Turbulence Theory: Spatial Energy Spectrum

This lecture focuses on understanding the spatial energy spectrum in turbulence theory, which plays a crucial role in analyzing the distribution and evolution of energy between different spatial scales. The instructor explains the concept of cumulative spatial energy spectrum and its derivative, the spatial energy spectrum, emphasizing the importance of considering an unbounded space for a smooth definition. The Wiener formula is introduced to relate the spatial energy spectrum to a spatial correlation function, highlighting the complexity arising from the vector-valued nature of the formula. The lecture concludes by discussing the connection between the energy spectrum and measurable quantities, setting the stage for further exploration of chaos theory in the course.