The mechanics of finite-time blowup in an Euler flow

CDSNS Colloquium
Friday, March 19, 2021 - 1:00pm for 1 hour (actually 50 minutes)
Zoom (see add'l notes for link)
Dwight Barkley – U Warwick –
Alex Blumenthal

Please Note: Zoom link:

One of the most fundamental issues in fluid dynamics is whether or not an initially smooth fluid flow can evolve over time to arrive at a singularity -- a state for which the classical equations of fluid mechanics break down and the flow field no longer makes physical sense.  While proof remains an open question, numerical evidence strongly suggests that a singularity arises at the boundary of a flow like that found in a stirred cup of tea.  The analysis here focuses on the interplay between inertia and pressure, rather than on vorticity.  A model is presented based on a primitive-variables formulation of the Euler equations on the cylinder wall, with closure coming from how pressure is determined from velocity. The model generalizes Burger's equation and captures key features in the mechanics of the blowup scenario.