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Explore wave-wave interactions in rotating stratified flows through this advanced mathematical physics lecture delivered at the Centre International de Rencontres Mathématiques. Delve into the complex dynamics of internal and inertial waves that propagate through rotating stratified fluids, examining their crucial role in oceanic and atmospheric systems. Learn how these waves interact nonlinearly, triggering instabilities and driving energy transfers across different scales through cascade processes. Focus specifically on applying wave turbulence theory to rotating and stratified fluid systems, understanding the main theoretical challenges that arise in this specialized field. Gain insights into current experimental approaches and numerical simulations used to study these phenomena. Examine the mathematical framework of wave kinetic equations and their application to describing wave turbulent cascades in geophysical contexts. Discover when theoretical descriptions remain mathematically valid and can be expected to manifest in real-world experiments and natural systems. This lecture forms part of a comprehensive series on wave turbulence theory, building upon foundational concepts to address the specific complexities introduced by rotation and stratification effects in fluid dynamics.
