Lecture
This lecture discusses the scale-by-scale energy budget in fluid dynamics, focusing on the redistribution of energy between different scales and the conservation laws involved. It covers the impact of nonlinearity, spatial filtering, and periodicity on the energy cascade. The instructor explains the concept of cumulative energy and enstrophy, emphasizing the role of small scales in influencing large-scale energy. Various terms in the energy budget equation are analyzed, highlighting the importance of understanding energy transfer mechanisms in fluid flows.