International Journal of Advanced Engineering Research and Science (IJAERS) Peer-Reviewed Journal ISSN: 2349-6495(P) | 2456-1908(O) Vol-8, Issue-10; Oct, 2021 Journal Home Page Available: https://ijaers.com/ Article DOI: https://dx.doi.org/10.22161/ijaers.810.22 www.ijaers.com Page | 194 Analytical Formulation of Breaker Equations Syawaluddin Hutahaean Ocean Engineering Program, Faculty of Civil and Environmental Engineering,-Bandung Institute of Technology (ITB), Bandung 40132, Indonesia Received: 09 Sep 2021, Received in revised form: 07 Oct 2021, Accepted: 15 Oct 2021, Available online: 22 Oct 2021 ©2021 The Author(s). Published by AI Publication. This is an open access article under the CC BY license (https://creativecommons.org/licenses/by/4.0/). Keywords— breaker height, breaker length, and breaker depth equations Abstract— In this study, equations to calculate breaker height, breaker length, and breaker depth were formulated. The analytical formulations were based on the velocity potential of the solution of the Laplace equation. The substitution of velocity potential to weighted kinematic free surface boundary condition yielded equation for wave amplitude function. The dispersion equation was obtained by substituting the velocity potential and wave amplitude function into the weighted momentum Euler equation. The relation between breaker height and breaker wavenumber is extracted from the wave amplitude function. The breaker wavenumber equation was obtained by substituting this relation into the dispersion equation. Furthermore, the breaker depth equation obtained was put to the wavenumber conservation equation with the variables of breaker height and breaker wavenumber. The breaker wave amplitude equation, the breaker wavenumber equation, and the breaker depth equation are simple equations that are very easy to use. I. INTRODUCTION There are quite a lot of empirically formulated equations to calculate the water wave characteristics at the point breaking wave. These equations are called the breaker index. There arebreaker height index to calculate breaker height,breaker depth index to calculate breaker depth with an input of breaker height, andbreaker length index to calculate breaker length with the inputs of breaker height and breaker depth. Some researchers who put forward equation for the breaker height index include Le Mehaut and Koh (1967), Komar and Gaughan (1972), Sunamura and Horikawa (1974), Singamsetti and Wind (1980), Ogawa and Sutto (1984), Larson and Kraus (1989a), Smith and Kraus (1990), Gourlay (1992), and Pittikon and Shibayama (2000). Meanwhile, studies dealing with breaker depth index are conducted by Mc Cowan (1984), Galvin (1969), Collins and Weir (1969), Goda (1970), Weggel (1972), Sunamura (1980), Singamsetti and Wind (1980), Seyama and Kimura (1988), Larson and Kraus (1989b), Smith and Kraus (1990). In terms of breaker length index, researchers proposing the studies include Miche (1944), Battjes and Jansen (1978), Ostendorf and Madsen (1979), Battjes and Stive (1985), Kamphuis (1991), Rattanapitikon and Shibayama (2000) and Rattanapitikon et al. (2003). This study formulated equations for water wave characteristics at the point breaking wave based on hydrodynamic equations including the equations for breaker height, breaker length, and breaker depth. Using this method, a relationship among the three is elaborated. In this research, the wave amplitude function was formulated using the weighted kinematic free surface boundary condition and the weighted Euler’s momentum equation. Hence,there is a weighting coefficient in the equations of breaker wavenumber, breaker depth, and shoaling in the dispersion equation. The weighting coefficient is obtained by calibrating the critical wave steepness with the critical wave steepness criteria from Michell (1893), where the critical wave height used is the maximum wave height from Wiegell (1949; 1964). In addition to calibrating the critical wave steepness, the weighting coefficient is also obtained by calibrating the breaker height with the breaker height from the breaker