BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jacob Bedrossian (University of Maryland) DTSTART:20200504T140000Z DTEND:20200504T150000Z DTSTAMP:20260404T042248Z UID:BIRS_20w5025/1 DESCRIPTION:Title: The Power Spectrum of Passive Scalar Turbulence in the Batchel or Regime\nby Jacob Bedrossian (University of Maryland) as part of BIR S Workshop: Mathematical Questions in Wave Turbulence\n\n\nAbstract\nIn 19 59\, Batchelor predicted that passive scalars advected in fluids at finite Reynolds number with small diffusivity κ should display a |k|−1 power spectrum over a small-scale inertial range in a statistically stationary e xperiment. This prediction has been experimentally and numerically tested extensively in the physics and engineering literature and is a core predic tion of passive scalar turbulence. Together with Alex Blumenthal and Sam P unshon-Smith\, we have provided the first mathematically rigorous proof of this prediction for a scalar field evolving by advection-diffusion in a f luid governed by the 2D Navier-Stokes equations and 3D hyperviscous Navier -Stokes equations in a periodic box subjected to stochastic forcing at arb itrary Reynolds number. As conjectured by physicists\, we also show the re sults in fact hold for a variety of toy models\, though Navier-Stokes at h igh Reynolds number is the most physically relevant and the most difficult mathematically that we have considered thus far. These results are proved by studying the Lagrangian flow map using extensions of ideas from random dynamical systems. We prove that the Lagrangian flow has a positive Lyapu nov exponent (Lagrangian chaos) and show how this can be upgraded to almos t sure exponential mixing of passive scalars at zero diffusivity and furth er to uniform-in-diffusivity mixing. This in turn is a sufficiently precis e understanding of the low-to-high frequency cascade to deduce Batchelor's prediction.\n LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5025/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexandru Ionescu (Princeton University) DTSTART:20200504T153000Z DTEND:20200504T163000Z DTSTAMP:20260404T042248Z UID:BIRS_20w5025/2 DESCRIPTION:Title: Nonlinear Stability of Vortices and Shear Flows\nby Alexan dru Ionescu (Princeton University) as part of BIRS Workshop: Mathematical Questions in Wave Turbulence\n\n\nAbstract\nI will talk about some recent work on the nonlinear asymptotic stability of point vortices and monotonic shear flows among solutions of the 2D Euler equations. This is joint work with Hao Jia.\n LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5025/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Sergey Nazarenko (Universite Cote d'Azur) DTSTART:20200505T153000Z DTEND:20200505T163000Z DTSTAMP:20260404T042248Z UID:BIRS_20w5025/4 DESCRIPTION:Title: Non-Stationary self-similar Solutions of the Wave Kinetic Equa tions\nby Sergey Nazarenko (Universite Cote d'Azur) as part of BIRS Wo rkshop: Mathematical Questions in Wave Turbulence\n\n\nAbstract\nUsually i n wave turbulence\, one looks for a scaling stationary solution. However\, the evolution preceeding the steady state is equally interesting and it m ay exhibit a nontrivial self-similar scalings. Problem of this kind natura lly arises when we ask \, for example\, about the rate at which the conden sate grows within the wave turbulence settings in the NLS model.\n LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5025/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Yulin Pan (University of Michigan) DTSTART:20200506T140000Z DTEND:20200506T150000Z DTSTAMP:20260404T042248Z UID:BIRS_20w5025/5 DESCRIPTION:Title: Wave Turbulence in Finite Domain – Role of Discrete Resonant Manifold\nby Yulin Pan (University of Michigan) as part of BIRS Works hop: Mathematical Questions in Wave Turbulence\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5025/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Thierry Dauxois (CNRS & ENS Lyon) DTSTART:20200506T153000Z DTEND:20200506T163000Z DTSTAMP:20260404T042248Z UID:BIRS_20w5025/6 DESCRIPTION:Title: Energy Cascade in Internal Wave Attractors\nby Thierry Dau xois (CNRS & ENS Lyon) as part of BIRS Workshop: Mathematical Questions in Wave Turbulence\n\n\nAbstract\nInternal gravity waves play a primary role in geophysical fluids : they contribute significantly to mixing in the oc ean and they redistribute energy and momentum in the middle atmosphere. In addition to their very interesting and very unusual theoretical propertie s\, these waves are linked to one of the important questions in the dynami cs of the oceans: the cascade of mechanical energy in the abyss and its co ntribution to mixing.\nI will discuss a setup that allows us to study expe rimentally the interaction of nonlinear internal waves in a stratified flu id confined in a trapezoidal tank. The set-up has been designed to produce internal wave turbulence from monochromatic and polychromatic forcing thr ough three processes. The first is a linear transfer in wavelength obtaine d by wave reflection on inclined slopes\, leading to an internal wave attr actor which has a broad wavenumber spectrum. Second is the broad banded\nt ime-frequency spectrum of the trapezoidal geometry\, as shown by the impul se\nresponse of the system. The third one is a nonlinear transfer in frequ encies\nand wavevectors via triadic interactions\, which results at large forcing\namplitudes in a power law decay of the wavenumber power spectrum. This first\nexperimental spectrum of internal wave turbulence displays a $k^{-3}$ behavior.\n LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5025/6/ END:VEVENT END:VCALENDAR