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Asymptotic methods applied to some oceanography-related problems
Stockholms universitet, Naturvetenskapliga fakulteten, Meteorologiska institutionen (MISU). (Physical Oceanography)
2010 (Engelska)Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
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. 

Ort, förlag, år, upplaga, sidor
Stockholm: Department of Meteorology, Stockholm University , 2010. , s. 34
Nyckelord [en]
Asymptotic analysis, internal waves, geophysical fluid dynamics, thermal oscillator
Nationell ämneskategori
Geovetenskap och miljövetenskap Oceanografi, hydrologi och vattenresurser
Forskningsämne
atmosfärvetenskap och oceanografi
Identifikatorer
URN: urn:nbn:se:su:diva-37763ISBN: 978-91-7447-038-3 (tryckt)OAI: oai:DiVA.org:su-37763DiVA, id: diva2:305005
Disputation
2010-04-23, De Geersalen, Geovetenskapens hus, Svante Arrhenius väg 14, Stockholm, 10:00 (Engelska)
Opponent
Handledare
Anmärkning
At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 3: Manuscript. Paper 4: Manuscript.Tillgänglig från: 2010-03-29 Skapad: 2010-03-22 Senast uppdaterad: 2018-01-12Bibliografiskt granskad
Delarbeten
1. Energetics of tidally generated internal waves
Öppna denna publikation i ny flik eller fönster >>Energetics of tidally generated internal waves
2010 (Engelska)Ingår i: Tellus. Series A, Dynamic meteorology and oceanography, ISSN 0280-6495, E-ISSN 1600-0870, Vol. 62, nr 1, s. 71-79Artikel i tidskrift (Refereegranskat) 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. 

Nyckelord
Tidal generation, WKB theory, Homogenization theory
Nationell ämneskategori
Oceanografi, hydrologi och vattenresurser
Forskningsämne
oceanografi
Identifikatorer
urn:nbn:se:su:diva-37760 (URN)10.1111/j.1600-0870.2009.00415.x (DOI)000272838100007 ()
Tillgänglig från: 2010-03-22 Skapad: 2010-03-22 Senast uppdaterad: 2019-12-17Bibliografiskt granskad
2. A note on the asymptotic analysis of a thermal relaxation oscillator
Öppna denna publikation i ny flik eller fönster >>A note on the asymptotic analysis of a thermal relaxation oscillator
2009 (Engelska)Ingår i: Zeitschrift für angewandte Mathematik und Mechanik, ISSN 0044-2267, E-ISSN 1521-4001, Vol. 89, nr 12, s. 995-1001Artikel i tidskrift (Refereegranskat) 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.

Nationell ämneskategori
Fysik
Forskningsämne
oceanografi
Identifikatorer
urn:nbn:se:su:diva-35207 (URN)10.1002/zamm.200900304 (DOI)000272783900004 ()
Tillgänglig från: 2010-01-15 Skapad: 2010-01-15 Senast uppdaterad: 2017-12-12Bibliografiskt granskad
3. Improving the lowest-order analysis of a nonlinear convective oscillator by applying a Mandelstam condition
Öppna denna publikation i ny flik eller fönster >>Improving the lowest-order analysis of a nonlinear convective oscillator by applying a Mandelstam condition
(Engelska)Manuskript (preprint) (Övrigt vetenskapligt)
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. 

Nyckelord
Asymptotic analysis, thermal relaxation
Nationell ämneskategori
Oceanografi, hydrologi och vattenresurser
Forskningsämne
oceanografi
Identifikatorer
urn:nbn:se:su:diva-37761 (URN)
Tillgänglig från: 2010-03-22 Skapad: 2010-03-22 Senast uppdaterad: 2018-01-12Bibliografiskt granskad
4. A heurestic higher-order analysis of a thermal relaxation oscillator
Öppna denna publikation i ny flik eller fönster >>A heurestic higher-order analysis of a thermal relaxation oscillator
(Engelska)Manuskript (preprint) (Övrigt vetenskapligt)
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.

Nyckelord
asymptotic analysis, thermal relaxation
Nationell ämneskategori
Oceanografi, hydrologi och vattenresurser
Forskningsämne
oceanografi
Identifikatorer
urn:nbn:se:su:diva-37762 (URN)
Tillgänglig från: 2010-03-22 Skapad: 2010-03-22 Senast uppdaterad: 2018-01-12Bibliografiskt granskad

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