Researches on breaking-induced currents by waves are summarized firstly in this paper. Then, a combined numerical model in orthogonal curvilinear coordinates is presented to simulate wave-induced current in areas with curved boundary or irregular coastline. The proposed wave-induced current model includes a nearshore current module established through orthogonal curvilinear transformation form of shallow water equations and a wave module based on the curvilinear parabolic approximation wave equation. The wave module actually serves as the driving force to provide the current module with required radiation stresses. The Crank-Nicolson finite difference scheme and the alternating directions implicit method are used to solve the wave and current module, respectively. The established surf zone currents model is validated by two numerical experiments about longshore currents and rip currents in basins with rip channel and breakwater. The numerical results are compared with the measured data and published numerical results.
The mild-slope equation is familiar to coastal engineers as it can effectively describe wave propagation in nearshore regions. However,its computational method in Cartesian coordinates often renders the model inaccurate in areas with irregular shorelines,such as estuaries and harbors. Based on the hyperbolic mild-slope equation in Cartesian coordinates,the numerical model in orthogonal curvilinear coordinates is developed. The transformed model is discretized by the finite difference method and solved by the ADI method with space-staggered grids. The numerical predictions in curvilinear coordinates show good agreement with the data obtained in three typical physical experiments,which demonstrates that the present model can be used to simulate wave propagation,for normal incidence and oblique incidence,in domains with complicated topography and boundary conditions.
Using unstructured meshes provides great flexibility for modeling the flow in complex geomorphology of tidal creeks,barriers and islands,with refined grid resolution in regions of interest and not elsewhere.In this paper,an unstructured three-dimensional fully coupled wave-current model is developed.Firstly,a parallel,unstructured wave module is developed.Variations in wave properties are governed by a wave energy equation that includes wave-current interactions and dissipation representative of wave breaking.Then,the existing Finite-Volume Coastal Ocean Model(FVCOM) is modified to couple with the wave module.The couple procedure includes depth dependent wave radiation stress terms,Stokes drift,vertical transfer of wave-generated pressure transfer to the mean momentum equation,wave dissipation as a source term in the turbulence kinetic energy equation,and mean current advection and refraction of wave energy.Several applications are presented to evaluate the developed model.In particular the wind and wave-induced storm surge generated by Hurricane Katrina is investigated.The obtained results have been compared to the in situ measurements with respect to the wave heights and water level elevations revealing good accuracy of the model in reproduction of the investigated events.In a comparison to water level measurements at Dauphin Island,inclusion of the wave induced water level setup reduced the normalized root mean square error from 0.301 to 0.257 m and increased the correlation coefficient from 0.860 to 0.929.Several runs were carried out to analyze the effects of waves.The experiments show that among the processes that represent wave effects,radiation stress and wave-induced surface stress are more important than wave-induced bottom stress in affecting the water level.The Hurricane Katrina simulations showed the importance of the inclusion of the wave effects for the hindcast of the water levels during the storm surge.
The purpose of this article is to model the detailed progress of wave propagation in curvilinear coordinates with an effective time-dependent mild slope equation.This was achieved in the following approach,firstly deriving the numerical model of the equation,i.e.,Copeland's hyperbolic mild-slope equation,in orthogonal curvilinear coordinates based on principal of coordinate transformation,and then finding the numerical solution of the transformed model by use of the Alternative Directions Implicit(ADI) method with a space-staggered grid.To test the curvilinear model,two cases of a channel with varying cross section and a semi-circular channel were studied with corresponding analytical solutions.The model was further investigated through a numerical simulation in Ponce de Leon Inlet,USA.Good agreement is reached and therefore,the use of the present model is valid to calculate the progress of wave propagation in areas with curved shorelines,nearshore breakwaters and other complicated geometries.
The variations of current, salt intrusion and vertical stratification under different conditions of river flow and wind in the Oujiang River Estuary (ORE) were investigated in this article using the Environmental Fluid Dynamics Code (EFDC). The model was verified against water level variation, velocity, and salinity variations in June 2005. The simulation results agreed well with measured data. Six sensitivity tests were conducted for different conditions of river flow and wind specified in the model. Model results show that salinity intrudes further upstream under scenarios with low flow and downriver local wind conditions. In contrast, the responses of salinity stratification to different environmental forcing functions were different in different portions of the estuary. Salinity stratification was enhanced under high flow condition. Model results also show that wind is not crucial to the salt intrusion and salinity stratification in the ORE.
