Statistical mechanics and numerical modelling of geophysical fluid dynamics - Preface

UvA-DARE is a service provided by the library of the University of Amsterdam (http

s

://dare.uva.nl)

UvA-DARE (Digital Academic Repository)

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.

General rights

It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s)

and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open

content license (like Creative Commons).

Disclaimer/Complaints regulations

If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please

let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material

inaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letter

to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You

will be contacted as soon as possible.

Preface

Statisti alme hani sisapowerfulapproa htounderstanding omplexphysi al

systems. The purpose of statisti al me hani sis to onstru t methods whi h

an handlein ompletelyknown systems;todes ribethemostlikelybehaviour

ofasystem;toworkwithtimeseriesdatafromexperimentsornumeri al

mod-els. Inthisthesisweusestatisti alme hani sasatooltoshowtheimportan e

of onservation laws of a numeri al method. Depending on what onserved

quantitiesthedis retesystemhas,thestatisti altheoryofthisdis retesystem

varies. Therefore,the hosenmethodhasaninuen e onthestatisti alresults

of thesimulatedmodel. Inthe thesisIshowthat statisti alme hani s anbe

alsoemployedasatoolbyanumeri alanalysttoverifythestatisti ala ura y

of a numeri al method. This is very important issue for appli ations su h as

limate variability, sin e in these appli ations long numeri al simulations are

run for dynami al systems that are known to be haoti , and for whi h it is

onsequentlyimpossible tosimulate aparti ularsolutionwithanya ura yin

the usual sense. Instead, the goalof su h simulations is to obtain a data set

suitable for omputing statisti al averages or otherwise to sample the

proba-bilitydistributionasso iatedwiththe ontinuousproblem. Dierentnumeri al

dis retizations havedierent dis rete dynami s. Therefore it is ru ial to

es-tablish the inuen e that a parti ular hoi e of method hason the statisti al

resultsobtainedfrom simulations.

Anotherattra tiveappli ation forstatisti al me hani s is themodeling of

sub-s ale motion. Invis iduidmodelsarenatural in a number of appli ation

areas, su h as atmosphere and o ean s ien e. These ows are hara terized

by onservation of energy, sensitive dependen e on initial onditions, and the

as adeofvorti itytoeverners ales. Forthesimulationofsu hows

numer-i ally,thevorti ity as adepresentsthe hallengethatanydire tdis retization

of the equation of motionmust eventually be omeunderresolved. To address

thisproblemee tivelyrequiresmodellingthesub-grids aledynami sandtheir

inuen eonthe oarses ale. Inthethesis,Ishowforapointvortexmodelthat

these ee ts an be parameterized using an adapted 'mathemati al

thermo-stat', ate hniqueusedin mole ularsimulationstomodela systemofparti les

intera ting ata onstanttemperature. I believethat this methodology anbe

extended for more omplex models with feasible appli ations in limate

vari-ability.

This proje t was funded in NWO Earth& Life S ien es Coun ilClimate

Variability program,anditaddress theproblemsarisingin numeri al

iv

Preface

a newte hniqueformodellingthesub-s alemotion,whi h anbeemployedin

atmosphereando eans ien e.

Thisthesisre ordsthenumeri almathemati sresear hI ondu tedbetween

August2005andJanuary2010intheModeling,AnalysisandSimulation(MAS)

departmentoftheCentrumWiskunde&Informati a(CWI)inAmsterdam.

Chapters2through 4ofthisthesishaveappearedasjournalarti les:

1. Chapter2isbasedonS.DubinkinaandJ.Frank,Statisti alme hani sof

Arakawa's dis retizations, Journal of Computational Physi s 227, pages

12861305,2007.

2. Chapter 3 is based on S. Dubinkina and J. Frank, Statisti al relevan e

of vorti ity onservation with the Hamiltonian parti le-mesh method,

a - eptedforpubli ationinJournal ofComputationalPhysi s,2010.

3. Chapter4 isbasedonS.Dubinkina,J.FrankandB.Leimkuhler,A

ther-mostat losureforpointvorti es,submitted,2009.

Chapter 1,theintrodu tory hapter olle ts mu hof theba kgroundmaterial

neededtoread therest ofthethesis.