Variational Derivation of the Green–Naghdi Shallow-Water Equations
- 10.1142/S1402925112400013How to use a DOI?
- Green–Naghdi equations; shallow-water waves; variational methods
We consider the two-dimensional irrotational water-wave problem with a free surface and a flat bottom. In the shallow-water regime and without smallness assumption on the wave amplitude we derive, by a variational approach in the Lagrangian formalism, the Green–Naghdi equations (1.1). The second equation in (1.1) is a transport equation, the free surface is advected by the fluid flow. We show that the first equation of the system (1.1) yields the critical points of an action functional in the space of paths with fixed endpoints, within the Lagrangian formalism.
- © 2012 The Authors. Published by Atlantis Press and Taylor & Francis
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- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Delia Ionescu-Kruse PY - 2012 DA - 2012/11/28 TI - Variational Derivation of the Green–Naghdi Shallow-Water Equations JO - Journal of Nonlinear Mathematical Physics SP - 1 EP - 12 VL - 19 IS - Supplement 1 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925112400013 DO - 10.1142/S1402925112400013 ID - Ionescu-Kruse2012 ER -