Lagrangian transport in geophysical jets and waves : the dynamical systems approach /
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| Author / Creator: | Samelson, R. M. (Roger M.) |
|---|---|
| Imprint: | New York, N.Y. : Springer, c2006. |
| Description: | 1 online resource (x, 147 p.) : ill. |
| Language: | English |
| Series: | Interdisciplinary applied mathematics ; v. 31 Interdisciplinary applied mathematics ; v. 31. |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/8878941 |
Table of Contents:
- Preface
- 1. Introduction
- 1.1. Trajectories and Transport in Geophysical Fluid Dynamics
- 1.2. Incompressible Two-Dimensional Flow
- 1.3. The Streamfunction
- 1.4. Meandering Jets
- 1.5. A Kinematic Traveling Wave Model
- 1.6. Critical Lines and Cellular Flow
- 1.7. The Onset of Fluid Exchange
- 1.8. Notes
- 2. Steadily Translating Waves and Meanders
- 2.1. The Comoving Frame
- 2.2. Stagnation Points
- 2.3. Linearization near Stagnation Points
- 2.4. Trajectories of Linearizations
- 2.5. The Traveling Wave: Linearizations
- 2.6. Material Curves and Invariant Subspaces
- 2.7. Material Manifolds of Stagnation Points
- 2.8. The Traveling Wave: Material Manifolds
- 2.9. Notes
- 3. Integrability of Lagrangian Motion
- 3.1. Scalar Advection: The Material Derivative
- 3.2. Linear Flows
- 3.3. Closed Material Curves and Integrability
- 3.4. Action-Angle Variables
- 3.5. Near-Integrable Fluid Flow
- 3.6. The KAM Theorem
- 3.7. Chaos, Integrability, and Advected Scalar Fields
- 3.8. Notes
- 4. Fluctuating Waves and Meanders
- 4.1. Time-Dependent Flow in the Comoving Frame
- 4.2. Linearized Motion: A Time-Dependent Example
- 4.3. Linearization About a Trajectory
- 4.4. Lyapunov Exponents
- 4.5. Exponential Dichotomies
- 4.6. Hyperbolic Trajectories
- 4.7. Material Manifolds of Hyperbolic Trajectories
- 4.8. Hyperbolic Trajectories for Near-Integrable Flows
- 4.9. The Traveling Wave
- 4.10. Notes
- 5. Material Manifolds, Flow Regimes, and Fluid Exchange
- 5.1. Fluid Exchange and Lobes
- 5.2. Transient Disturbances
- 5.3. Oscillatory Disturbances
- 5.4. Summary
- 5.5. Notes
- 6. Lobe Transport and Flux
- 6.1. Regime and Lobe Boundaries
- 6.2. The Traveling Wave with Time-Periodic Disturbance
- 6.3. General Oscillatory Disturbances
- 6.4. Transient Disturbances
- 6.5. Lobe Area and Flux Formulas
- 6.6. Notes
- 7. Transport and Dynamics
- 7.1. Dynamics of Geophysical Flows
- 7.2. Barotropic Jets
- 7.3. Baroclinic Jets
- 7.4. Boundary Currents and Recirculations
- 7.5. Advanced Topics
- 7.6. Summary
- A. Mathematical Properties of Fluid Trajectories
- B. Action-Angle Coordinates
- C. Numerical Methods
- D. Finite-Time Material Manifolds: An Example
- Glossary
- References
- Index