Foreword Preface Preface of the First Edition xiii xv xvii Parti Fundamentals 1. Introduction 1.1 Objective 3 1.2 Importance of Geophysical Fluid Dynamics 4 1.3 Distinguishing Attributes of Geophysical Flows 6 1.4 Scales of Motions 8 1.5 Importance of Rotation 10 1.6 Importance of Stratification 12 1.7 Distinction between the Atmosphere and Oceans 14 1.8 Data Acquisition 17 1.9 The Emergence of Numerical Simulations 19 1.10 Scales Analysis and Finite Differences 23 1.11 Higher-Order Methods 28 1.12 Aliasing 33 Analytical Problems 35 Numerical Exercises 35 2. The Coriolis Force 2.1 Rotating Framework of Reference 41 2.2 Unimportance of the Centrifugal Force 44 2.3 Free Motion on a Rotating Plane 47 2.4 Analogy and Physical Interpretation 50 2J> Acceleration on a Three-Dimensional Rotating Planet 52 2.6 Numerical Approach to Oscillatory Motions 55 2.7 Numerical Convergence and Stability 59 2.8 Predictor-Corrector Methods 63 2.9 Higher-Order Scheines 65 Analytical Problems 69 Numerical Exercises 72 Cushman-Roisin, Benoit Introduction to geophysical fluid dynamics 2011 digitalisiert durch: IDS Basel Bern
f vi J Contents 3. Equations of Fluid Motion 3.1 Mass Budget 77 3.2 Momentum Budget 78 3.3 Equation of State 79 3.4 Energy Budget 80 3.5 Salt and Moisture Budgets 82 3.6 Summary of Governing Equations 83 3.7 Boussinesq Approximation 83 3.8 Flux Formulation and Conservative Form 87 3.9 Finite-Volume Discretization 88 Analytical Problems 92 Numerical Exercises 94 4. Equations Governing Geophysical Flows 4.1 Reynolds-Averaged Equations 99 4.2 Eddy Coefficients 101 4.3 Scales of Motion 103 4.4 Recapitulation of Equations Governing Geophysical Flows 106 4.5 Important Dimensionless Numbers 107 4.6 Boundary Conditions 109 4.7 Numerical Implementation of Boundary Conditions 117 4.8 Accuracy and Errors 120 Analytical Problems 125 Numerical Exercises 126 5. Diffusive Processes 5.1 Isotropie, Homogeneous Turbulence 131 5.2 Turbulent Diffusion 137 53 One-Dimensional Numerical Scheme 140 5.4 Numerical Stability Analysis 144 53 Other One-Dimensional Schemes 150 5.6 Multi-Dimensional Numerical Schemes 154 Analytical Problems 157 Numerical Exercises 158 6. Transport and Fate 6.1 Combination of Advection and Diffusion 163 6.2 Relative Importance of Advection: The Peclet Number 167 63 Highly Advective Situations 168 6.4 Centered and Upwind Advection Schemes 169 6.5 Advection-Diffusion with Sources and Sinks 183 6.6 Multidimensional Approach 186 Analytical Problems 196 Numerical Exercises 198
Part II Rotation Effects 7. Geostrophic Flows and Vorticity Dynamics 7.1 Homogeneous Geostrophic Flows 205 7.2 Homogeneous Geostrophic Flows over an Irregulär Bottom 208 7.3 Generalization to Nongeostrophic Flows 210 7.4 Vorticity Dynamics 212 7.5 Rigid-Lid Approximation 215 7.6 Numerical Solution of the Rigid-Lid Pressure Equation 217 7.7 Numerical Solution ofthe Streamfunction Equation 221 7.8 Laplacian Inversion 224 Analytical Problems 231 Numerical Exercises 233 8. The Ekman Layer 8.1 Shear Turbulence 239 8.2 Friction and Rotation 243 83 The Bottom Ekman Layer 245 8.4 Generalization to Nonuniform Currents 247 8.5 The Ekman Layer over Uneven Terrain 250 8.6 The Surface Ekman Layer 251 8.7 The Ekman Layer in Real Geophysical Flows 254 8.8 Numerical Simulation of Shallow Flows 257 Analytical Problems 265 Numerical Exercises 267 9. Barotropic Waves 9.1 Linear Wave Dynamics 271 9.2 The Kelvin Wave 273 93 Inertia-Gravity Waves (Poincare Waves) 276 9.4 Planetary Waves (Rossby Waves) 278 93 Topographie Waves 283 9.6 Analogy between Planetary and Topographie Waves 287 9.7 Arakawa's Grids 289 9.8 Numerical Simulation of Tides and Storm Surges 300 Analytical Problems 309 Numerical Exercises 312 10. Barotropic Instability 10.1 What Makes a Wave Grow Unstable? 317 10.2 Waves on a Shear Flow 318 103 Bounds on Wave Speeds and Growth Rates 322 10.4 A Simple Example 324
