A set of three-dimensional equations was developed based on Generalized Lagranrian Mean method to simulate mean motion of fluid particle in the presence of finite amplitude surface waves. In the new equations, effects of waves are included through source terms. Both conservative and non-conservative waves are under consideration. A concept of three-dimensional wave radiation stress is introduced to express the effects of waves on the currents. Moreover, the relationship between three-dimensional wave radiation stress and vortex force representations is investigated in detail.
In the book, there are several well-known sets of equations of mean motion were selected to compare with the new set of equations. The results showed that the new set of equations is more suitable for coastal applications, especially in the presence of finite amplitude waves and strong ambient current.
To validate the new set of equations on various conditions of waves and currents, a two-dimensional numerical model was developed using Fortran language. The comparisons showed very good agreements between model results and experimental data. As shown by successful implementation and validations in the tests, the implementation of new equations in three-dimensional model code is straightforward and expected to provide consistent results from deep water to the surf zone.