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

We study the relevance of various scalar equations, such as inviscidBurgers', Korteweg-de Vries (KdV), extended KdV, and higher order equations (ofCamassa-Holm type), as asymptotic models for the propagation of internal wavesin a two-fluid system. These scalar evolution equations may be justified withtwo approaches. The first method consists in approximating the flow with twodecoupled, counterpropagating waves, each one satisfying such an equation. Onealso recovers homologous equations when focusing on a given direction ofpropagation, and seeking unidirectional approximate solutions. This secondjustification is more restrictive as for the admissible initial data, butyields greater accuracy. Additionally, we present several new coupledasymptotic models: a Green-Naghdi type model, its simplified version in theso-called Camassa-Holm regime, and a weakly decoupled model. All of the modelsare rigorously justified in the sense of consistency.

Decoupled and unidirectional asymptotic models for the propagation of internal waves