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A note on the asymptotic analysis of a thermal relaxation oscillator
Stockholms universitet, Naturvetenskapliga fakulteten, Meteorologiska institutionen (MISU).
Tabriz University, Department of Applied Mathematics.
Stockholms universitet, Naturvetenskapliga fakulteten, Meteorologiska institutionen (MISU).
2009 (engelsk)Inngår i: Zeitschrift für angewandte Mathematik und Mechanik, ISSN 0044-2267, E-ISSN 1521-4001, Vol. 89, nr 12, s. 995-1001Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

A nonlinear oscillator, based on two connected vessels which are thermally forced around the maximum-density temperature of the working fluid, is investigated. For a suitable choice of parameters, the system executes self-sustained relaxation oscillations. This process has been examined for a large volume difference between the vessels, in which case the solution makes almost discontinuous jumps between the two branches of the slow manifold of the problem. It was found that in this limit, a lowest-order analysis does reasonable justice to the periodic behaviour of the system.

sted, utgiver, år, opplag, sider
2009. Vol. 89, nr 12, s. 995-1001
HSV kategori
Forskningsprogram
oceanografi
Identifikatorer
URN: urn:nbn:se:su:diva-35207DOI: 10.1002/zamm.200900304ISI: 000272783900004OAI: oai:DiVA.org:su-35207DiVA, id: diva2:286675
Tilgjengelig fra: 2010-01-15 Laget: 2010-01-15 Sist oppdatert: 2017-12-12bibliografisk kontrollert
Inngår i avhandling
1. Asymptotic methods applied to some oceanography-related problems
Åpne denne publikasjonen i ny fane eller vindu >>Asymptotic methods applied to some oceanography-related problems
2010 (engelsk)Doktoravhandling, med artikler (Annet vitenskapelig)
Abstract [en]

In this thesis a number of issues related to oceanographic problems have been dealt with on the basis of applying asymptotic methods. 

The first study focused on the tidal generation of internal waves, a process which is quantifed by the conversion rates. These have traditionally been calculated by using the WKB approximation. However, the systematic imprecision of this theory for the lowest modes as well as turbulence at the seabed level affect the results. To handle these anomalies we introduced another asymptotic technique, homogenization theory, which led to signifcant improvements, especially for the lowest modes. 

The second study dealt with the dynamical aspects of a nonlinear oscillator which can be interpreted as a variant of the classical two-box models used in oceanography. The system is constituted by two connected vessels containing a fluid characterised by a nonlinear equation of state and a large volume differences between the vessels is prescribed. It is recognised that the system, when performing relaxation oscillations, exhibits almost-discontinuous jumps between the two branches of the slow manifold of the problem. The lowest-order analysis yielded reasonable correspondence with the numerical results. 

The third study is an extension of the lowest-order approximation of the relaxation oscillations undertaken in the previous paper. A Mandelstam condition is imposed on the system by assuming that the total heat content of the system is conserved during the discontinuous jumps. 

In the fourth study an asymptotic analysis is carried out to examine the oscillatory behaviour of the thermal oscillator. It is found that the analytically determined corrections to the zeroth-order analysis yield overall satisfying results even for comparatively large values of the vessel-volume ratio. 

sted, utgiver, år, opplag, sider
Stockholm: Department of Meteorology, Stockholm University, 2010. s. 34
Emneord
Asymptotic analysis, internal waves, geophysical fluid dynamics, thermal oscillator
HSV kategori
Forskningsprogram
atmosfärvetenskap och oceanografi
Identifikatorer
urn:nbn:se:su:diva-37763 (URN)978-91-7447-038-3 (ISBN)
Disputas
2010-04-23, De Geersalen, Geovetenskapens hus, Svante Arrhenius väg 14, Stockholm, 10:00 (engelsk)
Opponent
Veileder
Merknad
At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 3: Manuscript. Paper 4: Manuscript.Tilgjengelig fra: 2010-03-29 Laget: 2010-03-22 Sist oppdatert: 2018-01-12bibliografisk kontrollert

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