Lale Balas

An implicit three-dimensional numerical model to simulate transport processes in coastal water bodies

A three-dimensional baroclinic numerical model has been developed to compute water levels and water particle velocity distributions in coastal waters. The numerical model consists of hydrodynamic, transport and turbulence model components. In the hydrodynamic model component, the Navier-Stokes equations are solved with the hydrostatic pressure distribution assumption and the Boussinesq approximation. The transport model component consists of the pollutant transport model and the water temperature and salinity transport models. In this component, the three-dimensional convective diffusion equations are solved for each of the three quantities. In the turbulence model, a two-equation k-e formulation is solved to calculate the kinetic energy of the turbulence and its rate of dissipation, which provides the variable vertical turbulent eddy viscosity. Horizontal eddy viscosities can be simulated by the Smagorinsky algebraic sub grid scale turbulence model. The solution method is a composite finite difference-finite element method. In the horizontal plane, finite difference approximations, and in the vertical plane, finite element shape functions are used. The governing equations are solved implicitly in the Cartesian co-ordinate system. The horizontal mesh sizes can be variable. To increase the vertical resolution, grid clustering can be applied. In the treatment of coastal land boundaries, the flooding and drying processes can be considered. The developed numerical model predictions are compared with the analytical solutions of the steady wind driven circulatory flow in a closed basin and of the uni-nodal standing oscillation. Furthermore, model predictions are verified by the experiments performed on the wind driven turbulent flow of an homogeneous fluid and by the hydraulic model studies conducted on the forced flushing of marinas in enclosed seas.

APPLICATIONS OF A 3-D NUMERICAL MODEL TO CIRCULATION IN COASTAL WATERS

A three dimensional baroclinic numerical model which consists of hydrodynamic, transport and turbulence model components, has been applied to two test cases, including: the wind induced flow in a laboratory basin and tidal flow in a model rectangular harbor. The agreement between the physical and numerical model results is highly encouraging. Model has been implemented to Ölüdeniz Lagoon located at the Mediterranean coast of Turkey to simulate tidal and wind driven currents. M2 tide is the dominant tidal constituent for the area. There exist some field measurements performed on water salinity, water temperature and current pattern in Ölüdeniz Lagoon. Even though measurements provide only some preliminary data for the site, favorable results have been obtained from the application of the model to a real coastal water body.

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.

A baroclinic three dimensional numerical model applied to coastal lagoons

An implicit baroclinic unsteady three-dimensional model (HIDROTAM3) which consists of hydrodynamic, transport and turbulence model components, has been implemented to two real coastal water bodies namely, oludeniz Lagoon located at the Mediterranean coast and Bodrum Bay located at the Aegean Sea coast of Turkey. M2 tide is the dominant tidal constituent for the coastal areas. The flow patterns in the coastal areas are mainly driven by the wind force. Model predictions are highly encouraging and provide favorable results.

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.

Modelling of Interaction between Surface Waves and Mud Layer

The analytical and numerical modelling of interaction between the mud layer at the sea bottom and the surface waves have been presented. In the simulations the theory for linear water wave movement in a two-layer viscous fluid system has been considered. The upper layer represents water and the lower layer represents fluid-mud. The type of the bottom material over which waves are propagating is assumed to be similar to a viscous fluid, characterized by a viscosity and density greater than the overlying fluid. It is assumed that the two fluids are incompressible and isotropic, and the rigid strata is smooth and impermeable. At the surface the height of the surface wave is specified and the forced interfacial wave is determined. Developed model solves the equations of motion for an incompressible fluid by composite finite difference-finite element approximations on a staggered scheme. Results of analytical and numerical solutions are compared with the experimental results and favourable agreement has been obtained.