Seminar "How to grow and blow vorticity in a flow" by Prof. Gregory Falkovich

[Speaker]

Gregory Falkovich
The Israel Pollak Professorial Chair of Physics,
Department of Physics of Complex Systems,

Weizmann Institute of Science.

[Abstract]

How strong vorticity fluctuations appear in 3D incompressible turbulence driven by a large-scale (smooth) force?

Physicists and mathematicians address this question from seemingly very different perspectives. The former are interested in the most probable and thus frequently observable events. The latter are interested in the most singular events, even though they are unobservable. And yet these two ways recently started to converge to novel and similar flow configurations.

By combining analytical and numerical methods, we (physicists) constructed an instanton: the most probable random force history driving the flow to a prescribed large vorticity at a given point and time. We have shown how the smooth, large-scale force produces a long fast-rotating filament surrounded by a non-symmetric flow of complicated geometry. That flow contains both the standard mechanism of amplifying a vortex tube through radial compression and axial stretching, and a newly discovered mechanism of vorticity waves colliding at the center. These geometry and mechanism have striking similarities to the one independently suggested by OpenAI for a finite-time vorticity blow-up (Millennium problem). I shall also discuss wider aspects of human-AI science collaboration.