• Corpus ID: 3554917

A classical mistake and what it tells us. How to do better with an action principle for Hydro and Thermodynamics

@article{Frnsdal2018ACM,
  title={A classical mistake and what it tells us. How to do better with an action principle for Hydro and Thermodynamics},
  author={Christian Fr{\o}nsdal},
  journal={arXiv: General Physics},
  year={2018}
}
  • C. Frønsdal
  • Published 20 March 2018
  • Physics
  • arXiv: General Physics
Rayleigh's stability analysis of cylindrical Couette flow, of 1889 and 1916, is in contradiction with observation. The analysis is repeated in many textbooks and reviews up to 2017, and its failure to agree with observation was duly noted. More successful approaches have been found, but little was done to discover the weak point of Rayleigh's argument, what is the reason that it fails. This paper identifies the mistake as one that is endemic in the literature. Since the physics of the problem… 

References

SHOWING 1-10 OF 37 REFERENCES

Heat and Gravitation: The Action Principle

The entropy that allows for the popular isothermal equilibrium and the study of the associated adiabatic dynamics are determined, leading to the suggestion that the equilibrium of an ideal gas must be isentropic, in which case, the role of solar radiation would be merely to compensate for the loss of energy by radiation into the cosmos.

Action Principle for Hydrodynamics and Thermodynamics including general, rotational flows

The restriction of hydrodynamics to non-viscous, potential (gradient, irrotational) flows is a theory both simple and elegant; a favorite topic of introductory textbooks. It is known that this theory

Relativistic thermodynamics, a Lagrangian field theory for general flows including rotation

Any theory that is based on an action principle has a much greater predictive power than one that does not have such a formulation. The formulation of a dynamical theory of General Relativity,

Stability of a Viscous Liquid Contained between Two Rotating Cylinders

In recent years much information has been accumulated about the flow of fluids past solid boundaries. All experiments so far carried out seem to indicate that in all cases steady motion is possible

STABILITY OF PARALLEL FLOWS

On the Dynamics of Revolving Fluids

So much of meteorology depends ultimately upon the dynamics of revolving fluid that it is desirable to formulate as clearly as possible such simple conclusions as are within our reach, in the hope

The rotation of liquid helium II II. The theory of mutual friction in uniformly rotating helium II

  • H. E. HallW. Vinen
  • Physics
    Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
  • 1956
A discussion is given of models for the rotation of helium II involving regions of concentrated vorticity, and it is shown thermodynamically that an arrangement of vortex lines is energetically

Stability of fluid motions

The natural frequencies of small transverse vibration of a finite beam are governed by an eigenvalue problem. When the beam carries a distributed axial load, the axial load can be taken to remain

An introduction to the theory of superfluidity

A classic from 1965, this book covers the main aspects of the theory of quantum liquids, including the elementary excitation spectrum, hydrodynamics, and kinetic phenomena. The book requires no

Rotating trapped Bose-Einstein condensates

AbstractTrapped Bose-Einstein condensates (BECs) differ considerably from the standard textbook example of a uniform Bose gas. In an isotropic harmonic potential V(r) = ½Mω2r2, the single-particle