Asu Inan

A Numerical Model of Wave Propagation on Mild Slopes

ABSTRACT Propagation of waves from Deep Ocean to a shoreline has been numerically modeled. Model equations govern combined effects of shoaling, refraction, diffraction and breaking. Linear, harmonic, and irrotational waves are considered, and the effects of currents and reflection on the wave propagation are assumed to be negligible. To describe the wave motion, mild slope equation has been decomposed into three equations that are solved in terms of wave height, wave approach angle and wave phase function. It is assumed that energy propagates along the wave crests, however, the wave phase function changes to handle any horizontal variation in the wave height. Model does not have the limitation that one coordinate should follow the dominant wave direction. Different wave approach angles can be investigated on the same computational grid. Finite difference approximations have been applied in the solution of governing equations. Model predictions are compared with the results of semicircular shoal tests performed by WHALIN (1971) and with the measurements of elliptic shoal experiment conducted by BERKOFF et al. (1982). Utility of the model to real coastal areas is shown by application to Obaköy on the Mediterranean Sea of Turkey.

A Composite Finite Element-Finite Difference Model Applied to Turbulence Modelling

Turbulence has been modeled by a two equation k-?turbulence model to investigate the wind induced circulation patterns in coastal waters. Predictions of the model have been compared by the predictions of two equation k-?turbulence model. Kinetic energy of turbulence is k, dissipation rate of turbulence is ?, and frequency of turbulence is ?. In the three dimensional modeling of turbulence by k-?model and by k-?model, a composite finite element-finite difference method has been used. The governing equations are solved by the Galerkin Weighted Residual Method in the vertical plane and by finite difference approximations in the horizontal plane. The water depths in coastal waters are divided into the same number of layers following the bottom topography. Therefore, the vertical layer thickness is proportional to the local water depth. It has been seen that two equation k-?turbulence model leads to better predictions compared to k-?model in the prediction of wind induced circulation in coastal waters.

Modeling of Erosion at Göksu Coasts

ABSTRACT Numanoğlu Genç, A., İnan, A., Yılmaz, N. and Balas, L., 2013. Modeling of Erosion at Göksu Coasts. Göksu coastal area, located in the south of Silifke County of Mersin on the coastal plain formed by Göksu River, is one of the Specially Protected Areas with an area of almost 15000 hectares and at an altitude of 0–5 m. The Eastern and Western parts of the Göksu river mouth along the Mediterranean coast and the coast of Paradeniz Lagoon are suffering significantly from erosion. As a result of the coastal erosion and the consequent coastal recession problem along the coasts of Göksu, agricultural fields located near the coast are being lost, and especially the narrow barrier beach which separates Paradeniz Lagoon from the sea is getting narrower, creating a risk of uniting with the sea, thus disappearing of the Lagoon. In order to propose solutions for the problem, and to protect the coastal zone and the habitats of Göksu against coastal erosion, coastal dynamic processes and sediment transport characteristics of the region causing the erosion should be investigated and identified. Therefore, longshore sediment transport and suspended sediment transport in Göksu coastal area are examined. First of all, the wind and wave climate of the study area are determined. Then, current pattern, wave propagation, and longshore sediment movements are modeled numerically utilizing three dimensional hydrodynamic transport model HYDROTAM-3D. HYDROTAM-3D is a three (3) dimensional numerical Hydrodynamic and Transportation Model which simulates current patterns due to wind and wave actions, pollutant transport, wave propagation over mild slopes, and longshore sediment transport rates. Model includes hydrodynamics, transport, turbulence, wind and wave climate and wave propagation sub models. HYDROTAM 3D, is developed using “cloud computing” architecture and tightly integrated with Geographic Information System. The study outputs will be used for the determination of the coastal erosion.

