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Improving the lowest-order analysis of a nonlinear convective oscillator by applying a Mandelstam condition
Stockholm University, Faculty of Science, Department of Meteorology . (Physical Oceanography)
(English)Manuscript (preprint) (Other academic)
Abstract [en]

A lowest-order approximation of the relaxation oscillations of a nonlinear thermally forced system has been extended by prescribing a Mandelstam condition, in the present case by assuming that the total heat content of the system is conserved during rapid phase-point motion. Examples based on incorporating these improvements are shown, both of the limit-cycle representation in the phase-plane and of the calculated oscillation periods. 

Keyword [en]
Asymptotic analysis, thermal relaxation
National Category
Oceanography, Hydrology, Water Resources
Research subject
URN: urn:nbn:se:su:diva-37761OAI: diva2:304977
Available from: 2010-03-22 Created: 2010-03-22 Last updated: 2010-03-22Bibliographically approved
In thesis
1. Asymptotic methods applied to some oceanography-related problems
Open this publication in new window or tab >>Asymptotic methods applied to some oceanography-related problems
2010 (English)Doctoral thesis, comprehensive summary (Other academic)
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. 

Place, publisher, year, edition, pages
Stockholm: Department of Meteorology, Stockholm University, 2010. 34 p.
Asymptotic analysis, internal waves, geophysical fluid dynamics, thermal oscillator
National Category
Earth and Related Environmental Sciences Oceanography, Hydrology, Water Resources
Research subject
Atmospheric Sciences and Oceanography
urn:nbn:se:su:diva-37763 (URN)978-91-7447-038-3 (ISBN)
Public defence
2010-04-23, De Geersalen, Geovetenskapens hus, Svante Arrhenius väg 14, Stockholm, 10:00 (English)
At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 3: Manuscript. Paper 4: Manuscript.Available from: 2010-03-29 Created: 2010-03-22 Last updated: 2010-04-16Bibliographically approved

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Zarroug, Moundheur
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