An analytical solution for the local suspended sediment concentration profile in tidal sea region

Abstract

The time-averaged and oscillatory solutions of the one-dimensional vertical (1DV) advection-diffusion equation for the suspended sediment have been derived analytically in a tidal sea region of finite water depth. The basic equation assumes constant eddy diffusivity and settling velocity. No net flux condition is set at the sea surface, while a boundary condition with the erosion rate and depositional velocity is prescribed at the sea bottom. The time-averaged solution has been derived in a straightforward manner, while the advection-diffusion equation governing the oscillatory concentration has been first transformed to a simple diffusion equation and then solved using the Galerkin-eigenfunction method. The former is given in a closed form, while the latter is presented in a series solution. A set of calculations has been performed to examine the change in the vertical structure as well as magnitude of the concentration response function. A possible use of the solution to make an estimate of the erosion rate at the sea bottom based on the concentration information at the sea surface is discussed. (C) 2004 Elsevier Ltd. All rights reserved.