## Mild Slope Equations in Wave Propagation Modelling

9th International Conference on the Mediterranean Coastal Environment, Sochi, Rusya, 10 - 14 Kasım 2009, ss.733-737  • Cilt numarası:
• Basıldığı Şehir: Sochi
• Basıldığı Ülke: Rusya
• Sayfa Sayıları: ss.733-737

#### Özet

Wave propagation is one of the important subjects of the coastal engineering. Waves transform while propagation from deep water to shallow water. One of the wave propagation solution methods is mild slope equation. Mild slope equation considers refraction and diffraction phenomena together for regular waves. The basic assumption is that is vertical bar del h vertical bar/kh << 1. Here, h is water depth and k is wave number. General mild slope equation is proposed by Berkhoff in seventies. It includes shoaling, reflection, refraction and diffraction. With the addition of higher order bottom effects like bottom curvature and square of bottom slope to the general mild slope equation, the limitation of MSE is overcome. So the extended mild slope equation can be applied to the rapidly varying topographies. Another modification of mild slope equation is taking into account dissipations due to bottom friction and wave breaking. Until now, many researchers have been worked on the MSE. They have been dealt with the extension of mild slope equations and various types of solution procedures in numerical modelling of mild slope equations. Today, a mild slope equation can involve refraction, diffraction, shoaling, reflection, higher order bottom effects, harbour resonance, dissipations due to bottom friction and wave braking, current effects and spectral approach together. Mild slope equations have three types: Elliptic, hyperbolic and parabolic mild slope equations. Each of them has advantages and disadvantages compared with the others. Numerical solutions depend on the type of MSE. In this paper, the theoretical development of mild slope equation will be presented and some numerical solution procedures will be discussed.