| 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 change | p. 3 |
| Fundamental Ocean Equations | p. 5 |
| Basics Of Ocean Fluid Mechanics | |
| Some fundamental ocean processes | |
| The continuum hypothesis | |
| Kinematics of fluid motion | p. 1 |
| Kinematical and dynamical approximations | p. 1 |
| Averaging over scales and realizations | p. 2 |
| Numerical discretization | p. 2 |
| Chapter summary | p. 22 |
| Kinematics | p. 2 |
| Introduction | p. 2 |
| Mathematical preliminaries | p. 2 |
| The divergence theorem and budget analyses | p. 2 |
| Volume and mass conserving kinematics | p. 3 |
| Chapter summary | p. 40 |
| Dynamics | p. 4 |
| Introduction | p. 4 |
| Motion on a rotating sphere | p. 4 |
| Principles of continuum dynamics | p. 4 |
| Dynamics of fluid parcels | p. 5 |
| Hydrostatic pressure | p. 5 |
| Dynamics of hydrostatic fluid columns | p. 5 |
| Fluid motion in a rapidly rotating system | p. 6 |
| Vertical stratification | p. 6 |
| Vorticity and potential vorticity | p. 7 |
| 0 Particle dynamics on a rotating sphere | p. 7 |
| 1 Symmetry and conservation laws | p. 8 |
| 2 Chapter summary | p. 83 |
| Thermo-Hydrodynamics | p. 8 |
| General types of ocean tracers | p. 8 |
| Basic equilibrium thermodynamics | p. 9 |
| Energy of a fluid parcel | p. 9 |
| Global mechanical energy balance | p. 10 |
| Basic non-equilibrium thermodynamics | p. 11 |
| Thermodynamical tracers | p. 11 |
| Ocean density | p. 11 |
| Chapter summary | p. 118 |
| Generalized Vertical Coordinates | p. 12 |
| Introduction | p. 12 |
| Concerning the choice of vertical coordinate | p. 12 |
| Generalized surfaces | p. 12 |
| Local orthonormal coordinates | p. 13 |
| Mathematics of generalized vertical coordinates | p. 13 |
| Metric tensors | p. 13 |
| The dia-surface velocity component | p. 13 |
| Conservation of mass and volume for parcels | p. 14 |
| Kinematic boundary conditions | p. 14 |
| 0 Primitive equations | p. 14 |
| 1 Transformation of SGS tracer flux components | p. 14 |
| 2 Chapter summary | p. 149 |
| averaged Descriptions | p. 153 |
| Concerni Ng Unresolved Physics | p. 15 |
| Represented dynamics and parameterized physics | p. 15 |
| Lateral (neutral) and vertical processes | p. 15 |
| Basic mechanisms for dianeutral transport | p. 15 |
| Dianeutral transport in models | p. 16 |
| Numerically induced spurious dianeutral transport | p. 16 |
| Chapter summary | p. 167 |
| Eulerian Averaged Equations | p. 16 |
| Introduction | p. 16 |
| The nonhydrostatic shallow ocean equations | p. 17 |
| Averaged kinematics | p. 17 |
| Averaged kinematics over finite domains | p. 17 |
| Averaged tracer | p. 17 |
| Averaged momentum budget | p. 18 |
| Summary of the Eulerian averaged equations | p. 18 |
| Mapping to ocean model variables | p. 18 |
| Chapter summary | p. 187 |
| Kinematics Of An Isentropic Ensemble | p. 18 |
| Parameterizing mesoscale eddies | p. 18 |
| Advection and skewsion | p. 19 |
| Volume conservation | p. 19 |
| Ensemble mean tracer equation | p. 20 |
| Quasi-Stokes transport in z-models | p. 20 |
| Chapter summary | p. 212 |
| Semi-Discrete Equations And Algorithms | p. 215 |
| Discretization Basics | p. 217 |
| Discretization methods | p. 217 |
| An introduction to Arakawa grids | p. 218 |
| Time stepping | p. 219 |
| Chapter summary | p. 221 |
| Mass And Tracer Budgets | p. 222 |
| Summary of the continuous model equations | p. 222 |
| Tracer and mass/volume compatibility | p. 223 |
| Mass budget for a grid cell | p. 223 |
| Mass budget for a discrete fluid column | p. 227 |
| Tracer budget for a grid cell | p. 228 |
| Fluxes for turbulence mixed layer schemes | p. 232 |
| Flux plus restore boundary conditions | p. 233 |
| Z-like vertical coordinate models | p. 234 |
| Chapter summary | p. 235 |
| Algorithms for hydrostatic ocean model | |
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