In this monograph, a finite difference algorithm for study- ing two dimensional wave breaking in the vertical plane is developed. The essential feature of this algorithm is the combination of the Volume-of-Fluid (VOF) technique for arbi- trary free surfaces and the k-E turbulence model. This me- thodology allows a self-contained study for wave transforma- tion processes in shallow water before, during and after breaking. This capability is illustrated in several calcula- tions. This book will be of interest for final year graduates, postgraduates and researchers working in the fields of tur- bulence modelling, wave hydrodynamics, coastal engineering, and oceanography of coastal regions.