Study on Water Particle Velocities of Shoaling and Breaking Waves

In this paper, the wave shoaling problem is analyzed by the energy flux method in which the fifth-order Stokes and the third-order cnoidal wave theories are used appropriately according to the applicable range. This results in smooth wave height change from deep to shallow water. Various wave properties such as the wave profile, water particle velocities and pressure can be easily calculated from this wave height change.Calculated amplitude changes of the horizontal water particle velocity are compared with experimental results which include both regular waves in the laboratory and irregular waves in the field, and good agreement is found. Two parameters are introduced to represent the asymmetry of the velocity profile and expressions to evaluate these two parameters are derived based on experimental results. Velocity profiles computed from the calculated amplitude and the two parameters agree well with measured ones. Therefore, once the incident wave height and period are given, the velocity profile at an arbitrary depth can be easily calculated.For the surf zone, experimental results show that the relative velocity amplitude approaches a constant value for a mild bottom slope. However, further investigation is needed to predict the velocity field accurately.