Applications of Lie group analysis in Geophysical fluid dynamics

Document type: Monographs
Author(s): Nail H. Ibragimov, Ranis Ibragimov
Title: Applications of Lie group analysis in Geophysical fluid dynamics
Series: Series on Complexity, Nonlinearity and Chaos - Vol. 2
Year: 2011
Pagination: 240
ISBN: 978-981-4340-46-5
Publisher: World Scientific Publishing Co Pte Ltd
City: Singapore
Organization: Blekinge Institute of Technology
Department: School of Engineering - Dept. of Mathematics & Natural Sciences (Sektionen för ingenjörsvetenskap - Avd.för matematik och naturvetenskap)
School of Engineering S-371 79 Karlskrona
+46 455 38 50 00
Authors e-mail:
Language: English
Abstract: 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.
Subject: Mathematics\General
Keywords: Conservation laws, group invariant solutions, nonlinear internal waves, exakt solutions, non-hydrostatic equations of motion, ocean and atmospheric modeling