Stability and instability in nineteenth-century fluid mechanics

Olivier Darrigol

Revue d'histoire des mathématiques (2002)

  • Volume: 8, Issue: 1, page 5-66
  • ISSN: 1262-022X

Abstract

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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.

How to cite

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Darrigol, Olivier. "Stability and instability in nineteenth-century fluid mechanics." Revue d'histoire des mathématiques 8.1 (2002): 5-66. <http://eudml.org/doc/252119>.

@article{Darrigol2002,
abstract = {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.},
author = {Darrigol, Olivier},
journal = {Revue d'histoire des mathématiques},
keywords = {hydrodynamic instability; Stokes; Helmholtz; Kelvin; Rayleigh; Reynolds; Hydrodynamic instability},
language = {eng},
number = {1},
pages = {5-66},
publisher = {Société mathématique de France},
title = {Stability and instability in nineteenth-century fluid mechanics},
url = {http://eudml.org/doc/252119},
volume = {8},
year = {2002},
}

TY - JOUR
AU - Darrigol, Olivier
TI - Stability and instability in nineteenth-century fluid mechanics
JO - Revue d'histoire des mathématiques
PY - 2002
PB - Société mathématique de France
VL - 8
IS - 1
SP - 5
EP - 66
AB - 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.
LA - eng
KW - hydrodynamic instability; Stokes; Helmholtz; Kelvin; Rayleigh; Reynolds; Hydrodynamic instability
UR - http://eudml.org/doc/252119
ER -

References

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