| Foreword | 389 |
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| 6 | 389 |
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| Preface | 389 |
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| 8 | 389 |
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| Contents | 389 |
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| 14 | 389 |
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| Contributors | 389 |
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| 16 | 389 |
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| Part I Equations of Motion and Basic Ideas on Discretizations | 18 |
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| Chapter 1: Some Basic Dynamics Relevant to the Design of Atmospheric Model Dynamical Cores | 19 |
| 1.1 Introduction | 19 |
| 1.2 The Multiscale Nature of Atmospheric Dynamics | 20 |
| 1.3 Governing Equations | 21 |
| 1.3.1 Approximate Equation Sets | 23 |
| 1.4 Fast Waves | 25 |
| 1.4.1 Acoustic Waves | 25 |
| 1.4.2 Inertio-Gravity Waves | 26 |
| 1.4.3 Phase Velocity and Group Velocity | 28 |
| 1.5 Balance | 30 |
| 1.5.1 Hydrostatic Balance | 30 |
| 1.5.2 Geostrophic Balance | 31 |
| 1.5.3 Conditions for Hydrostatic Balance to be a Good Approximation | 31 |
| 1.5.4 Balance and Nonlocality | 32 |
| 1.6 Sketch of Quasigeostrophic Theory | 33 |
| 1.6.1 Rossby Waves | 35 |
| 1.7 Eulerian and Lagrangian Timescales | 36 |
| 1.8 Turbulence and Cascades | 37 |
| 1.8.1 Three Dimensional Turbulence | 37 |
| 1.8.2 Two-dimensional Turbulence | 38 |
| 1.8.3 Energy Upscale, Enstrophy Downscale | 39 |
| 1.8.4 Application to the Real Atmosphere | 41 |
| 1.9 Conclusion | 42 |
| References | 42 |
| Chapter 2: Waves, Hyperbolicity and Characteristics | 44 |
| 2.1 Introduction | 44 |
| 2.2 The Method of Characteristics | 45 |
| 2.3 The Normal Modes of the Hydrostatic Equations | 47 |
| 2.
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