Contents. Parti Fundamentals. 1. Introduction. 2. The Coriolis Force. Preface Preface of the First Edition

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1 Foreword Preface Preface of the First Edition xiii xv xvii Parti Fundamentals 1. Introduction 1.1 Objective Importance of Geophysical Fluid Dynamics Distinguishing Attributes of Geophysical Flows Scales of Motions Importance of Rotation Importance of Stratification Distinction between the Atmosphere and Oceans Data Acquisition The Emergence of Numerical Simulations Scales Analysis and Finite Differences Higher-Order Methods Aliasing 33 Analytical Problems 35 Numerical Exercises The Coriolis Force 2.1 Rotating Framework of Reference Unimportance of the Centrifugal Force Free Motion on a Rotating Plane Analogy and Physical Interpretation 50 2J> Acceleration on a Three-Dimensional Rotating Planet Numerical Approach to Oscillatory Motions Numerical Convergence and Stability Predictor-Corrector Methods Higher-Order Scheines 65 Analytical Problems 69 Numerical Exercises 72 Cushman-Roisin, Benoit Introduction to geophysical fluid dynamics 2011 digitalisiert durch: IDS Basel Bern

2 f vi J Contents 3. Equations of Fluid Motion 3.1 Mass Budget Momentum Budget Equation of State Energy Budget Salt and Moisture Budgets Summary of Governing Equations Boussinesq Approximation Flux Formulation and Conservative Form Finite-Volume Discretization 88 Analytical Problems 92 Numerical Exercises Equations Governing Geophysical Flows 4.1 Reynolds-Averaged Equations Eddy Coefficients Scales of Motion Recapitulation of Equations Governing Geophysical Flows Important Dimensionless Numbers Boundary Conditions Numerical Implementation of Boundary Conditions Accuracy and Errors 120 Analytical Problems 125 Numerical Exercises Diffusive Processes 5.1 Isotropie, Homogeneous Turbulence Turbulent Diffusion One-Dimensional Numerical Scheme Numerical Stability Analysis Other One-Dimensional Schemes Multi-Dimensional Numerical Schemes 154 Analytical Problems 157 Numerical Exercises Transport and Fate 6.1 Combination of Advection and Diffusion Relative Importance of Advection: The Peclet Number Highly Advective Situations Centered and Upwind Advection Schemes Advection-Diffusion with Sources and Sinks Multidimensional Approach 186 Analytical Problems 196 Numerical Exercises 198

3 Part II Rotation Effects 7. Geostrophic Flows and Vorticity Dynamics 7.1 Homogeneous Geostrophic Flows Homogeneous Geostrophic Flows over an Irregulär Bottom Generalization to Nongeostrophic Flows Vorticity Dynamics Rigid-Lid Approximation Numerical Solution of the Rigid-Lid Pressure Equation Numerical Solution ofthe Streamfunction Equation Laplacian Inversion 224 Analytical Problems 231 Numerical Exercises The Ekman Layer 8.1 Shear Turbulence Friction and Rotation The Bottom Ekman Layer Generalization to Nonuniform Currents The Ekman Layer over Uneven Terrain The Surface Ekman Layer The Ekman Layer in Real Geophysical Flows Numerical Simulation of Shallow Flows 257 Analytical Problems 265 Numerical Exercises Barotropic Waves 9.1 Linear Wave Dynamics The Kelvin Wave Inertia-Gravity Waves (Poincare Waves) Planetary Waves (Rossby Waves) Topographie Waves Analogy between Planetary and Topographie Waves Arakawa's Grids Numerical Simulation of Tides and Storm Surges 300 Analytical Problems 309 Numerical Exercises Barotropic Instability 10.1 What Makes a Wave Grow Unstable? Waves on a Shear Flow Bounds on Wave Speeds and Growth Rates A Simple Example 324

4 (viii ) Contents 10.5 Nonlinearities Filtering Contour Dynamics 334 Analytical Problems 340 Numerical Exercises 341 Part III Stratification Effects 11. Stratification 11.1 Introduction Static Stability A Note on Atmospheric Stratification Convective Adjustment The Importance of Stratification: The Froude Number Combination of Rotation and Stratification 358 Analytical Problems 361 Numerical Exercises Layered Models 12.1 From Depth to Density Layered Models Potential Vorticity Two-Layer Models Wind-Induced Seiches in Lakes Energy Conservation Numerical Layered Models Lagrangian Approach 387 Analytical Problems 390 Numerical Exercises Internal Waves 13.1 From Surface to Internal Waves Internal-Wave Theory Structure of an Internal Wave Vertical Modes and Eigenvalue Problems Lee Waves Nonlinear Effects 416 Analytical Problems 419 Numerical Exercises Turbulence in Stratified Fluids 14.1 Mrxingof Stratified Fluids Instability of a Stratified Shear Flow: The Rkhardson Number Turbulence Closure: k-models OtherClosures:k-eandk-k/ m 449

5 ( ix J 14.5 Mixed-Layer Modeling Patankar-Type Discretizations 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 Geostrophic Adjustment Energetics of Geostrophic Adjustment Coastal Upwelling Atmospheric Frontogenesis Numerical Handling of Large Gradients Nonlinear Advection Schemes 507 Analytical Problems 512 Numerical Exercises Quasi-Geostrophic Dynamics 16.1 Simplifying Assumption Governing Equation Length and Timescale Energetics Planetary Waves in a Stratified Fluid Some Nonlinear Effects Quasi-Geostrophic Ocean Modeling 542 Analytical Problems 546 Numerical Exercises Instabilities of Rotating Stratified Flows 17.1 Two Types of Instability Inertial Instability Baroclinic Instability The Mechanism Linear Theory of Baroclinic Instability Heat Transport BulkCriteria Finite-Amplitude Development 579 Analytical Problems 584 Numerical Exercises Fronts, Jets and Vortices 18.1 Fronts and Jets Vortices Geostrophic Turbulence 611

6 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 Planetary Heat Budget Direct and Indirect Convective Cells Atmospheric Circulation Models Brief Remarks on Weather Forecasting Cloud Parameterizations Spectral Methods Semi-Lagrangian Methods 649 Analytical Problems 652 Numerical Exercises Oceanic General Circulation 20.1 What Drives the Oceanic Circulation Large-Scale Ocean Dynamics (Sverdrup Dynamics) Western Boundary Currents Thermohaline Circulation Abyssal Circulation Oceanic Circulation Models 681 Analytical Problems 695 Numerical Exercises Equatorial Dynamics 21.1 Equatorial Beta Plane Linear Wave Theory El Nino - Southern Oscillation (ENSO) ENSO Forecasting 716 Analytical Problems 720 Numerical Exercises Data Assimilation 22.1 Need for Data Assimilation Nudging Optimal Interpolation Kaiman Fiftering 739 ZLS Inverse Methods 743

7 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