Application of partial differential equations to solving wave equations related to coastal hydrodynamics

In this thesis, the solution of Partial Differential Equations (PDE) using Finite Difference Method (FDM) is studied based on flow through porous media with a certain thickness due to hydrodynamic pressure occuring on the bottom surface in front of a offshore breakwater due to random wave. A random wave record is characterized by Spectral analysis by Fast Fourier Transform Technique (FFT). Many sinusoidal waves representing random wave are generated by evaluating wave spectrum curve obtained from FFT. The new wave form based on the superposition of generated sinusoidal waves should fit to the real wave form. For this purpose, the confidence between the wave forms and spectrum curves which belong to two different waves is investigated by Chi-square test. Hydodynamic pressures on the sea bottom due to the new generated sinusoidal waves are yielded by considering the transformation of each non-breaking wave propagating to shore and adding hydrodynamic pressures with each other. In this case, the offshore breakwater is of course located at a water depth in which the non-breaking wave for each wave will arise and on the inclined porous sea bottom. However, it is assumed that the propagating of multi sinusoidal waves on impermeable sea bottom is considered. Porous media under offshore breakwater is defined as a planar grid system and the flow characteristics are determined along the horizantal and vertical axes.The bottom boundary conditions on the axes are defined by the velocity potentials taken equal to hydrodynamic pressures. Porous layer with constant thickness is extended to the shore paralel to the sea bottom. Under this layer, there is a impermeable zone. Flow through this media is characterized as Laplace equation based on partial differential form. In this thesis, this equation is solved by using the FDM. The outputs from these studies are the velocity potentials, horizantal and vertical flow velocities at each point of grid system and the volume of flow passing through the vertical cross-section under breakwater. These flow parameters are calculated by changing bottom boundary conditions in different time intervals. Consequently, such flow parameters obtained under random wave condition are tried to be obtained by generating multi sinusoidal waves satisfying the same condition.