Abrashkin A. Analytical Fluid Dynamics in Lagrangian Variables 2025

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Abrashkin A. Analytical Fluid Dynamics in Lagrangian Variables 2025

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Textbook in PDF format The monograph focuses on the analytical challenges of describing incompressible fluid flows using Lagrangian variables. The Lagrangian method is presented as a complementary approach to the Eulerian method for studying fluid motion. The fundamental nature of fluid dynamics is linked to tracing the trajectories of individual fluid particles, which is precisely what the Lagrangian method facilitates.The purpose of this publication is to reflect as fully as possible the achievements of analytical fluid dynamics in Lagrangian variables. A significant part of it consists of original articles by the author. Considerable attention is paid to the subtleties of the Lagrangian description and its popularization among experts in fluid dynamics, students, postgraduates, and anyone interested in problems of fluid mechanics.The book can be considered, among other things, as a tutorial on Lagrangian fluid dynamics. The book covers issues of the general description of the movement of incompressible fluid, problems of classical hydrodynamics and geophysical hydrodynamics. Fundamental topics include free-boundary motion, vortices in fluids, and water waves. The book includes a number of problems that take into account the stratification and viscosity of fluids, as well as the rotation of the Earth. Preface Part I. Description of Basics Chapter 1. Ideal Fluid Equations Chapter 2. Potential Motion Chapter 3. Vortex Motion Part II. Waves on Water Chapter 4. Potential Approximation Chapter 5. Gerstner Wave Chapter 6. Weakly Vortex Waves Part III. Exact Solutions in Vortex Dynamics Chapter 7. Two-Dimensional Vortex Flow Chapter 8. Localized Two-Dimensional Vortices in the External Flow Chapter 9. Spatial Vortex Flows Part IV. Generalized Gerstner Waves Chapter 10. Waves on Water at Unstable Pressure Chapter 11. Vortex Model of Rogue Waves Chapter 12. Breaking of the Surface Gravity Wave Chapter 13. Non-Stationary Edge Waves Part V. Viscous Fluid Flows Chapter 14. Basic Equations and Examples Chapter 15. Gravity Waves on the Surface of a Viscous Fluid Part VI. The Earth’s Rotation Effect Chapter 16. Exact Solutions for Waves Chapter 17. Vortices in a Rotating Fluid Appendix 1. Speed and Acceleration in a Cylindrical Coordinate System Appendix 2. Speed and Acceleration in a Spherical Coordinate System