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Instanton filtering for the stochastic Burgers equation

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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 [Phys. Rev. E 64, (2001)]. These results are then compared to direct numerical simulations of the stochastic Burgers equation by extracting prescribed rare events from massive data sets of realizations. Using this approach we obtain the entire time history of the instanton evolution which allows us to identify the different phases predicted by the direct method of Chernykh and Stepanov with remarkable agreement. These results confirm the relevance of the instanton in turbulent flows.

Author(s):

Tobias Grafke    
Ruhr-University Bochum
Germany

Rainer Grauer    
Ruhr-University Bochum
Germany

Tobias Schaefer    
City University New York
United States