UMR 5672

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Singularities, Turbulence and Instantons

Rainer Grauer (Ruhr Universität, Bochum)
When May 26, 2015
from 11:00 AM to 12:30 PM
Where Salle Fontaine
Attendees Rainer Grauer
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It is evident that coherent nearly singular structures play a dominant role in understanding the anomalous scaling behavior in turbulent systems.
We ask the question, which role these singular structures play in turbulence statistics. More than 15 years ago, for certain turbulent systems the door for attacking this issue was opened by getting access to the probability density function to rare and strong fluctuations by the instanton approach. We address the question whether one can identify instantons in direct numerical simulations of the stochastically driven Burgers equation. For this purpose, we first solve the instanton equations using the Chernykh
Stepanov method [2001]. These results are then compared to direct numerical simulations by introducing a filtering technique to extract prescribed rare events from massive data sets of realizations.

In addition, we solve the issue why earlier simulations by Gotoh [1999] were in disagreement with the asymptotic prediction of the instanton method and demonstrate that this approach is capable to describe the probability distribution of velocity differences for various Reynolds numbers. Finally, we will present and discuss first results on the instanton solution for vorticity in 3D NavierStokes turbulence.

References

T. Grafke, R. Grauer, T. Schäfer, Instanton filtering for the stochastic Burgers equation, Journal of Physics A: Mathematical and Theoretical (FAST TRACK COMMUNICATION), 46, 62002, 2013.

T. Grafke, R. Grauer, T. Schäfer, E. VandenEijnden, Relevance of instantons in Burgers turbulence, European Physics Letters, 109, 34003, 2015.

T. Grafke, R. Grauer, St. Schindel, Efficient Computation of Instantons for MultiDimensional Turbulent Flows with Large Scale Forcing, arXiv:1410.6331

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