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:20260422T185748Z UID:BIRS_20w5025/1 DESCRIPTION:Title: The Power Spectrum of Passive Scalar Turbulence in the Batchelor Regi me\nby Jacob Bedrossian (University of Maryland) as part of BIRS Works hop: Mathematical Questions in Wave Turbulence\n\n\nAbstract\nIn 1959\, Ba tchelor predicted that passive scalars advected in fluids at finite Reynol ds number with small diffusivity κ should display a |k|−1 power spectru m over a small-scale inertial range in a statistically stationary experime nt. This prediction has been experimentally and numerically tested extensi vely in the physics and engineering literature and is a core prediction of passive scalar turbulence. Together with Alex Blumenthal and Sam Punshon- Smith\, we have provided the first mathematically rigorous proof of this p rediction for a scalar field evolving by advection-diffusion in a fluid go verned by the 2D Navier-Stokes equations and 3D hyperviscous Navier-Stokes equations in a periodic box subjected to stochastic forcing at arbitrary Reynolds number. As conjectured by physicists\, we also show the results i n fact hold for a variety of toy models\, though Navier-Stokes at high Rey nolds number is the most physically relevant and the most difficult mathem atically that we have considered thus far. These results are proved by stu dying the Lagrangian flow map using extensions of ideas from random dynami cal systems. We prove that the Lagrangian flow has a positive Lyapunov exp onent (Lagrangian chaos) and show how this can be upgraded to almost sure exponential mixing of passive scalars at zero diffusivity and further to u niform-in-diffusivity mixing. This in turn is a sufficiently precise under standing of the low-to-high frequency cascade to deduce Batchelor's predic tion.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5025/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexandru Ionescu (Princeton University) DTSTART:20200504T153000Z DTEND:20200504T163000Z DTSTAMP:20260422T185748Z UID:BIRS_20w5025/2 DESCRIPTION:Title: Nonlinear Stability of Vortices and Shear Flows\nby Alexandru Ion escu (Princeton University) as part of BIRS Workshop: Mathematical Questio ns 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 H ao Jia.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5025/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Sergey Nazarenko (Universite Cote d'Azur) DTSTART:20200505T153000Z DTEND:20200505T163000Z DTSTAMP:20260422T185748Z UID:BIRS_20w5025/4 DESCRIPTION:Title: Non-Stationary self-similar Solutions of the Wave Kinetic Equations\nby Sergey Nazarenko (Universite Cote d'Azur) as part of BIRS Workshop: Mathematical Questions in Wave Turbulence\n\n\nAbstract\nUsually in wave turbulence\, one looks for a scaling stationary solution. However\, the ev olution preceeding the steady state is equally interesting and it may exhi bit a nontrivial self-similar scalings. Problem of this kind naturally ari ses when we ask \, for example\, about the rate at which the condensate gr ows within the wave turbulence settings in the NLS model.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5025/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Yulin Pan (University of Michigan) DTSTART:20200506T140000Z DTEND:20200506T150000Z DTSTAMP:20260422T185748Z UID:BIRS_20w5025/5 DESCRIPTION:Title: Wave Turbulence in Finite Domain – Role of Discrete Resonant Manifo ld\nby Yulin Pan (University of Michigan) as part of BIRS Workshop: Ma thematical Questions in Wave Turbulence\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/BIRS_20w5025/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Thierry Dauxois (CNRS & ENS Lyon) DTSTART:20200506T153000Z DTEND:20200506T163000Z DTSTAMP:20260422T185748Z UID:BIRS_20w5025/6 DESCRIPTION:Title: Energy Cascade in Internal Wave Attractors\nby Thierry Dauxois (C NRS & ENS Lyon) as part of BIRS Workshop: Mathematical Questions in Wave T urbulence\n\n\nAbstract\nInternal gravity waves play a primary role in geo physical fluids : they contribute significantly to mixing in the ocean and they redistribute energy and momentum in the middle atmosphere. In additi on to their very interesting and very unusual theoretical properties\, the se waves are linked to one of the important questions in the dynamics of t he oceans: the cascade of mechanical energy in the abyss and its contribut ion to mixing.\nI will discuss a setup that allows us to study experimenta lly the interaction of nonlinear internal waves in a stratified fluid conf ined in a trapezoidal tank. The set-up has been designed to produce intern al wave turbulence from monochromatic and polychromatic forcing through th ree processes. The first is a linear transfer in wavelength obtained by wa ve reflection on inclined slopes\, leading to an internal wave attractor w hich has a broad wavenumber spectrum. Second is the broad banded\ntime-fre quency spectrum of the trapezoidal geometry\, as shown by the impulse\nres ponse of the system. The third one is a nonlinear transfer in frequencies\ nand wavevectors via triadic interactions\, which results at large forcing \namplitudes in a power law decay of the wavenumber power spectrum. This f irst\nexperimental spectrum of internal wave turbulence displays a $k^{-3} $ behavior.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5025/6/ END:VEVENT END:VCALENDAR