The propagation of inhomogeneous inlet waves is simulated by the Boussinesq equations with an inhomogeneous wavemaker. The inhomogeneous wavemaker is based on the source wavemaker of the Boussinesq model, and the spatial varying wave heights are simulated by changing 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.


A lagoon surrounded by reefs and islands is a typical topography in South China Sea. Waves in a lagoon are mostly much smaller than those outside the lagoon. Averaged 73% energy is reduced when waves enter the lagoon (Cai et al., 2019). Thus, the lagoon is suitable for the deployments 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 very complex. Firstly, the source of the waves is very complex. Both of wind generated local waves and waves from the open sea have impacts on the waves in the lagoon. Secondly, the propagation of waves are affected by lots of factors. Mostly, the wave energy is reduced by the wave breaking and 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, the spatial distribution of waves changes rapidly, which is named as inhomogeneous waves. This study focusses on the simulation and analysis 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 take account of wave nonlinearity, dispersion, wave breaking and bottom friction (Shi, Kirby, Harris, Geiman, & Grilli, 2012), and it also can be applied to simulate the interaction between wave, current and tide (K. 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 and relatively mature. However, the wavemaker in the FUNWAVE-TVD model and other open source programs can only generate homogeneous inlet waves.

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