[Stabilité et instabilité en mécanique des fluides au XIXe siècle]
Au dix-neuvième siècle, la stabilité ou l'instabilité de quelques écoulements simples fut l'objet de conjectures, de débats et parfois de preuves mathématiques. Les motivations pour ce type de recherche variaient considérablement, de la turbulence observée d'écoulements réels à la permanence attendue dans les théories hydrodynamiques de la matière. Les mathématiques contemporaines étaient rarement en mesure de fournir des réponses rigoureuses et les intuitions des uns et des autres conduisirent parfois à des résultats faux. Néanmoins, quelques grands de la physique mathématique britannique et allemande - Stokes, Kelvin, Helmholtz et Rayleigh - développèrent certaines idées et méthodes de base de la théorie moderne des instabilités hydrodynamiques. Ils y parvinrent en réfléchissant à des problèmes spécifiques concrets, avec une étonnante diversité de styles.
The stability or instability of a few basic flows was conjectured, debated, and sometimes proved in the nineteenth century. Motivations varied from turbulence observed in real flows to permanence expected in hydrodynamic theories of matter. Contemporary mathematics often failed to provide rigorous answers, and personal intuitions sometimes gave wrong results. Yet some of the basic ideas and methods of the modern theory of hydrodynamic instability occurred to the elite of British and German mathematical physics, including Stokes, Kelvin, Helmholtz, and Rayleigh. This usually happened by reflecting on concrete specific problems, with a striking variety of investigative styles.
@article{RHM_2002__8_1_5_0,
author = {Darrigol, Olivier},
title = {Stability and instability in nineteenth-century fluid mechanics},
journal = {Revue d'histoire des math\'ematiques},
pages = {5--65},
publisher = {Soci\'et\'e math\'ematique de France},
volume = {8},
number = {1},
year = {2002},
zbl = {1119.76301},
language = {en},
url = {http://www.numdam.org/item/RHM_2002__8_1_5_0/}
}
TY - JOUR AU - Darrigol, Olivier TI - Stability and instability in nineteenth-century fluid mechanics JO - Revue d'histoire des mathématiques PY - 2002 SP - 5 EP - 65 VL - 8 IS - 1 PB - Société mathématique de France UR - http://www.numdam.org/item/RHM_2002__8_1_5_0/ LA - en ID - RHM_2002__8_1_5_0 ER -
Darrigol, Olivier. Stability and instability in nineteenth-century fluid mechanics. Revue d'histoire des mathématiques, Tome 8 (2002) no. 1, pp. 5-65. http://www.numdam.org/item/RHM_2002__8_1_5_0/
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