Breaker Indices in Water Wave Formulated from Kinematic Free Surface Boundary Condition, Conservation Equation of Wave Number and Equation of Energy Conservation

Abstract

In this research, the breaker index equations are formulated using the kinematic free surface boundary condition. By substituting the potential velocity equation for the solution of Laplace's equation in this equation, it is obtained the wave amplitude function equation. From the wave amplitude function equation two breaker indices are extracted, they are the breaker length index which is the ratio between the breaker height and the breaker length; and the breaker depth index which is the ratio between the breaker height and the breaker depth. The next breaker index, which is a ratio between breaker depth and breaker length, is obtained from the wave number conservation law. Consistency testing of the three breaker index equations obtained shows that there is consistency in the three equations. Consistency testing is done by using the connectivity equation, where a breaker index is the product of the multiplication of the other two breaker indexes. The breaker height index, which is the ratio between the breaker height and the deep water wave height, is obtained by substituting the breaker length index in the energy conservation equation. Thus the breaker height equation is obtained which works a function of the breaker length at the breaking point. With the availability of the four breaker indexes, the breaking parameter can be calculated easily.