Les mouvements premiers à vorticité stationnaire uniforme composent une corolle d'espaces vectoriels isomorphes dérivés des déplacements solides ou des écoulements de Couette. Proches cadets des écoulements potentiels, ils vérifient deux extensions du théorème de Lagrange, s'étudient à l'aide des fonctions holomorphes, et sont célèbres quand ils sont plans. Ils interviennent en hydrodynamique, aérodynamique, géophysique, astrophysique, turbulence, physiques des plasmas et de l'hélium superfluide. À chaque fois, des translations transversales non stationnaires arbitraires permettent de générer des mouvements premiers tridimensionnels complexes. Trois écoulements périodiques méconnus servent d'illustration, et approchent l'instabilité de cisaillement dans pléthore de fluides.
Universal motions with uniform steady vorticity form a corolla of linear spaces derived from rigid body motions. Closely related to potential flows, they satisfy two extensions of Lagrange theorem, are investigated with the help of complex functions, as stand celebrated when be plane. They take place in hydrodynamics, aerodynamics, geophysics, astrophysics, turbulence, physics of plasmas and superfluid helium. In all the cases, arbitrary unsteady span-wise translations permit to generalise as well as to exhibit helical or 3D universal motions. Three misunderstood periodic flows illustrate our purpose, as they approach shear instabilities in numerous fluids.
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Keywords: Material engineering, Rankine, Kirchhoff and Batchelor's vortex patches, Visco-elastic critical layers, Tollmien–Schlichting waves
@article{CRMECA_2004__332_12_1019_0,
author = {Michel Bouthier},
title = {Espaces d'\'ecoulements dits {\guillemotleft} universels {\guillemotright}, 3},
journal = {Comptes Rendus. M\'ecanique},
pages = {1019--1025},
publisher = {Elsevier},
volume = {332},
number = {12},
year = {2004},
doi = {10.1016/j.crme.2004.05.004},
language = {fr},
}
Michel Bouthier. Espaces d'écoulements dits « universels », 3. Comptes Rendus. Mécanique, Volume 332 (2004) no. 12, pp. 1019-1025. doi : 10.1016/j.crme.2004.05.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2004.05.004/
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