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Explore the fundamental principles of wave turbulence theory in this comprehensive lecture focusing on internal and inertial waves in rotating stratified fluids. Begin with an introduction to general wave turbulence theory, including insights into the derivation of the wave kinetic equation (WKE) in general cases. Learn how the WKE describes wave turbulent cascades and understand the mathematical validity conditions for this description, as well as when it can be expected to occur in experimental and natural settings. Discover the crucial role these waves play in oceanic and atmospheric systems, where they interact nonlinearly, triggering instabilities and energy transfers across different scales through cascade processes. Gain foundational knowledge that prepares you for advanced applications of wave turbulence concepts to rotating and stratified fluids, including theoretical challenges and current experimental and simulation approaches in the field.
