book chapter · 2005
Instability
Cited by 0Abstract and details only
Abstract
Abstract In the previous chapter, we encountered a special kind of instability, now called the Kelvin–Helmholtz instability, which occurs when two fluid masses slide on each other, for instance along smoke jets or on a plane water surface under wind. Helmholtz arrived at this instability by reasoning on vortex sheets and used it to explain phenomena that seemed to elude Euler’s equations. He was neither the first nor the last theorist to emphasize the role of instabilities in fluid mechanics. The nineteenth-century interest in this question was for two reasons. Firstly, the discrepancy between actual fluid behavior and known solutions of the hydrodynamic equations suggested the instability of these solutions. Secondly, the British endeavor to reduce all physics to the motion of a perfect liquid presupposed the stability of the forms of motion used to describe matter and ether. Instability in the former case and stability in the latter case needed to be proved. In nineteenth-century parlance, kinetic instability broadly meant a departure from an expected regularity of motion. In hydrodynamics alone, this notion included unsteadiness of motion, non-uniqueness of the solutions of the fundamental equations under given boundary conditions, sensibility of these solutions to infinitesimal local perturbation, sensibility to infinitesimal harmonic perturbations, sensibility to finite perturbations, and sensibility to infinitely-small viscosity. Although this spectrum of meanings is much wider than a modern treatise on hydrodynamic stability would tolerate, it must be respected in a historical study that does not artificially separate issues that nineteenth- century writers conceived as a whole.
Cite this paper
Darrigol, O. (2005). Instability. https://doi.org/10.1093/oso/9780198568438.003.0005
Darrigol, Olivier. “Instability.” 2005, pp. 183–218, https://doi.org/10.1093/oso/9780198568438.003.0005.
Darrigol, Olivier. 2005. “Instability.” https://doi.org/10.1093/oso/9780198568438.003.0005.
Darrigol, O. (2005) ‘Instability’. Available at: https://doi.org/10.1093/oso/9780198568438.003.0005.
@incollection{darrigol2005instability,
title = {{Instability}},
author = {Darrigol, Olivier},
pages = {183--218},
year = {2005},
doi = {10.1093/oso/9780198568438.003.0005}
}Made from the index record. Check names, capitalisation and page numbers against the paper. Need another style? AI for Research has over 10,000.