Long nonlinear internal waves. (English) Zbl 1098.76018

Helfrich, Karl R.; Melville, W. Kendall

Davis, Stephen H. (ed.) et al., Annual review of fluid mechanics. Vol. 38. Palo Alto, CA: Annual Reviews (ISBN 0-8243-0738-0/hbk). Annu. Rev. Fluid Mech. 38, 395-425 (2006).

Summary: Over the past four decades, the combination of in situ and remote sensing observations has demonstrated that long nonlinear internal solitary-like waves are ubiquitous features of coastal oceans. The following provides an overview of the properties of steady internal solitary waves and the transient processes of wave generation and evolution, primarily from the point of view of weakly nonlinear theory, of which the Korteweg-de Vries equation is the most frequently used example. However, the oceanographically important processes of wave instability and breaking, generally inaccessible with these models, are also discussed. Furthermore, observations often show strongly nonlinear waves whose properties can only be explained with fully nonlinear models.
For the entire collection see [Zbl 1081.76003].

MSC:

76B55	Internal waves for incompressible inviscid fluids
76B25	Solitary waves for incompressible inviscid fluids
86A05	Hydrology, hydrography, oceanography
76-02	Research exposition (monographs, survey articles) pertaining to fluid mechanics

Keywords:

solitary waves; stratified flow; Korteweg-de Vries equation