Vorticity and Turbulence

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.