Published on June 13, 2023
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Updated on September 28, 2024
Dates
from June 26, 2023 to July 7, 2023
- Lecture 1: Fr, June 30., 9am (Valrose, M37)
- Lecture 2: We, July 5., 9am (Porquerolles)
- Lecture 3: Th, July 6., 9am (Porquerolles)
Location
Campus Valrose
Valrose - Bâtiment M
Stochastic fluid mechanics and Boussinesq hypothesis
In the last few years, a new technique in the the theory of Stochastic Partial Differential Equations (SPDEs) was devised to prove rigorously the emergence of additional dissipative terms from stochastic transport-advection terms, in a suitable scaling limit of small-space-scale turbulence. We shall exemplify this technique in the case of passive scalar equations, passive magnetic field in a 2D-3C regime, 2D and 2D-3C Navier-Stokes equations (Boussinesq hypothesis), including AKA effect. There are however several open problems, in particular related on one side to potential negative viscosity arising in 2D due to the inverse cascade, on the other to the fluctuations of the random stretching exerted by small-scale turbulence on large scales in 3D. We shall also briefly discuss the application of this technique to the enhancement of particle aggregation by turbulence.
This research is supported by the European Commission Project NoisyFLuid, n 101053472
- This minicourse is part of the summer school program: 100 years of cascades, organized in the framework of the thematic semester in turbulence.
- For the lectures held in Valrose, attendance is open to anyone interested.