Vortex Dynamics and Chaotic Phenomena

This book presents the modern views on one of the oldest subjects in hydromechanics. The main idea is to show how, when and why chaotic behaviour enters in well-posed problem of vortex motion of ideal fluid. For many classes of the vortex motion - point vortices and axisymmetrical vortex rings - problems are reduced to the Hamiltonian systems. The detailed classification of ordered and chaotic motions is presented for these cases. Special attention is paid to the problem of chaotic advection of fluid particles in the velocity field of point or ring vortices. Some aspects of the history of vortex dynamics are outlined. The book may serve as a textbook on vortex motion. No specific mathematical knowledge is required. The introductory chapters present the basic concepts of vortex dynamics and deterministic chaos. Subsequent chapters describe special examples of regular and chaotic behaviour of vortex structures.