A nonlocal shallow-water model arising from the full water waves with the Coriolis effect
Abstract
In the present study a mathematical model of long-crested water waves propagating mainly in one direction with the effect of Earth's rotation is derived by following the formal asymptotic procedures. Such a model equation is analogous to the Camassa-Holm approximation of the two-dimensional incompressible and irrotational Euler equations and has a formal bi-Hamiltonian structure. Its solution corresponding to physically relevant initial perturbations is more accurate on a much longer time scale. It is shown that the deviation of the free surface can be determined by the horizontal velocity at a certain depth in the second-order approximation. The effects of the Coriolis force caused by the Earth rotation and nonlocal higher nonlinearities on blow-up criteria and wave-breaking phenomena are also investigated. Our refined analysis is approached by applying the method of characteristics and conserved quantities to the Riccati-type differential inequality.
Keywords
Cite
@article{arxiv.1801.04665,
title = {A nonlocal shallow-water model arising from the full water waves with the Coriolis effect},
author = {Guilong Gui and Yue Liu and Junwei Sun},
journal= {arXiv preprint arXiv:1801.04665},
year = {2019}
}