This book provides an introduction to the theory of turbulence in fluids based on the representation of the flow by means of its vorticity field. It has long been understood that, at least in the case of incompressible flow, the vorticity representation is natural and physically transparent, yet the development of a theory of turbulence in this representation has been slow. The pioneering work of Onsager and of Joyce and Montgomery on the statistical mechanics of two-dimensional vortex systems has only recently been put on a firm mathematical footing, and the three-dimensional theory remains...

This book covers basic stochastic tools used in physics, chemistry, engineering and the life sciences. Each chapter is followed by exercises. The book will be useful for scientists and engineers working in a wide range of fields and applications.