A three-dimensional numerical model has been developed to simulate stratied ows with free surfaces. The model is based on the Reynolds-averaged Navier-Stokes (RANS) equations with variable-uid density. The equations are solved in a transformed-coordinate system with the use of operatorsplitting method (Int. J. Numer. Meth. Fluids 2002; 38: 1045-1068). The numerical model is validated against the one-dimensional diusion problem and the two-dimensional density-gradient-ow. Excellent agreements are obtained between numerical results and analytical solutions. The model is then used to study transport phenomena of dumped sediments into a water body, which has been modelled as a strongly stratied-ow. For the two-dimensional problem, the numerical results compare well with experimental data in terms of mean particle falling velocity and spreading rate of the sediment cloud for both coarse and medium-size sediments. The model is also employed to study the dumping of sediments in a three-dimensional environment with the presence of free surface. It is found that during the descending process an annulus-like cloud is formed for ne sediments whereas a plate-like cloud for medium-size sediments. The model is proven to be a good tool to simulate strongly stratied free surface ows. Copyright.

The flow motion of incompressible fluid can be described by Navier-Stokes equations with the continuity equation, which requires zero divergence of the velocity vector (i.e.,

In this paper, we develop an analytical technique in terms of series expansions to solve the mild-slope equation on an axisymmetric topography. This technique is applied to study the combined refraction and diffraction of plane monochromatic waves by a circular cylindrical island mounted on a paraboloidal shoal. By using the direct solution for the wave dispersion equation by Hunt [J. Waterw., Port, Coast., Ocean Div. Proc ASCE 4 (1979) 457], the mild-slope equation becomes explicit and it is then solved in terms of combined Fourier series and Taylor series. It is found that, to calculate the wave elevation along a perimeter with a specific radius, more terms in the Taylor series and angular modes in the Fourier series are needed for shorter waves. On the other hand, for the same incident wave, the outer the solutions are sought, more angular modes are needed to obtain the converged result of Fourier series. The comparison with the analytical solution based on the linear shallow-water equation by Homma [Geophys. Mag. 21 (1950) 199] is made for long wave incidence and excellent agreements are obtained. For long waves and waves in intermediate water depth, comparisons are made with other numerical results of the mild-slope equation and an equally good quality of agreement is achieved. D 2004 Elsevier B.V. All rights reserved.