English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The Green-Naghdi system is used to model highly nonlinear weakly dispersivewaves propagating at the surface of a shallow layer of a perfect fluid. Thesystem has three associated conservation laws which describe the conservationof mass, momentum, and energy due to the surface wave motion. In addition, thesystem features a fourth conservation law which is the main focus of this note.It is shown how this fourth conservation law can be interpreted in terms of aconcrete kinematic quantity connected to the evolution of the tangent velocityat the free surface. The equation for the tangent velocity is first derived forthe full Euler equations in both two and three dimensional flows, and in bothcases, it gives rise to an approximate balance law in the Green-Naghdi theorywhich turns out to be identical to the fourth conservation law for this system.

A Kinematic Conservation Law in Free Surface Flow