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.

CORMIX-GTS simulations are carried out to study suspended muddy sediment plumes following the discharge of the spoils taken from the seabed during a marine outfall pipeline dredging operation. Single port discharges are considered at three different locations at 400 m, 800 m, and 1200 m from the shoreline with water depths ranging from 3.5 m to 10.5 m. For discharges in the shallow near-shore region at 400 m offshore, most of the dredge materials are deposited at the seabed and the simulated suspended sediment plumes are found to be carrying a concentration of less than 1 kg/m3 of mainly fine silt and clay. For discharges in the deeper far-shore region at 1200 m offshore, the sediment plumes are more elongated and carrying a concentration of more than 3 kg/m3. Iterative simulations are also conducted to analyse the inherent uncertainty in the input data by varying the ambient velocity and the port’s horizontal angle of discharge.

A class of damped quasi-Newton methods for nonlinear optimization has recently been proposed by extending the damped-technique of Powell for the BFGS method to the Broyden family of quasi-Newton methods. It has been shown that this damped class has the global and superlinear convergence property that a restricted class of 'undamped' methods has for convex objective functions in unconstrained optimization. To test this result, we applied several members of the Broyden family and their corresponding damped methods to a simple quadratic function and observed several useful features of the damped-technique. These observations and other numerical experiences are described in this paper. The important role of the damped-technique is shown not only for enforcing the above convergence property, but also for improving the performance of efficient, inefficient and divergent undamped methods substantially (significantly in the latter case). Thus, some appropriate ways for employing the damped-technique are suggested.