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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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Contents
Prefa e iii
1 Introdu tion 1
1.1 Hamiltoniansystemsand geometri integration . . .
2
1.1.1 Hamiltoniansystems . . .
2
1.1.2 Geometri integration . . .
6
1.2 Hamiltonian uiddynami s . . .
8
1.2.1 HamiltonianPDEs . . .
8
1.2.2 EulerianandLagrangiandes riptions . . .
10
1.2.3 Numeri almethods. . .
12
1.3 Statisti alme hani sof uids . . .
14
1.3.1 Statisti alensembles . . .
16
1.3.2 Informationtheory . . .
20
1.3.3 Statisti altheoriesforquasigeostrophi ow . . .
22
2 Statisti al me hani sof Arakawa's dis retizations 27 2.1 Introdu tion. . .
27
2.2 Thequasigeostrophi model . . .
28
2.3 Spatialsemi-dis retization . . .
29
2.3.1 Arakawa'sdis retizations . . .
30
2.3.2 Volumepreservation . . .
33
2.4 Energy-enstrophystatisti al theory . . .
34
2.4.1 Mean eldpredi tions . . .
35
2.4.2 PV u tuationpredi tions. . .
36
2.4.3 Approximationof
µ
andα
. . .37
2.4.4 Alternativestatisti al theories. . .
38
2.5 Timeintegration . . .
39
2.6 Numeri alexperiments. . .
40
2.7 Con lusions . . .
47
3 Statisti alme hani softheHamiltonianparti le-meshmethod 53 3.1 Introdu tion. . .
53
3.2 Reviewof ontinuumstatisti alequlibriumtheories. . .
55
3.3 Hamiltonianparti le-meshmethod . . .
57
3.3.1 HPMdes ription . . .
57
3.3.2 Propertiesofthedis retization . . .
59
3.4 ALagrangian statisti almodelbasedon anoni alparti ledistributions . . .
63
ii
Contents
3.5 Eulerianstatisti almodelforHPM . . .
65
3.6 Numeri alVeri ationoftheHPMStatisti alEquilibriumTheories
68
3.6.1 NormallydistributedPV . . .70
3.6.2 SkewPVdistributions . . .
70
3.6.3 PVdistributions withkurtosis . . .
73
3.7 Con lusions . . .
75
4 Athermostat losure forpointvorti es 77 4.1 Ba kground . . .
77
4.2 Generalized thermostats . . .
78
4.2.1 Langevinthermostat . . .
80
4.2.2 AgeneralizedBulga -Kusnezovmethod . . .
82
4.3 Statisti alme hani sofpointvorti es . . .
83
4.4 Athermostated integratorforpointvorti es . . .
86
4.4.1 In niteand nitereservoir ensembles . . .
86
4.4.2 Choi eof
s
1
. . .87
4.4.3 Implementationdetails. . .
87
4.4.4 Computationoftemperatures . . .
88
4.5 Numeri alexperiments. . .
90
4.5.1 Ergodi itytests. . .
90
4.5.2 Momentum onservation . . .
90
4.5.3 Temperatureee ts . . .
92
4.6 Con lusions . . .
96
Summary 103
