Peregrine系统重新审视
Peregrine's system revisited
AI总结：
本文重新审视传统称为Peregrine系统的长波模型，提出了一种改进的控制方程，使其在弱非线性波条件下与初始模型渐近相似，同时保留了完整水波问题的额外对称性，从而在滑动区具有良好的散射项，允许高效稳定的上溯计算。
摘要：
1967年，D.H. Peregrine提出了一种Boussinesq型模型，用于描述浅水层中长波的传播。这篇重要论文在海岸流体力学中掀开了新的篇章，随后F.Serre、A.E.Green和P.M.Naghdi等人的贡献也推动了该领域的发展。近年来，许多现代Boussinesq型系统均源于这些开创性工作。在本文中，我们重新审视传统上称为Peregrine系统的长波模型。具体而言，我们提出了一种改进的控制方程，该方程在弱非线性波条件下与初始模型渐近相似，同时保留了完整水波问题的额外对称性。这种改进过程被称为不变化。我们证明，改进后的系统在滑动区具有良好的散射项，从而允许高效且稳定的上溯计算。
英文摘要：
In 1967 D. H. Peregrine proposed a Boussinesq-type model for long waves in shallow waters of varying depth. This prominent paper turned a new leaf in coastal hydrodynamics along with contributions by F. Serre, A. E. Green \& P. M. Naghdi and many others since then. Several modern Boussinesq-type systems stem from these pioneering works. In the present work we revise the long wave model traditionally referred to as the Peregrine system. Namely, we propose a modification of the governing equations which is asymptotically similar to the initial model for weakly nonlinear waves, while preserving an additional symmetry of the complete water wave problem. This modification procedure is called the invariantization. We show that the improved system has well conditioned dispersive terms in the swash zone, hence allowing for efficient and stable run-up computations.
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