Analytical solutions for sediment concentration in waves based on linear diffusivity

摘要

Two kinds of analytical solutions are derived through Laplace transform for the equation that governswave-induced suspended sediment concentration with linear sediment diffusivity under two kinds ofbottom boundary conditions,namely the reference concentration(Dirichlet)and pickup function(Nu-mann),based on a variable transformation that is worked out to transform the governing equation intoa modified Bessel equation.The ability of the two analytical solutions to describe the profiles of sus-pended sediment concentration is discussed by comparing with different experimental data.And it isdemonstrated that the two analytical solutions can well describe the process of wave-induced suspendedsediment concentration,including the amplitude and phase and vertical profile of sediment concentra-tion.Furthermore,the solution with boundary condition of pickup function provides better results thanthat of reference concentration in terms of the phase-dependent variation of concentration.