Alexandre Chorin Livres

The textbook is designed to address the growing importance of mathematics in the physical and biological sciences, reflecting a shift toward interdisciplinary approaches and modern applied techniques. Based on a course taught at UC Berkeley, it aims to introduce advanced undergraduate and beginning graduate students to fluid mechanics without attempting to cover the subject exhaustively or evaluate engineering approximations. The series seeks to foster excitement in research and teaching, incorporating both traditional and innovative mathematical methods.

The book explores turbulence theory through the vorticity field, emphasizing its natural fit for incompressible flow. It highlights the historical contributions of Onsager and Joyce and Montgomery to two-dimensional vortex systems, while acknowledging the ongoing challenges in developing a robust three-dimensional theory. The initial chapters provide a foundational overview of homogeneous turbulence, including a detailed review of fluid mechanics and Fourier theory, and discuss Kolmogorov's inertial range theory, suggesting a potential equilibrium spectrum for the inertial spectrum.

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.