chebyshev polynomials

ABSTRACT In this paper the effect of stratification on vertical variation of sediment concentration in the suspended-load layer in turbulent flows through open channels under unsteady and nonequilibrium condition is investigated. Unlike previous studies, the model includes the effect of stratification in terms of reduction of the eddy diffusivity. A new approach for solving the governing advection-diffusion equation using orthogonal shifted Chebyshev polynomials of fourth kind is presented. In this approach, the solution of the problem is obtained using a finite degree Chebyshev polynomial. The distribution of the sediment diffusivity is considered including the effect of stratification. Three different types (constant, linear and parabolic) of sediment diffusivity distribution is considered both in neutral and stratified flow condition. The final transport equation is solved under both neutral and stratified condition and appropriate bottom boundary condition using the conventional backward Euler scheme. The method is unconditionally convergent and converges more rapidly than previous methods as Laplace transformation and generalized integral transformation technique. The solutions are compared with previous methods and satisfactory results are obtained. The proposed solutions are also validated with experimental data under steady flow conditions. Results show that under stratified flow condition, sediment concentration also decreases when flow is still unsteady.