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 2006 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.

"...the first book devoted to providing a unified exposition of dynamics in the Lagrangian frame. The treatment is comprehensive, making the book valuable to all fluid dynamicists seeking to expand their backgrounds in the Lagrangian perspective..."--Russ Davis, Research Oceanographer; Scripps Institution of Oceanography, University of California, San Diego, CA, USA.

...A superb collection of well-written survey materials, covering the state-of-the-art in the theoretical aspects of problems arising in Lagrangian hydrodynamics...On the whole, this is an indispensable and obligatory book for anyone seriously interested in Lagrangian Fluid Dynamics...Also, this book will be of interest to applied mathematicians, particularly those interested in mathematical aspects of environmental fluid dynamics."-Andrzej Icha, Institute of Mathematics, Pomeranian Academy in Slupsk, Poland.