Proceedings of the Thirty-second (2022) International Ocean and Polar Engineering Conference
Shanghai, China, June 5–10, 2022
Copyright © 2022 by the International Society of Offshore and Polar Engineers (ISOPE)
ISBN 978-1-880653-81-4; ISSN 1098-6189

www.isope.org

Simulation of inhomogeneous inlet waves by the Boussinesq equations
Zhiwen Cai1, Chunrong He1, Xiaolong Liu1, Wenwei Chen2
1Department of Offshore Structures, China Ship Scientific Research Center

Wuxi, Jiangsu Province, China
2Shanghai Branch, China Ship Scientific Research Center

Shanghai, China

Hirayama, Nakamura, & Itsui, 2017; Qin, Madsen, & Schaffer, 1998).
Lots of open source programs are developed by researchers (Lynett, Liu,Sitanggang, & Kim, 2002; O. G. Nwogu & Demirbilek, 2001; Shi, et al.,2012). Among these programs, FUNWAVE-TVD is widely used andrelatively mature. However, the wavemaker in the FUNWAVE-TVD
model and other open source programs can only generate homogeneous
inlet waves.
In the past several decades, the study on the simulation ofinhomogeneous inlet waves is few. The only works are taken by
Hirayama and his collaborators, who consider the influence of variablebathymetry on the wavemaker (K. Hirayama, 2014; Katsuya Hirayama,2016; Katsuva Hirayama, Aida, & Nakamura, 2017; Katsuya Hirayama,Naganuma, & Uno, 2015). However, systematic analysis on thepropagation of inhomogeneous inlet waves and validation of thenumerical model is lacking in their works.
In this paper, the inhomogeneous waves are simulated and analyzed by
Boussinesq equations and the linear wave theory, respectively. An
overall description of the simulation model is given in Section 1.
Analysis of the inhomogeneous waves by linear wave theory is given inSection 2. Validation of the numerical model by the theory results ispresented in Section 3. In Section 4, the numerical model is employed tosimulate waves in a lagoon. Finally, the conclusions are drawn.

ABSTRACTThe propagation of inhomogeneous inlet waves is simulated by theBoussinesq equations with an inhomogeneous wavemaker. The
inhomogeneous wavemaker is based on the source wavemaker of theBoussinesq model, and the spatial varying wave heights are simulated bychanging the parameters of the source wavemaker. Theoretical analysis
is made for the propagation of inhomogeneous inlet waves by the linear
wave theory. Finally, the model is validated by the theory results.

KEYWORDS:

inhomogeneous inlet waves; inhomogeneouswavemaker; Boussinesq equations

INTRODUCTION
A lagoon surrounded by reefs and islands is a typical topography inSouth China Sea. Waves in a lagoon are mostly much smaller than thoseoutside the lagoon. Averaged 73% energy is reduced when waves enter
the lagoon (Cai et al., 2019). Thus, the lagoon is suitable for thedeployments of floating marine structures for different applications(Ding et al., 2017; Y. S. Wu et al., 2018).
Affected by the complex topography the waves in a lagoon can be verycomplex. Firstly, the source of the waves is very complex. Both of wind
generated local waves and waves from the open sea have impacts on thewaves in the lagoon. Secondly, the propagation of waves are affected bylots of factors. Mostly, the wave energy is reduced by the wave breakingand bottom friction and diffraction plays the most important role
(Abohadima & Isobe, 1999; Bai & Taylor, 2007; Isaacson & Cheung,
1991; Lee, Kim, & Suh, 2003; O. Nwogu, 1993; Tang & Ouellet, 1997;
Y. Wu, He, Song, Ye, & Rong, 2016; Yu, 1981). Last but not least, waves
in the lagoon often interact with the tide and current (Lugo-Fernández,Roberts, Wiseman, & Jr, 1998; Mao & Meng, 2018). As a result, thespatial distribution of waves changes rapidly, which is named asinhomogeneous waves. This study focusses on the simulation andanalysis of the inhomogeneous waves.
Boussinesq model is one of the most common model to simulate waves
in the reef lagoon (Zhang, Zhu, & Li, 2018). Boussinesq equations takeaccount of wave nonlinearity, dispersion, wave breaking and bottom
friction (Shi, Kirby, Harris, Geiman, & Grilli, 2012), and it also can beapplied to simulate the interaction between wave, current and tide (K.

WAVE MODEL
Governing Equations
In this paper, the FUNWAVE-TVD model (Shi, et al., 2012) is employed
to simulate the inhomogeneous waves. The FUNWAVE-TVD model isa fully nonlinear Boussinesq-type wave model. The governing equations
include the mass conservation equations and the momentum
conservation equation:

t    M  0(1) MM Mt     +g  h      S
 h+ (2)where 𝜂 is the wave elevation, 𝑴 is the momentum, ℎ is the water depth,
𝑔 is the gravity acceleration and 𝑺 is the source term. The governing
equations are discretized by a hybrid method combining finite-volume2686