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Statistical mechanics and numerical modelling of geophysical fluid dynamics
Dubinkina, S.B.
Publication date
2010
Link to publication
Citation for published version (APA):
Dubinkina, S. B. (2010). Statistical mechanics and numerical modelling of geophysical fluid
dynamics.
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Summary
Theresear hinthisthesisisdevotedtothestatisti alme hani sandnumeri al
modellingofgeophysi al uiddynami s.
Theresultsofstatisti alanalysisofsimulationdataobtainedfromlongtime
in-tegrationsofgeophysi al uidmodelsgreatlydependonthe onservation
prop-erties ofthenumeri aldis retizationused. InChapter2,this isillustratedfor
quasigeostrophi owwithtopographi for ing,forwhi hawellestablished
sta-tisti alme hani sexists. We onstru tedstatisti alme hani altheoriesforthe
dis rete dynami al systems arising from three dis retizations due to Arakawa
(J.Comput. Phys.,1966)whi h onserveenergy,enstrophyorboth. Numeri al
experimentswith onservativeandproje tedtimeintegratorshaveshownthat
the statisti al theoriesa urately explainthe dieren esobservedin statisti s
derivedfromthedis retizations.
InChapter3,we ondu tedlong-timesimulationswithaHamiltonian
parti le-meshmethodforideal uid ow,todeterminethestatisti almeanvorti ity eld
of thedis retization. Weproposed Lagrangianand Eulerianstatisti al models
forthe dis retedynami s,and omparedthemagainstnumeri alexperiments.
Theobservedresultsareinex ellentagreementwiththeoreti almodels,aswell
aswiththe ontinuumstatisti alme hani altheoryforideal owdevelopedby
Ellis,Haven&Turkington(Nonlinearity,2002). Inparti ulartheresultsveri ed
that the apparently trivial onservation of potential vorti ity along parti le
paths using the HPM method signi antly in uen es the mean state. As a
side note,thenumeri alexperimentsshowedthat a nonzerofourth momentof
potentialvorti ity an in uen ethestatisti almean.
Invis id uid modelsare hara terizedby onservation ofenergy, sensitive
de-penden eoninitial onditions,andthe as adeofvorti itytoever ners ales.
Fornumeri alsimulationsofsu h ows,thevorti ity as adepresentsthe
hal-lenge that any dire t dis retization oftheequation of motionmusteventually
be ome underresolved. To address this problem ee tivelyrequires modelling
thesubgrids aledynami sandtheirin uen eonthe oarses ale. InChapter4,
usingthepointvortex owonadis asa prototype,wepresenteda losurefor
in ompressible ideal uid owin the form of a generalized thermostating
de-vi e, a te hniqueusedin mole ular simulationsto model asystemof parti les
intera ting at a onstant temperature. We showed that the thermostat an
modeleitheranin niteor nitereservoirwithsto hasti allyfor edthermostat
