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

This paper studies the structural implications of constant vorticity forsteady three-dimensional internal water waves. It is known that in manyphysical regimes, water waves beneath vacuum that have constant vorticity arenecessarily two dimensional. The situation is more subtle for internal wavesthat traveling along the interface between two immiscible fluids. When thelayers have the same density, there is a large class of explicit steady waveswith constant vorticity that are three-dimensional in that the velocity fieldand pressure depend on one horizontal variable while the interface is anarbitrary function of the other. We prove the following rigidity result: everythree-dimensional traveling internal wave with bounded velocity for which thevorticities in the upper and lower layers are nonzero, constant, and parallelmust belong to this family. If the densities in each layer are distinct, thenin fact the flow is fully two dimensional.

Rigidity of three-dimensional internal waves with constant vorticity