Tide-induced vertical suspended sediment concentration profiles: phase lag and amplitude attenuation

Abstract

In tidal environments, the response of suspended sediment concentration (SSC) to the current velocity is not instantaneous, the SSC lagging behind the velocity (phase lag), and the amplitude of SSC variation decreasing with height above the bed (amplitude attenuation). In order to quantitatively describe this phenomenon, a one-dimensional vertical advection–diffusion equation of SSC is derived analytically for uniform unsteady tidal flow by defining a concentration boundary condition using a constant vertical eddy diffusivity and sediment settling velocity. The solution, in simple and straightforward terms, shows that the vertical phase lag increases linearly with the height above the bed, while the amplitude of the SSC variation decreases exponentially with the height. The relationship between the SSC and the normalized current velocity can be represented by an ellipse or a line, depending on the phase lag. The lag of sediment movement or “diffusion/settling lag” is the mechanism generating the phase lag effect. Field observations used for validation show that the theoretically predicted and the observed curves of the vertical SSC phase lag and amplitude attenuation show reasonable agreement. The procedure proposed in this paper substantially simplifies the modeling of suspended matter transport in tidal flows.