Numerical modelling of coastal currents

A numerical model has been developed for the simulation of transformations of traveling coastal waves and wave induced coastal currents. The model is applicable to varying bottom topographies and has two components, a wave propagation model and a wave driven current model. Wave propagation model is based on nonlinear parabolic mild slope equation and could simulate wave shoaling, refraction, diffraction and breaking. Different wave approach angles can be investigated on the same computational grid. Wave driven current model is based on vertically averaged non-linear shallow water equations. In the solution method, partial differential equations are replaced by a set of finite difference equations on a space staggered grid. Model has been applied to Obakoy coastal waters located at the Mediterranean coast of Turkey where there exist current measurements.

Numerical Modeling Of Refraction And Diffraction

A numerical model which simulates the propagation of waves over a complex bathymetry where the bottom contours are not straight and parallel, has been developed. In the model, the combined effects of refraction and diffraction can be considered. It is assumed that waves are linear, harmonic, and irrotational, and the effects of currents and reflection on the wave propagation are negligible. Mild slope equation is modified, assuming that there is no energy propagation along the wave crests, however, the wave phase function changes to handle any horizontal variation in the wave height. In this manner, the disadvantage of the parabolic approximation that one grid coordinate should follow the dominant wave direction, which causes problems in complex bathymetries, has been overcome. The finite difference method has been selected as the solution method. Applied methodology allows the check for breaking. Model results are compared with those from laboratory experiments published in the literature, and model is applied to Marmara Sea.

Coastal erosion problem, modelling and protection

Göksu Delta, located in the south of Silifke County of Mersin on the coastal plain formed by Göksu River, is one of the Specially Protected Areas in Turkey. Along the coastal area of the Delta, coastline changes at significant rates are observed, concentrating especially at four regions; headland of İncekum, coast of Paradeniz Lagoon, river mouth of Göksu and coast of Altınkum. The coast of Paradeniz Lagoon is suffering significantly from erosion and the consequent coastal retreating problem. Therefore, the narrow barrier beach which separates Paradeniz Lagoon from the Mediterranean Sea is getting narrower, creating a risk of uniting with the sea, thus causing the disappearance of the Lagoon. The aim of this study was to understand the coastal transport processes along the coastal area of Göksu Delta to determine the coastal sediment transport rates, and accordingly, to propose solutions to prevent the loss of coastal lands in the Delta. To this end, field measurements of currents and sediment grain sizes were carried out, and wind climate, wave climate, circulation patterns and longshore sediment transport rates were numerically modeled by HYDROTAM-3D, which is a three dimensional hydrodynamic transport model. Finally, considering its special importance as an environmentally protected region, some coastal structures of gabions were proposed as solutions against the coastal erosion problems of the Delta. The effects of proposed structures on future coastline changes were also modeled, and the coastlines predicted for the year 2017 are presented and discussed in the paper.

Liman Yapılarının Tasarımı İçin Dalga Tahmini

Ports and marinas have a vital importance in sea transportation and boat tourism. In the design of these areas, one of the most important steps is the design of the coastal defence structure which provides the safe berthing of the ships and the boats calling ports and marinas. Wave climate providing information on the wave characteristics that will affect the design of the defence structure is the basic aspect of the design process. Modelling the wave climate is of great importance in reaching on sound coastal defence structure. Like the overall practice in the world, wave prediction studies in Turkey are based on either the data gained out of wave measurements or models. However, as there is no continuous wave measurement data along the Turkish coasts, models of wave climate are preferred in the design process. In this study, the wind and wave climate sub-models of HYDROTAM-3D, a three dimensional hydrodynamic transport model are used and and developed for Turkish coasts, and the results of a case study for Edremit, Balikesir are discussed

A Moving Boundary Wave Run-Up Model

A numerical model has been developed for the simulation long wave propagation and run-up accounting for the bottom friction. Shallow water continuity and momentum equations are solved numerically by a two time step finite difference method. The upwind/downwind method is applied to the nonlinear advection terms and the continuity equation. Effects of damping and bottom friction on the computations are investigated. Since the equations lose their validity when waves break, wave breaking has been checked at every step of the computations. A point can be either wet or dry at different time levels. A moving boundary description and staggered grid are used to overcome the difficulty of determining wet and dry points. Equations are solved by the finite difference approximations of second and third order accuracy. Furthermore, space filters are applied to prevent parasitic short wave oscillations.