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Fundamentals of Ocean Climate Models - Stephen Griffies

Fundamentals of Ocean Climate Models

Hardcover Published: 5th September 2004
ISBN: 9780691118925
Number Of Pages: 528

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This book sets forth the physical, mathematical, and numerical foundations of computer models used to understand and predict the global ocean climate system. Aimed at students and researchers of ocean and climate science who seek to understand the physical content of ocean model equations and numerical methods for their solution, it is largely general in formulation and employs modern mathematical techniques. It also highlights certain areas of cutting-edge research.

Stephen Griffies presents material that spans a broad spectrum of issues critical for modern ocean climate models. Topics are organized into parts consisting of related chapters, with each part largely self-contained. Early chapters focus on the basic equations arising from classical mechanics and thermodynamics used to rationalize ocean fluid dynamics. These equations are then cast into a form appropriate for numerical models of finite grid resolution. Basic discretization methods are described for commonly used classes of ocean climate models. The book proceeds to focus on the parameterization of phenomena occurring at scales unresolved by the ocean model, which represents a large part of modern oceanographic research. The final part provides a tutorial on the tensor methods that are used throughout the book, in a general and elegant fashion, to formulate the equations.

"Stephen Griffie's book ... will be found open on the desks of those who develop ocean models for years to come... This is a unique and useful work."--Matthew Hecht, Bulletin of the American Meteorological Society

Foreword XIII
Preface XV
Acknowledgments XXV
About the cover XXVII
List of symbols XXIX
Ocean Climate Models
Ocean models as tools for ocean science
Ocean climate models
Challenges of climate changep. 3
Fundamental Ocean Equationsp. 5
Basics Of Ocean Fluid Mechanics
Some fundamental ocean processes
The continuum hypothesis
Kinematics of fluid motionp. 1
Kinematical and dynamical approximationsp. 1
Averaging over scales and realizationsp. 2
Numerical discretizationp. 2
Chapter summaryp. 22
Kinematicsp. 2
Introductionp. 2
Mathematical preliminariesp. 2
The divergence theorem and budget analysesp. 2
Volume and mass conserving kinematicsp. 3
Chapter summaryp. 40
Dynamicsp. 4
Introductionp. 4
Motion on a rotating spherep. 4
Principles of continuum dynamicsp. 4
Dynamics of fluid parcelsp. 5
Hydrostatic pressurep. 5
Dynamics of hydrostatic fluid columnsp. 5
Fluid motion in a rapidly rotating systemp. 6
Vertical stratificationp. 6
Vorticity and potential vorticityp. 7
0 Particle dynamics on a rotating spherep. 7
1 Symmetry and conservation lawsp. 8
2 Chapter summaryp. 83
Thermo-Hydrodynamicsp. 8
General types of ocean tracersp. 8
Basic equilibrium thermodynamicsp. 9
Energy of a fluid parcelp. 9
Global mechanical energy balancep. 10
Basic non-equilibrium thermodynamicsp. 11
Thermodynamical tracersp. 11
Ocean densityp. 11
Chapter summaryp. 118
Generalized Vertical Coordinatesp. 12
Introductionp. 12
Concerning the choice of vertical coordinatep. 12
Generalized surfacesp. 12
Local orthonormal coordinatesp. 13
Mathematics of generalized vertical coordinatesp. 13
Metric tensorsp. 13
The dia-surface velocity componentp. 13
Conservation of mass and volume for parcelsp. 14
Kinematic boundary conditionsp. 14
0 Primitive equationsp. 14
1 Transformation of SGS tracer flux componentsp. 14
2 Chapter summaryp. 149
averaged Descriptionsp. 153
Concerni Ng Unresolved Physicsp. 15
Represented dynamics and parameterized physicsp. 15
Lateral (neutral) and vertical processesp. 15
Basic mechanisms for dianeutral transportp. 15
Dianeutral transport in modelsp. 16
Numerically induced spurious dianeutral transportp. 16
Chapter summaryp. 167
Eulerian Averaged Equationsp. 16
Introductionp. 16
The nonhydrostatic shallow ocean equationsp. 17
Averaged kinematicsp. 17
Averaged kinematics over finite domainsp. 17
Averaged tracerp. 17
Averaged momentum budgetp. 18
Summary of the Eulerian averaged equationsp. 18
Mapping to ocean model variablesp. 18
Chapter summaryp. 187
Kinematics Of An Isentropic Ensemblep. 18
Parameterizing mesoscale eddiesp. 18
Advection and skewsionp. 19
Volume conservationp. 19
Ensemble mean tracer equationp. 20
Quasi-Stokes transport in z-modelsp. 20
Chapter summaryp. 212
Semi-Discrete Equations And Algorithmsp. 215
Discretization Basicsp. 217
Discretization methodsp. 217
An introduction to Arakawa gridsp. 218
Time steppingp. 219
Chapter summaryp. 221
Mass And Tracer Budgetsp. 222
Summary of the continuous model equationsp. 222
Tracer and mass/volume compatibilityp. 223
Mass budget for a grid cellp. 223
Mass budget for a discrete fluid columnp. 227
Tracer budget for a grid cellp. 228
Fluxes for turbulence mixed layer schemesp. 232
Flux plus restore boundary conditionsp. 233
Z-like vertical coordinate modelsp. 234
Chapter summaryp. 235
Algorithms for hydrostatic ocean model
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780691118925
ISBN-10: 0691118922
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 528
Published: 5th September 2004
Publisher: Princeton University Press
Country of Publication: US
Dimensions (cm): 25.4 x 17.8  x 3.81
Weight (kg): 1.13