Artykuł w czasopiśmie
Brak miniatury
Licencja
CC-BY - Uznanie autorstwaKinetic energy represented in terms of moments of vorticity and applications
| dc.abstract.en | We study 2d vortex sheets with unbounded support. First we show a version of the Biot–Savart law related to a class of objects including such vortex sheets. Next, we give a formula associating the kinetic energy of a very general class of flows with certain moments of their vorticities. It allows us to identify a class of vortex sheets of unbounded support being only σ-finite measures (in particular including measures ω such that ω(R<sup>2</sup>)=∞), but with locally finite kinetic energy. One of such examples are celebrated Kaden approximations. We study them in details. In particular our estimates allow us to show that the kinetic energy of Kaden approximations in the neighbourhood of an origin is dissipated, actually we show that the energy is pushed out of any ball centered in the origin of the Kaden spiral. The latter result can be interpreted as an artificial viscosity in the center of a spiral. |
| dc.affiliation | Uniwersytet Warszawski |
| dc.contributor.author | Preisner, Marcin |
| dc.contributor.author | Oleszkiewicz, Krzysztof |
| dc.contributor.author | Szumańska, Marta |
| dc.contributor.author | Cieślak, Tomasz |
| dc.date.accessioned | 2024-01-25T04:47:37Z |
| dc.date.available | 2024-01-25T04:47:37Z |
| dc.date.copyright | 2019-09-09 |
| dc.date.issued | 2019 |
| dc.description.accesstime | BEFORE_PUBLICATION |
| dc.description.finance | Nie dotyczy |
| dc.description.number | 4 |
| dc.description.version | FINAL_PUBLISHED |
| dc.description.volume | 21 |
| dc.identifier.doi | 10.1007/S00021-019-0456-Z |
| dc.identifier.issn | 1422-6928 |
| dc.identifier.uri | https://repozytorium.uw.edu.pl//handle/item/110372 |
| dc.identifier.weblink | http://dx.doi.org/10.1007/s00021-019-0456-z |
| dc.language | eng |
| dc.pbn.affiliation | mathemathics |
| dc.relation.ispartof | Journal of Mathematical Fluid Mechanics |
| dc.relation.pages | 1-19 |
| dc.rights | CC-BY |
| dc.sciencecloud | nosend |
| dc.subject.en | vortex sheet |
| dc.subject.en | spherical averages |
| dc.subject.en | Biot-Savart law |
| dc.subject.en | Kaden spirals |
| dc.title | Kinetic energy represented in terms of moments of vorticity and applications |
| dc.type | JournalArticle |
| dspace.entity.type | Publication |