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• Cover image
• Title page
• Table of Contents
• Preface
• Chapter 1 Introduction: Fundamentals of Rotating Shallow Water Model in the Geophysical Fluid Dynamics Perspective
• 1 Introduction
• 2 Derivation of the model
• 3 General properties of the RSW model
• 4 An overview of the two-layer RSW model
• 5 Wave–vortex interactions
• 6 RSW model on the equatorial β-plane
• 7 Concluding remarks
• Chapter 2 Asymptotic Methods with Applications to the Fast–Slow Splitting and the Geostrophic Adjustment
• 1 Introduction
• 2 Nonlinear geostrophic adjustment in the unbounded domain. One-layer RSW
• 3 Nonlinear geostrophic adjustment in the unbounded domain. Two-layer RSW
• 4 Nonlinear geostrophic adjustment in the presence of a lateral boundary
• 5 Nonlinear geostrophic adjustment in the equatorial region
• 6 Summary and discussion
• Chapter 3 The Method of Normal Forms and Fast–Slow Splitting
• 1 Introduction
• 2 Slow manifold in the spatial variables on the f-plane
• 3 Slow manifold in the spectral variables on the f-plane
• 4 Poincaré normal forms
• 5 Skew-gradient normal forms for gradient systems
• 6 Hamiltonian normal forms
• 7 Normal form of the Poisson bracket for one-dimensional fluid
• 8 Conclusion
• Chapter 4 Efficient Numerical Finite Volume Schemes for Shallow Water Models
• 1 A few notions on hyperbolic systems
• 2 Finite volume schemes for conservative systems
• 3 Finite volumes for systems with source terms
• 4 Second-order well-balanced schemes
• 5 Two-dimensional finite volumes on a rectangular grid
• 6 Numerical tests
• Chapter 5 Nonlinear Wave Phenomena in Rotating Shallow Water with Applications to Geostrophic Adjustment
• 1 Introduction
• 2 Nonlinear wave phenomena and geostrophic adjustment in 1dRSW
• 3 Nonlinear wave phenomena and geostrophic adjustment in 2-layer 1dRSW
• 4 Nonlinear wave phenomena and geostrophic adjustment in the equatorial waveguide
• 5 Summary and conclusions
• Chapter 6 Experimental Reality of Geostrophic Adjustment
• 1 The Holy Graal of rotating shallow-water flows
• 2 Potential vorticity measurements: a new challenge
• 3 Simple case studies of geostrophic adjustment
• 4 What do we learn from laboratory experiments?
• List of Contributors
• Author Index
• Subject Index