Chapter 1 Introduction Fundamentals of Rotating Shallow Water Model in the Geophysical Fluid Dynamics Perspective推荐.pdf

Chapter 1 Introduction: Fundamentals of Rotating Shallow Water Model in the Geophysical Fluid Dynamics Perspective V. Zeitlin LMD, Ecole Normale Supérieure, 24, rue Lhomond, 75231 Paris Cedex 05, France Contents 1. Introduction 2 2. Derivation of the model 3 2.1. Primitive equations model of GFD 3 2.2. Vertical averaging of the primitive equations and multi-layer RSW models 5 3. General properties of the RSW model 8 3.1. The conservation laws 8 3.2. Hamiltonian formulation of the RSW model 10 3.3. The spectrum of linear excitations in the RSW model on the f -plane and the first notion of the geostrophic adjustment 11 3.4. Characteristic parameters of the RSW model on the f -plane. Geostrophic balance and slow motions 13 3.5. Slow motions on the β-plane. Rossby waves 16 3.6. The fast-slow splitting and geostrophic adjustment 19 3.7. Lateral boundaries and Kelvin waves 19 3.8. Topographic effects in RSW 20 4. An overview of the two-layer RSW model 22 4.1. Conservation laws. Linearization. Fast and slow motions 22 4.2. Characteristic parameters and scali