Turbulence in Compressible Systems and Energy Transfer Across Scale

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In this talk, I began with the levels of describing a system of particles, arrived at the Navier-Stokes equation as the first-order approximation of the Chapman-Enskog expansion, and laid the foundation for the study of turbulence. I then began with the theory we have in incompressible turbulence, elaborated on coarse-graining as a direct application of the representation theory, and discussed the theory of scale dynamics in compressible systems.