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Provides the first detailed and comprehensive analytical development of the Lagrangian formulation of fluid dynamics.
The emergence of observing systems such as acoustically-tracked floats in the deep ocean, and surface drifters navigating by satellite has seen renewed interest in Lagrangian fluid dynamics. Starting from the foundations of elementary kinematics and assuming some familiarity of Eulerian fluid dynamics, this book reviews the classical and new exact solutions of the Lagrangian framework, and then addresses the general solvability of the resulting general equations of motion. A unified account of turbulent diffusion and dispersion is offered, with applications among others to plankton patchiness in the ocean. Written at graduate level, the book provides the first detailed and comprehensive analytical development of the Lagrangian formulation of fluid dynamics, of interest not only to applied mathematicians but also oceanographers, meteorologists, mechanical engineers, astrophysicists and indeed all investigators of the dynamics of fluids.
Table of contents:
Part I. The Lagrangian Formulation: 1. Lagrangian kinematics; 2. Lagrangian statistics; 3. Lagrangian dynamics; 4. Coordinates; 5. Real fluids; Part II. Lagrangian Flows: 6. Some analytical Lagrangian solutions; 7. Waves, instabilities and vortices; 8. Viscous incompressible flow; 9. General solvability; Part III. Diffusion: 10. Absolute dispersion; 11. Relative dispersion; 12. Convective subranges, scalar variance spectrum; 13. Diffusion; Part IV. Lagrangian data: 14. Observing systems; 15. Data analysis: the single particle; 16. Data analysis: particle clusters; References.
The emergence of observing systems such as acoustically-tracked floats in the deep ocean, and surface drifters navigating by satellite has seen renewed interest in Lagrangian fluid dynamics. Starting from the foundations of elementary kinematics and assuming some familiarity of Eulerian fluid dynamics, this book reviews the classical and new exact solutions of the Lagrangian framework, and then addresses the general solvability of the resulting general equations of motion. A unified account of turbulent diffusion and dispersion is offered, with applications among others to plankton patchiness in the ocean. Written at graduate level, the book provides the first detailed and comprehensive analytical development of the Lagrangian formulation of fluid dynamics, of interest not only to applied mathematicians but also oceanographers, meteorologists, mechanical engineers, astrophysicists and indeed all investigators of the dynamics of fluids.
Table of contents:
Part I. The Lagrangian Formulation: 1. Lagrangian kinematics; 2. Lagrangian statistics; 3. Lagrangian dynamics; 4. Coordinates; 5. Real fluids; Part II. Lagrangian Flows: 6. Some analytical Lagrangian solutions; 7. Waves, instabilities and vortices; 8. Viscous incompressible flow; 9. General solvability; Part III. Diffusion: 10. Absolute dispersion; 11. Relative dispersion; 12. Convective subranges, scalar variance spectrum; 13. Diffusion; Part IV. Lagrangian data: 14. Observing systems; 15. Data analysis: the single particle; 16. Data analysis: particle clusters; References.