An analytic study of intermittency and multifractality through Riemann's non differentiable function

Series
CDSNS Colloquium
Time
Friday, March 4, 2022 - 1:00pm for 1 hour (actually 50 minutes)
Location
Skiles 05
Speaker
Victor Vilaça Da Rocha – Georgia Tech – vrocha3@gatech.edu
Organizer
Victor Vilaça Da Rocha

Different ways have been introduced to define intermittency in the theory of turbulence, like for example the non-gaussianity, the lack of self-similarity or the deviation of the theory of turbulence by Kolmogorov from 1941.

The usual tool to measure intermittency is the flatness, a measure of the variation of the velocity at small scale, using structure functions in the spatial domain, or high-pass filters in the frequency domain. However, these two approaches give different results in some experiences.

The goal here is to study and compare these two methods and show that the result depends on the regularity of the studied function. For that purpose, we use Riemann's non-differentiable functions. To motivate this choice, we'll present the link between this function, the vortex filament equation, and the multifractal formalism.
This is a work in collaboration with Daniel Eceizabarrena (University of Massachusetts Amherst) and Alexandre Boritchev (University of Lyon)