BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alex Blumenthal (Georgia Institute of Technology) DTSTART:20200903T130000Z DTEND:20200903T135000Z DTSTAMP:20260423T035627Z UID:IMS/53 DESCRIPTION:Title: Lag rangian Chaos\, Scalar Mixing\, and passive scalar turbulence for models i n fluid mechanics\nby Alex Blumenthal (Georgia Institute of Technology ) as part of PDE seminar via Zoom\n\n\nAbstract\nIn models of fluid mechan ics\, Lagrangian flow $\\phi^t$ on the fluid domain describes the motion o f a passive particle advected by the fluid. It is anticipated that typical ly\, Lagrangian flow $\\phi^t$ is chaotic in the sense of (1) sensitivity with respect to initial conditions and (2) fast mixing of passive scalars (equivalently $H^{-1}$ decay for passive scalars). I will present joint wo rk with Jacob Bedrossian (U Maryland) and Sam Punshon-Smith (Brown U) in w hich we rigorously verify these chaotic properties for various incompressi ble and stochastically forced fluid models on the periodic box\, including stochastic 2D Navier-Stokes and hyperviscous 3D Navier-Stokes. I will als o present our recent application of these result to the study of passive s calar turbulence in the Batchelor regime\, i.e.\, the steady state of pass ive scalars in a fluid (at fixed viscosity) attained as molecular diffusiv ity goes to 0. In this setting\, we are able to prove Batchelor's inverse power law for the power spectrum\, the passive scalar analogue of Kolmogor ov's $-4/3$ law for the power spectrum in the inertial range of a turbulen t 3D fluid.\n\nhttps://nguyenquochung1241.wixsite.com/qhung/post/pde-semin ar-via-zoom\n LOCATION:https://researchseminars.org/talk/IMS/53/ END:VEVENT END:VCALENDAR