Journal of Waterway, Port, Coastal, and Ocean Engineering

A vertical two-dimensional numerical model for local scour beneath an offshore pipeline exposed to waves is developed in this study. Waves are modeled as sinusoidally oscillatory flows, and the phase-resolved velocity field around the pipeline is simulated by solving the Reynolds-averaged Navier-Stokes equations with a $k\text{-}\omega$ turbulence closure. Both suspended and bed loads of sediment transport are considered in the model. A special technique for coupling the solution of the flow field to the scour calculation is developed to accommodate different timescales of the flow and morphological changes. The seabed morphology calculation is based on the period-averaged sediment transport rate with a morphological time step that is chosen by designating a maximum allowable bed deformation in each update. Numerical tests indicate that this technique significantly reduces the computational costs and is of acceptable accuracy. A sand-slide method is employed after each bed update to smooth out small bed irregularities. The model is applied to simulate three cases of wave-induced scour below a pipeline where laboratory measurements were published in the literature. The predicted scour-hole profiles compare favorably with the laboratory observations.

To investigate changes in the mean velocity profile owing to the interaction between waves and a current, the horizontal and vertical velocity components in the oscillating fluid were measured by a two-dimensional laser anemometer in a recirculating wave tank. The observed instantaneous velocity data concerning waves following and opposing a current were analyzed to obtain the Eulerian-mean velocity, the wave-current Reynolds stress, and the wave-current turbulent intensities. The wave-current Reynolds stress behaves differently when current direction changes. The general characteristic of the Eulerian-mean velocity is greatly affected by the wave-current Reynolds stress. The mean velocity for waves following (opposing) a current is reduced (increased) towards the free surface, when compared with the logarithmic profile. These velocity data were used to verify the results by velocity equations based on the phase-averaged Prandtl momentum-transfer theory. In addition, measurement of water-surface elevations revealed that the phase-averaged waveform for a pure wave is peaked near the crest but flatter near the trough and the variation of the water surface is well predicted by the third-order Stokes wave equation. The original pattern of the waveform varies due to the wave-current interaction, but the current direction only minimally affects the attenuation of the surface waves.

This paper describes the validation and application of a hydrodynamic and sediment transport submodel of the Lake Okeechobee environment model (LOEM). This model simulates the sediment resuspension and transport due to wind driven current and waves. The LOEM simulated conditions in Lake Okeechobee from October 1, 1999 to September 30, 2000. The model reasonably simulated water depth, water temperature, current velocity, and suspended sediment concentrations in the validation period. To model sediment resuspension, the processes of wind generated waves and the resulting stresses on the lake bed were simulated. The LOEM is used to predict the impact of sediment processes in the lake under different management scenarios and environmental conditions (high/low lake stages and storm events/hurricanes). This model also is used to estimate light extinction coefficient. Results from the LOEM allow managers to predict how phosphorus-rich mud sediments move in the lake between the marsh and open water areas, and under what conditions they are most likely to be resuspended and transported.

A new numerical model based on the incompressible, nonhydrostatic Navier-Stokes equations for free surface flow is developed. The equations are transformed vertically to the $\sigma$ coordinate system and laterally to an orthogonal curvilinear system and solved in a fractional step manner in which the pressure is split into hydrostatic and nonhydrostatic components. The model treats the nonhydrostatic term implicitly and uses a collocated grid and pressure interpolation to prevent checkerboard solutions that occur when the velocity and pressure become decoupled. Advection and hydrostatic pressure terms are integrated explicitly with a second-order accurate predictor-corrector scheme. The corrector utilizes fluxes that are computed in a Godunov-based manner by solving a Riemann problem at each cell face. Flow variables are reconstructed at each cell face to obtain second-order spatial accuracy. Numerical simulations of Stokes, cnoidal, and solitary waves with the proposed method and a reference method in which the hydrostatic pressure is implicitly integrated are compared with analytical solutions and experimental data.

A tank might be simultaneously excited by surge, heave, and pitch ground motions during earthquakes. A time-independent finite-difference method is used to intensively study the combined effects of surge, heave, and pitch motions on sloshing viscous fluid in a rigid, rectangular tank. A complete fully nonlinear free-surface condition is used in the analysis. The numerical results are validated by the existing reported results. The evolution of the velocity vectors are described and discussed in detail. The coupled surge and heave and combined surge, heave, and pitch motions would enhance the free-surface stability during the transition period, during which the free surface variation ceases and sloshing begins in the opposite direction. No clear eddies are generated during a surge motion as they are during a heave motion. While the tank is experiencing pitch motion, a clear clockwise eddy occurs during the transition period, when the slope of the surface is negative. However, the eddy is counterclockwise when the slope is positive. A comparison between the surface elevation with combined surge, heave, and pitch motion and that of the superposition of separated excitation is made. The coupling effects are significant, and simultaneous surge and pitch motions should be included during a real earthquake analysis. The dominance of the frequency of excitation, ${\omega }_x$ , on the frequency of the sloshing displacement is presented when ${\omega }_x$ is less than the first fundamental frequency of water in tank, ${\omega }_1$ . The first fundamental frequency dominates the frequency of the sloshing displacement throughout the sloshing when ${\omega }_x$ is greater than ${\omega }_1$ .