A Numerical Model of the Wave-Induced Currents in the Turbulent Coastal Zone

A numerical model is developed, validated and applied to the turbulent coastal currents. The currents are driven by the sea surface slope and the radiation stresses of water waves. They are resisted by friction due to turbulent eddies and sea bottom. The k-ε model is used to model the turbulent stresses. Five simultaneous nonlinear partial differential equations govern the depth-averaged dynamics in the surf zone. An implicit finite-difference scheme is used to obtain an accurate numerical solution of the resulting initial-boundary value problem. It is tested against the case of straight coast with uniform bottom slope and a protective jetty. To investigate the actual wave-induced currents, the model is applied to simulate the currents for three real case studies. Results show that the model could be used to compute currents caused by the constructing coastal protection measures and could predict the locations of accretion and scouring. 1. Introduction As surface waves progress onshore, through the nearshore zone, they transform due to the combined effect of ambient currents and bottom variations. As they approach the surfzone—between the shoreline and the breaker line—the energy of the broken waves is transformed into radiation stresses, which drive turbulent currents. The effects of these currents on exciting bottom sediments and transporting them offshore and longshore were studied by Martinez and Harbaugh [1]. Fahmy [2] showed that if the horizontal dimensions of the flow domain are much larger than the vertical dimension, the depth-averaged and wave period-averaged mass and momentum equations can be used to represent the flow. As a result of large horizontal scales in the surf zone area, the flow can be considered turbulent even for very small velocity values. There are two approaches of mathematical models of wave-induced current: the first is based on the radiation stress theory, while the second is based on the Boussinesq equation. Recently, many researchers dealt with this topic. Significant publications include the one of Mengguo and Chongren [3]. They used a simplified model for the resisting force caused by eddy viscosity. Kim and An [4] presented a numerical model that takes the wave-current interaction into consideration and quasi-3D equations were used in circulation analyses. 2. Model Theoretical Formulation 2.1. Model Assumptions The depth-average shallow water model equations (SWE) are invoked for coastal regions where hydrostatic approximation is valid [5]. These equations are based on the following assumptions. (i) The flow is