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Boussinesq-type model for energetic breaking waves in fringing reef environments

机译：Boussinesq型模型在边缘礁环境中的高能破碎波

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摘要

The steep offshore slope and abrupt transition to a shallow lagoon are conducive to formation of energetic breaking waves in fringing reef environments. This paper describes an extension of a one-dimensional, shock-capturing Boussinesq-type model to account for these processes in two dimensions and the numerical formulation to facilitate adaptive time integration and code parallelization. The governing equations contain the conservative form of the nonlinear shallow-water equations to capture shock-related hydraulic processes. The finite volume method with a Godunov-type scheme provides a compatible, conservative numerical procedure. A two-dimensional TVD (Total Variation Diminishing) reconstruction procedure evaluates the flow variables on either side of the cell interface, while a Riemann solver supplies the flux and bathymetry source terms at the interface. A well-balanced scheme eliminates depth-interpolation errors in the domain and preserves continuity across moving boundaries over irregular topography. Time integration of the governing equations evaluates the conserved variables, which in turn provide the horizontal velocity components through systems of linear equations corresponding to series of one-dimensional problems. The application of the model to fringing reef environments is validated with laboratory experiments performed at Oregon State University as well as field data collected in Hawaii. The model describes the flux-dominated wave breaking processes through the Riemann solver without predefined empirical energy dissipation and reproduces transitions between sub and supercritical flows as well as development of dispersive and infra-gravity waves in the processes.
机译：陡峭的海上坡度和突然过渡到浅泻湖有利于在礁石环境中形成高能的破碎波。本文描述了一维，捕捉冲击的Boussinesq型模型的扩展，以在二维中考虑这些过程，并提供了数值公式化以促进自适应时间积分和代码并行化。控制方程包含非线性浅水方程的保守形式，以捕获与冲击有关的水力过程。带有Godunov型格式的有限体积方法提供了一种兼容的，保守的数值程序。二维TVD（总变化量减小）重建过程将评估单元界面两侧的流量变量，而Riemann求解器则在界面处提供流量和测深源项。良好的平衡方案可以消除域中的深度插值误差，并在不规则地形上跨移动边界保持连续性。控制方程的时间积分评估了守恒变量，守恒变量又通过对应于一系列一维问题的线性方程组提供了水平速度分量。通过俄勒冈州立大学进行的实验室实验以及在夏威夷收集的现场数据，验证了该模型在边缘礁环境中的应用。该模型描述了通过Riemann求解器的磁通控制的破碎过程，而没有预先定义的经验能量耗散，并重现了次临界流和超临界流之间的过渡以及过程中色散波和超重力波的发展。

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