Challenging ‘one of the last open problems of classical physics’

How can the instanton approach be used to tackle unsolved problems in fluid dynamics?

Comparison of filtered vorticity field (right) versus instanton solution (left) for the 3D incompressible Navier–Stokes equation in cylindrical coordinates.

Comparison of filtered vorticity field (right) versus instanton solution (left) for the 3D incompressible Navier–Stokes equation in cylindrical coordinates.

In their review Tobias Grafke from the Weizmann Institute (Israel), Rainer Grauer from Ruhr-Universität Bochum (Germany) and Tobias Schäfer from the College of Staten Island (NY, USA) investigate this question and consider recent developments related to the application of instanton methods to turbulence.

The review focuses on how to compute the instantons numerically. Grafke et al provide algorithms to do this by efficient solution of corresponding Euler–Lagrange equations and then as a further focus discuss a recently developed numerical filtering technique that allows the extraction of instantons from direct numerical simulations.

Further Reading?

Instanton filtering for the stochastic Burgers equation – T Grafke, R Grauer, T Schäfer.

Numerical study of impeller-driver von Kármán flows via a volume penalization method – S Kreuzahler, D Schulz, H Homann, Y Ponty, R Grauer.

 


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This work is licensed under a Creative Commons Attribution 3.0 Unported License.  Image: Tobias Grafke et al 2015 J. Phys. A: Math. Theor. 48 333001 copyright IOP Publishing Ltd 2015



Categories: Journal of Physics A: Mathematical and Theoretical

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