Boussinesq-Green-Naghdi rotational water wave theory
Boussinesq-Green-Naghdi rotational water wave theory
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DOI：
10.1016/j.coastaleng.2012.09.005
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发表时间：
2013-03
影响因子：
4.4
通讯作者：
Yao Zhang;A. Kennedy;N. Panda;C. Dawson;J. Westerink
中科院分区：
文献类型：
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作者：
Yao Zhang;A. Kennedy;N. Panda;C. Dawson;J. Westerink
在不施加旋转性约束的情况下，使用水波的Boussinesq标度，我们推导并测试了在不同深度下非线性水波变换的模型方程。这些使用多项式基函数来创建速度剖面，这些速度剖面插入到运动的基本方程中，保持项达到所需的Boussinesq标度顺序，并以加权残差意义求解。模型对线性色散、浅滩和轨道速度的精确解具有快速收敛性；然而，对于使用渐近重排的给定阶数的近似，性质可以得到实质性的改进。这种改进是利用多项式基函数定义中固有的大量自由度来完成的，这些自由度要么匹配泰勒级数中的附加项，要么在一个范围内最小化误差。在O（μ2）和O（μ4）处给出显式系数，在高阶处给出更广义的基函数。由于复杂性的原因，我们只提供明确的低阶非线性项，因此非线性性能在某种程度上受到限制。对于O（μ4）方程，二阶谐波在kh≈10范围内仍然保持良好。浅滩上波浪变换的数值试验结果与实验结果吻合较好。未来的工作将利用这些系统的全部旋转性能，将湍流和粘性应力纳入方程，使其成为冲浪区模型。
Using Boussinesq scaling for water waves while imposing no constraints on rotationality, we derive and test model equations for nonlinear water wave transformation over varying depth. These use polynomial basis functions to create velocity profiles which are inserted into the basic equations of motion keeping terms up to the desired Boussinesq scaling order, and solved in a weighted residual sense. The models show rapid convergence to exact solutions for linear dispersion, shoaling, and orbital velocities; however, properties may be substantially improved for a given order of approximation using asymptotic rearrangements. This improvement is accomplished using the large numbers of degrees of freedom inherent in the definitions of the polynomial basis functions either to match additional terms in a Taylor series, or to minimize errors over a range. Explicit coefficients are given at O(μ2) and O(μ4), while more generalized basis functions are given at higher order. Nonlinear performance is somewhat more limited as, for reasons of complexity, we only provide explicitly lower order nonlinear terms. Still, second order harmonics may remain good to kh≈10 for O(μ4) equations. Numerical tests for wave transformation over a shoal show good agreement with experiments. Future work will harness the full rotational performance of these systems by incorporating turbulent and viscous stresses into the equations, making them into surf zone models.