(viii ) Contents 10.5 Nonlinearities 328 10.6 Filtering 331 10.7 Contour Dynamics 334 Analytical Problems 340 Numerical Exercises 341 Part III Stratification Effects 11. Stratification 11.1 Introduction 347 11.2 Static Stability 348 11.3 A Note on Atmospheric Stratification 349 11.4 Convective Adjustment 354 11.5 The Importance of Stratification: The Froude Number 356 11.6 Combination of Rotation and Stratification 358 Analytical Problems 361 Numerical Exercises 361 12. Layered Models 12.1 From Depth to Density 365 12.2 Layered Models 369 12.3 Potential Vorticity 374 12.4 Two-Layer Models 374 12.5 Wind-Induced Seiches in Lakes 379 12.6 Energy Conservation 381 12.7 Numerical Layered Models 383 12.8 Lagrangian Approach 387 Analytical Problems 390 Numerical Exercises 391 13. Internal Waves 13.1 From Surface to Internal Waves 395 13.2 Internal-Wave Theory 397 13.3 Structure of an Internal Wave 399 13.4 Vertical Modes and Eigenvalue Problems 401 13.5 Lee Waves 412 13.6 Nonlinear Effects 416 Analytical Problems 419 Numerical Exercises 421 14. Turbulence in Stratified Fluids 14.1 Mrxingof Stratified Fluids 425 14.2 Instability of a Stratified Shear Flow: The Rkhardson Number 429 143 Turbulence Closure: k-models 435 14.4 OtherClosures:k-eandk-k/ m 449
( ix J 14.5 Mixed-Layer Modeling 450 14.6 Patankar-Type Discretizations 455 14.7 Wind Mixing and Penetrative Convection 458 Analytical Problems 466 Numerical Exercises 467 Part IV Combined Rotation and Stratification Effects 15. Dynamics of Stratified Rotating Flows 15.1 Thermal Wind 473 15.2 Geostrophic Adjustment 475 15.3 Energetics of Geostrophic Adjustment 480 15.4 Coastal Upwelling 482 15.5 Atmospheric Frontogenesis 490 15.6 Numerical Handling of Large Gradients 502 15.7 Nonlinear Advection Schemes 507 Analytical Problems 512 Numerical Exercises 516 16. Quasi-Geostrophic Dynamics 16.1 Simplifying Assumption 521 16.2 Governing Equation 522 16.3 Length and Timescale 527 16.4 Energetics 530 16.5 Planetary Waves in a Stratified Fluid 532 16.6 Some Nonlinear Effects 539 16.7 Quasi-Geostrophic Ocean Modeling 542 Analytical Problems 546 Numerical Exercises 547 17. Instabilities of Rotating Stratified Flows 17.1 Two Types of Instability 553 17.2 Inertial Instability 554 173 Baroclinic Instability The Mechanism 561 17.4 Linear Theory of Baroclinic Instability 566 17.5 Heat Transport 574 17.6 BulkCriteria 576 17.7 Finite-Amplitude Development 579 Analytical Problems 584 Numerical Exercises 585 18. Fronts, Jets and Vortices 18.1 Fronts and Jets 589 18.2 Vortices 601 183 Geostrophic Turbulence 611
CD Contents 18.4 Simulations of Geostrophic Turbulence 613 Analytical Problems 618 Numerical Exercises 621 PartV Special Topics 19. Atmospheric General Circulation 19.1 Climate Versus Weather 627 19.2 Planetary Heat Budget 627 19.3 Direct and Indirect Convective Cells 631 19.4 Atmospheric Circulation Models 637 19.5 Brief Remarks on Weather Forecasting 642 19.6 Cloud Parameterizations 642 19.7 Spectral Methods 644 19.8 Semi-Lagrangian Methods 649 Analytical Problems 652 Numerical Exercises 653 20. Oceanic General Circulation 20.1 What Drives the Oceanic Circulation 657 20.2 Large-Scale Ocean Dynamics (Sverdrup Dynamics) 660 20.3 Western Boundary Currents 669 20.4 Thermohaline Circulation 673 20.5 Abyssal Circulation 677 20.6 Oceanic Circulation Models 681 Analytical Problems 695 Numerical Exercises 696 21. Equatorial Dynamics 21.1 Equatorial Beta Plane 701 21.2 Linear Wave Theory 703 213 El Nino - Southern Oscillation (ENSO) 707 21.4 ENSO Forecasting 716 Analytical Problems 720 Numerical Exercises 721 22. Data Assimilation 22.1 Need for Data Assimilation 725 223 Nudging 730 223 Optimal Interpolation 731 22.4 Kaiman Fiftering 739 ZLS Inverse Methods 743
C xi) 22.6 Operational Models 750 Analytical Problems 754 Numerical Exercises 756 Part VI Web site Information Appendix A Elements of Fluid Mechanics A.1 Budgets 763 A.2 Equations in Cylindrical Coordinates 768 A3 Equations in Spherical Coordinates 769 A4 Vorticity and Rotation 770 Analytical Problems 771 Numerical Exercise 772 Appendix B Wave Kinematics B.1 Wavenumber and Wavelength 773 B.2 Frequency, Phase Speed, and Dispersion 776 B.3 Group Velocity and Energy Propagation 778 Analytical Problems 781 Numerical Exercises 781 Appendix G Recapitulation of Numerical Schemes C.1 The Tridiagonal System Solver 783 C.2 1D Finite-Difference Schemes of Various Orders 785 C.3 Time-Stepping Algorithms 786 C.4 Partial-Derivatives Finite Differences 787 C.5 Discrete Fourier Transform and Fast Fourier Transform 787 Analytical Problems 792 Numerical Exercises 793 References 795 Index 815