SIAM Journal on Mathematical Analysis, Volume 53, Issue 4, Page 3772-3800, January 2021.
In order to improve the frequency dispersion effects of irrotational shallow water models in coastal oceanography, several full dispersion versions of classical models have been formally derived in the literature. The idea, coming from G. Whitham in [Proc. A, 299 (1967), pp.6--25] 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 deduce 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 nontrivial precision results characterizing the order of approximation of the full dispersion models. They are nontrivial in the sense that they are better than the ones for the corresponding classical models.

中文翻译：

---

一些全弥散浅水模型的水波方程的严格推导

SIAM 数学分析杂志，第 53 卷，第 4 期，第 3772-3800 页，2021 年 1 月。
为了改善沿海海洋学中无旋浅水模型的频率色散效应，文献中已经正式推导出了经典模型的几种全色散版本。这个想法来自 G. Whitham 在 [Proc. A, 299 (1967), pp.6--25] 是修改它们，使它们的色散关系与水波方程相同。在本文中，我们构建了速度势的新浅水近似值，然后在速度的垂直平均水平分量上推导了近似值。我们利用它们从水波方程中严格推导出两个新的哈密顿全色散模型。这首次提供了表征全色散模型近似阶数的非平凡精度结果。