Application of Weighted Total Acceleration Equation on Wavelength Calculation

Abstract

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.

New Weighted Total Acceleration on Momentum Euler Equation for Formulating Water Wave Dispersion Equation

“…Furthermore, if the wavelength of ( 4) is used to calculate the critical wave height with (2) and (3), a very large critical wave height is obtained as presented in table (2) below. In table (2), it can be seen that the maximum wave height that is calculated using the wavelength of the linear wave theory produces a very large wave height. In table (2), ℎ the wave height is calculated using the Michell's criteria, while the wave height is calculated using the Toffoli's criteria.…”

“…In table (2), it can be seen that the maximum wave height that is calculated using the wavelength of the linear wave theory produces a very large wave height. In table (2), ℎ the wave height is calculated using the Michell's criteria, while the wave height is calculated using the Toffoli's criteria. Considering that Toffoli et al's criteria produce a greater maximum wave height than Michell's criteria, this research uses the Toffoli et al's critical wave steepness criteria to calibrate the wavelengths produced by the dispersion equations of this study.…”

“…The effect of wave amplitude on wavelength is shown in Fig. (2) where the larger the wave amplitude, the shorter the wavelength. When waves move from deeper waters to shallower waters, an enlargement of the wave height and shortening of the wavelength occurs, known as the shoaling phenomenon.…”

A Continuity Equation For Time Series Water Wave Modeling Formulated Using Weighted Total Acceleration

“…Bases on wave number conservation equation (Hutahaean (2019a)), the relation between wave number in a depth , with wave number in deep water is, (ℎ + ) = 0 ( 0 + 0 ). Assuming that 0 0 ≪ 1, then 20) is controlled by water surface equation.…”