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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.

A shoaling and breaking water wave model was developed in this study using the velocity potential of the solution of the Laplace equation. Formulation was carried out using Weighted Kinematic Free Surface Boundary Condition Equation, wave number conservation equation, and energy conservation equation. In the Weighted Kinematic Free Surface Boundary Condition equation, a weighting coefficient was used which needs to be determined. The value of the weighting coefficient was extracted from the dispersion equation. The dispersion equation was formulated using Weighted Kinematic Free Surface Boundary Condition and Weighted Momentum Equation to obtain weighting coefficient that meets the hydrodynamic equilibrium equation. By using the weighting coefficient, good shoaling and breaking results were obtained.

In this present study, weighted total acceleration for Kinematic Free Surface Boundary Condition (KFSBC) and in momentum Euler equation was formulated. Furthermore, by using both aforementioned equations, the nonlinear water wave dispersion equation was then formulated. The wavelength obtained from dispersion equation is determined by weighting coefficient. The weighting coefficient value was determined by using the maximum wave height and critical wave steepness criteria which have been obtained from the previous studies.

In this research, total acceleration equation is formulated where there is time scale coefficient at its time differential term. The formulation was done based on Courant Number equation and by using Taylor series. Then this total acceleration is applied to kinematic free surface boundary condition and Euler momentum equations. Potential velocity and water surface equations of linear water wave theory as well as wave number conservation equation were substituted to momentum and kinematic free surface boundary condition equations produced dispersion equation with wave amplitude as its variable and which fits with wave number conservation equation. Wave number conservation equation is an equation that regulates changes in wavelength as a result of water depth changes. This equation was extracted from potential velocity equation.

This study conducted a comparative study between groin and T-groin. The study was done by developing stable coastline equation between groins and between T-Head groins. Stable coastline equation is the follow up of previous research by the same researcher. Meanwhile, stable equilibrium coastline equation between T-Head groins is the development of stable coastline between groins equations. Comparation study in erosion on the downstream groin and the maximum erosion shows that T-groin provides better coastal protection than groin.

In this research an equation of static equilibrium geometry shoreline on coastal segment between two groins with quadratic polynomial equations is developed. Equation coefficients were formulated based on the characteristic of stable coastline geometry of the previous study and conservation law of mass, where volume of erosion and sedimentation are identical. The equation is capable of predicting erosion and accretion for coastline between two groin. Furthermore, with the predicted erosion and sedimentation, the groins gap and the length of groin can be planned using maximum permitted erosion criteria.