2017/11/20 by Tomasz Cieślak, Krzysztof Oleszkiewicz, Cieślak, Tomasz +5 · 1 citation
Chemical Engineering · Engineering · Medicine · #Blood properties and coagulation #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Mathematical Physics (math-ph) #Rheology and Fluid Dynamics Studies
paper · pdf · doi:10.48550/arxiv.1711.07590
openalex publication_date 2017/11/20 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
We study 2d vortex sheets with unbounded support. First we show a version of\nthe Biot- Savart law related to a class of objects including such vortex\nsheets. Next, we give a formula associating the kinetic energy of a very\ngeneral class of ows with certain moments of their vorticities. It allows us to\nidentify a class of vortex sheets of unbounded support being only ?-finite\nmeasures (in particluar including measures \ω such that \ω(R2) =\n\∞), but with locally finite kinetic energy. One of such examples are\ncelebrated Kaden approximations. We study them in details. In particular our\nestimates allow us to show that the kinetic energy of Kaden approximations in\nthe neighbourhood of an origin is dissipated, actually we show that the energy\nis pushed out of any ball centered in the origin of the Kaden spiral. The\nlatter result can be interpreted as an artificial viscosity in the center of a\nspiral.\n