An analytical study of intermittency through Riemann’s non-differentiable functions

Analysis Seminar
Wednesday, April 21, 2021 - 2:00pm for 1 hour (actually 50 minutes)
ONLINE — see abstract for the Zoom link
Victor Vilaça Da Rocha – Georgia Tech
Benjamin Jaye

Intermittency is a property observed in the study of turbulence. Two of the most popular ways to measure it are based on the concept of flatness, one with structure functions in the physical space and the other one with high-pass filters in the frequency space. Experimental and numerical simulations suggest that the two approaches do not always give the same results. In this talk, we prove they are not analytically equivalent. For that, we first adapt them to a rigorous mathematical language, and we test them with generalizations of Riemann’s non-differentiable function. This work is motivated by the discovery of Riemann’s non-differentiable function as a trajectory of polygonal vortex filaments.

The seminar will be held on Zoom.  Here is the link