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This paper presents recent and ongoing research in mathematical fluid dynamics and emphasizes the interdisciplinary interaction of ideas from large-scale computation, asymptotic methods, and mathematical theory. Three contemporary research topics are discussed in detail: (1) The generation of energetic small scales for incompressible fluid flow; (2) theories for eddy diffusivity and renormalization for turbulent transport; and (3) the interaction between nonlinear acoustics and vorticity in the development of instability in supersonic shear layers.
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Andrew J. Majda (1991) studied this question.
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