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Applications of Lie group analysis in Geophysical fluid dynamics
Responsible organisation
2011 (English)Book (Other academic)
Abstract [en]

This book introduces an effective method for seeking local and nonlocal conservation laws and exact solutions for nonlinear two-dimensional equations which provide a basic model in describing internal waves in the ocean. The model consists of non-hydrostatic equations of motion which uses the Boussinesq approximation and linear stratification. The Lie group analysis is used for constructing non-trivial conservation laws and group invariant solutions. It is shown that nonlinear equations in question have remarkable property to be self-adjoint. This property is crucial for constructing physically relevant conservation laws for nonlinear internal waves in the ocean. The comparison with the previous analytic studies and experimental observations confirrms that the anisotropic nature of the wave motion allows to associate some of the obtained invariant solutions with uni-directional internal wave beams propagating through the medium. Analytic examples of the latitude-dependent invariant solutions associated with internal gravity wave beams are considered. The behavior of the invariant solutions near the critical latitude is investigated.

Place, publisher, year, edition, pages
Singapore: World Scientific Publishing Co Pte Ltd , 2011. , 240 p.
Keyword [en]
Conservation laws, group invariant solutions, nonlinear internal waves, exakt solutions, non-hydrostatic equations of motion, ocean and atmospheric modeling
National Category
Mathematics
Identifiers
URN: urn:nbn:se:bth-7512Local ID: oai:bth.se:forskinfo686B1CC1CF267A93C12578BD0066B43DISBN: 978-981-4340-46-5 (print)OAI: oai:DiVA.org:bth-7512DiVA: diva2:835136
Available from: 2012-09-18 Created: 2011-06-28 Last updated: 2015-06-30Bibliographically approved

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