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. Thek-εmodel 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.
Two numerical models are investigated to model random water waves (RWWs) transformation due to mild depth variation. Modelling of steady on-shore propagation of small-amplitude RWWs is based on superposition principle of waves of different heights and directions. Each component is simulated through either the parabolic model (PM) or the elliptic model (EM). PM simulates weak refraction, diffraction, shoaling, and wave breaking. EM simulates strong refraction, diffraction, and shoaling. Both models neglect wave reflection. Comparison between PM and EM, in test cases that are experimentally measured, proved that both models give good results for unidirectional and narrow-directional RWW. However, EM is more accurate in modelling broad-directional RWWs.
Propagation of irregular water wave from deep water to a shoreline has been numerically modeled. Linear and irregular waves are considered. Model equations govern effects of shoaling, refraction, and diffraction over a varying bathymetry. The model requires the input of the incoming directional random sea at the offshore boundary. Statistical energy dissipation model is incorporated to predict realistically energy losses due to wave breaking in surf zone. Unlike most of the previous models, this model can predict wave transformation in surf zone where energy dissipation and bottom friction must be taken into consideration. The model does not have the limitation of parabolic approximation models (PAM) that are valid only in case of weak refraction. Finite difference approximations have been used to solve the governing equation. The model results are compared with experimental data for directional random wave propagation over a submerged shoal. Good agreements between the model results and experimental data are shown. Applicability of the model to real coastal areas is shown by application to coastal areas along the Nile Delta Coast, Egypt.
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