A new shallow water model, by asymptotic analysis, with linear dependence on depth | Zendy

Rodríguez José M. | Zendy; TaboadaVázquez Raquel | Zendy

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A new shallow water model, by asymptotic analysis, with linear dependence on depth

Author(s) -

Rodríguez José M.,

TaboadaVázquez Raquel

Publication year - 2007

Publication title -

pamm

Language(s) - English

Resource type - Journals

ISSN - 1617-7061

DOI - 10.1002/pamm.200700316

Subject(s) - constant (computer programming) , euler equations , euler's formula , domain (mathematical analysis) , zero (linguistics) , waves and shallow water , asymptotic analysis , mathematics , mathematical analysis , shallow water equations , vorticity , vortex , physics , mechanics , computer science , thermodynamics , programming language , linguistics , philosophy

In this paper, we study Euler equations in a domain with small depth. With this aim, we introduce a small a‐dimensional parameter ε related to the depth and we use asymptotic analysis to study what happens when ε becomes small. In this way we obtain a shallow water model that considers the possibility of a non‐constant bottom and the horizontal velocity components depend on z if the vorticity is not zero. The new model is able to calculate exactly the solutions to Euler equations that are linear in z , whereas the classic model just obtains the average velocities. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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