Conditions for nonlinear stability of flows of an ideal incompressible liquid

Research output: Contribution to journalArticle

Abstract

Stability of steady state flows of an ideal incompressible liquid with homogeneous density with some type of symmetry (translational, axial, rotational, or helical) is considered. Two types of sufficient conditions for nonlinear stability are obtained, which can be proven by constructing two types of functionals which have absolute minima at the given steady state solutions. Each of the functionals used is the sum of the kinetic energy and some other integral, specific to the given class of motion. The first type of stability conditions are a generalization to the case of finite perturbations and a new class of flows of the well known Rayleigh criterion [1] for "centrifugal" stability of rotating flows relative to perturbations with rotational symmetry. In the same sense the second type of stability conditions generalize another result, also originally proposed by Rayleigh, according to which plane-parallel flow of a liquid is stable in the absence of an inflection point in the velocity profile [1]. A nonlinear variant of the latter condition for the class of planar motions was first obtained in [2]. To systematize the results extensive use is made of the analogy between the effects of density stratification and rotation in the form of [3], The results to be presented relate to stability of a wide class of hydrodynamic flows having the required symmetry. For example, they relate to flows in tubes and channels which rotate or are at rest, and flows with concentrated annular or spiral vortices.

Original languageEnglish
Pages (from-to)382-389
Number of pages8
JournalJournal of Applied Mechanics and Technical Physics
Volume27
Issue number3
DOIs
Publication statusPublished - May 1986

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Liquids
liquids
functionals
symmetry
perturbation
equilibrium flow
parallel flow
Parallel flow
inflection points
stratification
Kinetic energy
Vortex flow
Hydrodynamics
velocity distribution
kinetic energy
hydrodynamics
vortices
tubes

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)
  • Engineering(all)

Cite this

Conditions for nonlinear stability of flows of an ideal incompressible liquid. / Vladimirov, V. A.

In: Journal of Applied Mechanics and Technical Physics, Vol. 27, No. 3, 05.1986, p. 382-389.

Research output: Contribution to journalArticle

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