### Wilhelm Killing Kolloquium: Prof. Dr. Jacob Bedrossian (University of Maryland): per ZOOM: Almost-sure exponential mixing for stochastic Navier-Stokes with applications to passive scalar turbulence

##### Thursday, 12.11.2020 16:30 per ZOOM: Link to Zoom info

Together with Alex Blumenthal and Sam Punshon-Smith, we study the mixing of passive scalars by advection-diffusion with advection by sufficiently regular solutions of the stochastically-driven Navier-Stokes equations at arbitrary Reynolds number in a periodic box (in 3d with subcritical hyper-viscosity). We show that there is a deterministic, exponential rate such that all passive scalar fields are mixed at least this fast (with a random constant depending on the noise path and initial velocity field) and that this rate can be taken uniform in diffusivity of the scalar. These results are proved by studying the Lagrangian flow map using infinite dimensional extensions of ideas from random dynamical systems, especially a la Furstenberg rigidity and two-point geometric ergodicity for quenched correlation decay. In 1959, Batchelor predicted that passive scalars advected in fluids at fixed Reynolds number with small diffusivity ? should display a |k|^?1 power spectrum over a small-scale inertial range in a statistically stationary experiment. This prediction has been experimentally and numerically tested extensively in the physics and engineering literature. Our results provide the first mathematically rigorous proof of this law in the restricted case fixed Reynolds number in a periodic box under stochastic forcing/source.

Angelegt am 08.10.2020 von N. N

Geändert am 04.11.2020 von Frank Wübbeling

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Kolloquium Wilhelm Killing