Sinusoidal Water Wave Dispersion Equation Formulated Using the Total Velocity Potential Equation

In this study, the dispersion equation was formulated with the same procedure as the linear wave theory dispersion equation formulation procedure, but in this study, the total velocity potential was used. The dispersion equation obtained has the same form as the linear wave theory dispersion equation. There is a difference in its coefficients which causes the obtained wavelength to be half of the wavelength dispersion equation of the linear wave theory.