Modeling Dredging-Induced Turbidity Plumes in the Far Field under Oscillatory Tidal Currents

A mathematical model previously developed based on a tide-averaged approach was extended to evaluate the temporal evolution of dredging-induced turbidity plumes in the far field under oscillatory tidal currents. The transient term ($\partial c/\partial t$) was retained in the governing advection-diffusion equation to predict the temporal evolution of the turbidity plume. An oscillatory tidal current velocity [$u(t)=V+U_0\hspace{0.17em}\text{sin}\hspace{0.17em}(\omega t)$] was assumed in the model formulation to represent the oscillatory tidal current. After being verified against benchmark simulations, the present model was used to simulate the diffusion of the turbidity plume, in particular its approach to quasi-steady state [i.e., when the suspended sediment concentration (SSC) exhibits periodic variation as a response to oscillatory tidal currents] as well as the SSC level at quasi-steady state. Sensitivity analyses were further performed to assess how key dimensionless modeling parameters—namely, the residual-to-oscillatory velocity ratio ($\nu$), Li and Kozlowski’s parameter ($\lambda$), the longitudinal-to-transverse diffusion coefficient ratio ($\alpha$), and the ratio of tide to settling time scale ($\phi$)—affect the model predictions. The model predicts distinctively different turbidity plume behaviors under mean and oscillatory tidal currents, which highlights the significance of incorporating the effects of tidal oscillation to model dredging-induced turbidity plumes in the far field more realistically.