Some Variants of Water Wave Dispersion Equation, Formulated with Small Amplitude Wave Assumption

Abstract

This research formulates some dispersion equations with formulating procedure similar to the one in formulating dispersion equation of the small amplitude and long wave theory, i.e. by applying velocity potential equation on the Bernoulli surface equation and Kinematic Free Surface Boundary Condition equation. Furthermore, this research uses non-linear term of the Bernoulli equation, whereas the Kinematic Free Surface Boundary Condition equation is applied with two scenarios, i.e. neglected non-linear term and not-neglected non-linear term Wave length from various dispersion equations that are obtained are then compared with breaker length of the breaker index equation. This research aims only to show that using similar governing equations can be obtained some dispersions equations to produce different wave length.