论文标题
来自某些完整分散浅水模型的水波方程的严格推导
Rigorous derivation from the water waves equations of some full dispersion shallow water models
论文作者
论文摘要
为了改善沿海海洋学中无层浅水模型的频率分散效应，文献中正式得出了几种经典模型的完整分散版本。这个想法来自[21]中的G. Whitham，是为了修改它们，以使它们的分散关系与水波方程相同。在本文中，我们构建了速度电势的新浅水近似值，然后在速度的垂直平均水平分量上推断出速度电位。我们利用它们严格从水浪方程中得出了两个新的哈密顿全面色散模型。这是第一次表征完整分散模型的近似顺序的非平凡精度结果。它们的意思是，它们比相应的古典模型要好。
In order to improve the frequency dispersion effects of irrotational shallow water models in coastal oceanography, several full dispersion versions of classical models were formally derived in the literature. The idea, coming from G. Whitham in [21], was to modify them so that their dispersion relation is the same as the water waves equations. In this paper we construct new shallow water approximations of the velocity potential then deducing ones on the vertically averaged horizontal component of the velocity. We make use of them to derive rigorously from the water waves equations two new Hamiltonian full dispersion models. This provides for the first time non-trivial precision results characterizing the order of approximation of the full dispersion models. They are non-trivial in the sense that they are better than the ones for the corresponding classical models.
