Lectures on turbulence

Fluid dynamics turbulence refers to the chaotic and unpredictable dynamics of flows. Despite the fact that the equations governing the motion of fluids are known since more than two centuries, a comprehensive theory of turbulence is still a challenge for the scientific community. Rather recently a number of important breakthroughs have clarified many relevant, fascinating, and largely unexpected, statistical features of turbulent fluctuations. In these lectures, we discuss recent advances in the field with the aim of highlighting the physical meaning and implication of these new ideas and their role in contributing to disentangling different parts of our understanding of the turbulence problem. The lectures aim at introducing non-experts to the subject and no previous knowledge of the field is required.