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Alex Blumenthal, RLM 10.178: Lagrangian chaos for models in fluid mechanics
Wednesday, March 13, 2019, 01:00pm - 02:00pm
In models of fluid mechanics, the Lagrangian flow $\phi^t$ describesthe motion of a passive particle advected by the fluid. It isanticipated that in many regimes (e.g., when the fluid is subjectedto some forcing/stirring) that the Lagrangian flow $\phi^t$ shouldbe chaotic in the sense of sensitivity with respect to initialconditions. I will present a recent joint work with Jacob Bedrossian(U Maryland) and Sam Punshon-Smith (Brown U) in which we rigorouslyverify this chaotic property (i.e., the presence of a positiveLypaunov exponent) for various incompressible and stochasticallyforced fluid models on the periodic box, including stochastic2D Navier-Stokes and stochastic hyperviscous 3D Navier-Stokes.A consequence of our work is a rigorous verification of Yaglom'slaw, a scaling law for passive scalar advection analogous tothe famous Kolmogorov 4/5 law for turbulence in the Navier-Stokesequations.
Location: RLM 10.178

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