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Asymptotic methods applied to some oceanography-related problems
Stockholm University, Faculty of Science, Department of Meteorology . (Physical Oceanography)
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.
Keyword [en]
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
Identifiers
URN: urn:nbn:se:su:diva-37763ISBN: 978-91-7447-038-3 (print)OAI: oai:DiVA.org:su-37763DiVA: diva2:305005
Public defence
2010-04-23, De Geersalen, Geovetenskapens hus, Svante Arrhenius väg 14, Stockholm, 10:00 (English)
Opponent
Supervisors
Note
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
List of papers
1. Energetics of tidally generated internal waves
Open this publication in new window or tab >>Energetics of tidally generated internal waves
2010 (English)In: Tellus. Series A, Dynamic meteorology and oceanography, ISSN 0280-6495, E-ISSN 1600-0870, Vol. 62, no 1, 71-79 p.Article in journal (Refereed) Published
Abstract [en]

The generation of internal waves from barotropic tides can be quantified in terms of the conversion rates. These have often been obtained by applying the WKB approximation, which yields an expression for the conversion rates which is proportional to the seabed buoyancy frequency NB . For small values of NB or strong variations of the buoyancy profile N (z), this gives unreliable results. Using homogenization theory it is here shown that the conversion rate instead depends on the value of N (z) averaged over a vertical region at the bottom of the same magnitude as the vertical length-scale of the internal wave, which for the lowest modes is of the same order as the entire ocean depth. This gives a substantially larger conversion rate. 

Keyword
Tidal generation, WKB theory, Homogenization theory
National Category
Oceanography, Hydrology, Water Resources
Research subject
Oceanography
Identifiers
urn:nbn:se:su:diva-37760 (URN)10.1111/j.1600-0870.2009.00415.x (DOI)000272838100007 ()
Available from: 2010-03-22 Created: 2010-03-22 Last updated: 2017-12-12Bibliographically approved
2. A note on the asymptotic analysis of a thermal relaxation oscillator
Open this publication in new window or tab >>A note on the asymptotic analysis of a thermal relaxation oscillator
2009 (English)In: Zeitschrift für angewandte Mathematik und Mechanik, ISSN 0044-2267, E-ISSN 1521-4001, Vol. 89, no 12, 995-1001 p.Article in journal (Refereed) 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.

National Category
Physical Sciences
Research subject
Oceanography
Identifiers
urn:nbn:se:su:diva-35207 (URN)10.1002/zamm.200900304 (DOI)000272783900004 ()
Available from: 2010-01-15 Created: 2010-01-15 Last updated: 2017-12-12Bibliographically approved
3. Improving the lowest-order analysis of a nonlinear convective oscillator by applying a Mandelstam condition
Open this publication in new window or tab >>Improving the lowest-order analysis of a nonlinear convective oscillator by applying a Mandelstam condition
(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
Asymptotic analysis, thermal relaxation
National Category
Oceanography, Hydrology, Water Resources
Research subject
Oceanography
Identifiers
urn:nbn:se:su:diva-37761 (URN)
Available from: 2010-03-22 Created: 2010-03-22 Last updated: 2010-03-22Bibliographically approved
4. A heurestic higher-order analysis of a thermal relaxation oscillator
Open this publication in new window or tab >>A heurestic higher-order analysis of a thermal relaxation oscillator
(English)Manuscript (preprint) (Other academic)
Abstract [en]

The oscillatory behaviour of a differentially heated system, based on two connected vessels containing a fluid with a nonlinear equation of state, has been sub jected to an asymptotically valid analysis. The quotient of the vessel volumes was used as expansion parameter, and it was found that the analytically determined corrections to the zeroth-order results served a useful purpose even for quite large values of the volume ratio.

Keyword
asymptotic analysis, thermal relaxation
National Category
Oceanography, Hydrology, Water Resources
Research subject
Oceanography
Identifiers
urn:nbn:se:su:diva-37762 (URN)
Available from: 2010-03-22 Created: 2010-03-22 Last updated: 2010-03-22Bibliographically approved

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