应用数学研究所
学术报告


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Speaker:

Dr.Jaco Bedrossian,University of Maryland

Inviter: 朱湘禅 研究员
Title:
Almost-sure exponential mixing and the Batchelor spectrum in stochastic fluid dynamics
Time & Venue:

2021.5.11 16:00 Zoom会议: 942 676 4296 密码:123456

Abstract:

In 1959, Batchelor predicted that passive scalars advection in incompressible fluids at fixed Reynolds number with small diffusivity k should display a |k|^?1 power spectrum in a statistically stationary experiment, which has since been tested extensively in the physics and engineering literature. Results obtained with Alex Blumenthal and Sam Punshon-Smith provide the first mathematically rigorous proof of this law in the fixed Reynolds number case under stochastic forcing (with the caveat that in the 3d case, the Navier-Stokes equations are regularized with hyperviscosity). The origin of the spectrum is the uniform, exponential rate that all passive scalar fields mix (up to a random prefactor), which we prove using ideas from random dynamical systems such as a la Furstenberg and two-point geometric ergodicity.

Affiliation:  

学术报告中国科学院数学与系统科学研究院应用数学研究所
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