Boussinesq-type model for energetic breaking waves in fringing reef environments
Boussinesq-type model for energetic breaking waves in fringing reef environments
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DOI：
10.1016/j.coastaleng.2012.06.001
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发表时间：
2012-12
影响因子：
4.4
通讯作者：
V. Roeber;K. Cheung
中科院分区：
文献类型：
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作者：
V. Roeber;K. Cheung
陡的离岸斜坡和向浅泻湖的突然过渡有利于边缘礁环境中能量破碎波的形成。本文介绍了一个扩展的一维，冲击捕获Boussinesq型模型，以考虑这些过程中的二维和数值公式，以方便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，以捕捉冲击相关的水力过程。有限体积法与Godunov型格式提供了一个兼容的，保守的数值程序。一个二维的TVD（总变差递减）重建程序评估的细胞界面的两侧的流量变量，而黎曼求解器提供的接口处的通量和测深源项。一个平衡良好的计划消除了深度插值误差的域，并保持连续性跨越移动边界不规则的地形。控制方程的时间积分计算守恒变量，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水平速度分量。在俄勒冈州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，验证了该模型的边缘礁环境的应用。该模型描述了通量占主导地位的波破碎过程中，通过黎曼求解器没有预定义的经验能量耗散和再现子和超临界流之间的过渡，以及分散和亚重力波的发展过程中。
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.