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The role of pressure in an incompressible Euler singularity

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TUR - Mathematical aspects of turbulence: where do we stand?

The blowup mechanism for an inviscid wall-bounded flow is investigated from a primitive-variables point of view.  The analysis focuses on the interplay between inertia and pressure, rather than on vorticity.  The incompressible Euler equations are numerically simulated in a cylindrical container. The flow is axisymmetric with the swirl. The simulations reproduce and corroborate aspects of prior studies by Luo and Hou reporting strong evidence for a finite-time singularity. The linearity of the pressure Poisson equation is exploited to decompose the pressure field into independent contributions. A model is presented based on a primitive-variables formulation of the Euler equations, with closure coming from how pressure is determined from velocity. The model captures key features in the mechanics of the blowup scenario.

This talk is part of the Isaac Newton Institute Seminar Series series.

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