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Internal gravity wave beams as invariant solutions of Boussinesq equations in geophysical fluid dynamics
Ansvarig organisation
2010 (Engelska)Ingår i: Communications in nonlinear science & numerical simulation, ISSN 1007-5704, E-ISSN 1878-7274, Vol. 15, nr 8, s. 1989-2002Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

It is shown that Lie group analysis of differential equations provides the exact solutions of two-dimensional stratified rotating Boussinesq equations which are a basic model in geophysical fluid dynamics. The exact solutions are obtained as group invariant solutions corresponding to the translation and dilation generators of the group of transformations admitted by the equations. The comparison with the previous analytic studies and experimental observations confirms that the anisotropic nature of the wave motion allows to associate these invariant solutions with uni-directional internal wave beams propagating through the medium. It is also shown that the direction of internal wave beam propagation is in the transverse direction to one of the invariants which corresponds to a linear combination of the translation symmetries. Furthermore, the amplitudes of a linear superposition of wave-like invariant solutions forming the internal gravity wave beams are arbitrary functions of that invariant. Analytic examples of the latitude-dependent invariant solutions associated with internal gravity wave beams that have different general profiles along the obtained invariant and propagating in the transverse direction are considered. The behavior of the invariant solutions near the critical latitude is illustrated. © 2009 Elsevier B.V. All rights reserved.

Ort, förlag, år, upplaga, sidor
Elsevier , 2010. Vol. 15, nr 8, s. 1989-2002
Nyckelord [en]
Internal waves, Invariant solutions, Stratified fluid
Nationell ämneskategori
Matematik
Identifikatorer
URN: urn:nbn:se:bth-7878DOI: 10.1016/j.cnsns.2009.09.006ISI: 000275730200004Lokalt ID: oai:bth.se:forskinfo38C809F43A34218CC12576D40036DB5AOAI: oai:DiVA.org:bth-7878DiVA, id: diva2:835546
Tillgänglig från: 2012-09-18 Skapad: 2010-02-24 Senast uppdaterad: 2017-12-04Bibliografiskt granskad

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