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On the vorticity of long gravity waves in water of variable depth

โœ Scribed by John Miles; Rick Salmon

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
120 KB
Volume
25
Category
Article
ISSN
0165-2125

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โœฆ Synopsis

Yoon and Liu's analysis of long gravity waves in water of slowly varying depth is modified to allow for conservation of potential vorticity in place of their (incorrect) conservation at conventional vorticity.

Yoon and Liu [l] derive a Boussinesq approximation to the Hamiltonian for long gravity waves in water of slowly varying depth and, following Broer [2], modify this Hamiltonian to protect against short-wave instability. They assume irrotational flow, overlooking the fact that topographical variation vitiates the conservation of the conventional vorticity but that a potential vorticity is conserved .

The Hamiltonian functional for gravity waves in a laterally unbounded body of water of density p and ambient depth h(x) is given by

๐Ÿ“œ SIMILAR VOLUMES

Three-dimensional gravity waves in a cha
Three-dimensional gravity waves in a channel of variable depth
โœ Ranis N. Ibragimov; Dmitry E. Pelinovsky ๐Ÿ“‚ Article ๐Ÿ“… 2008 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 194 KB

We consider existence of three-dimensional gravity waves traveling along a channel of variable depth. It is well known that the long-wave small-amplitude expansion for such waves results in the stationary Korteweg-de Vries equation, coefficients of which depend on the transverse topography of the ch