THREE-DIMENSIONAL INSTABILITIES IN QUASI-TWO DIMENSIONAL INVISCID FLOWS.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

26 Citations (Scopus)

Abstract

The three-dimensional inviscid Navier-Stokes equations have a large family of exact steady 'quasi-two-dimensional' solutions, in which the velocity in the x,y plane is determined by a stream function psi (x,y), with the z-velocity and z-vorticity functions of psi (x,y) alone. If the projected streamlines in the x,y plane are closed curves, the flow may be subject to a broad band three-dimensional instability in the form of a wave packet centered on a particular surface of constant psi . The structure of the wave is determined by a Floquet system of ordinary differential equations around the corresponding psi contour in the x,y plane, and the Floquet exponent gives the growth rate. This family of instabilities includes the Rayleigh centrifugal instability, the Leibovich-Stewartson columnar vortex instability, and the secondary instability of finite-amplitude waves in plane shear flows.

Original languageEnglish (US)
Title of host publicationAmerican Society of Mechanical Engineers, Applied Mechanics Division, AMD
EditorsR.W. Miksad, T.R. Akylas, T. Herbert
PublisherASME
Pages71-77
Number of pages7
Volume87
StatePublished - 1987
Externally publishedYes

Fingerprint

Wave packets
Shear flow
Vorticity
Ordinary differential equations
Navier Stokes equations
Vortex flow

ASJC Scopus subject areas

  • Mechanical Engineering

Cite this

Bayly, B. J. (1987). THREE-DIMENSIONAL INSTABILITIES IN QUASI-TWO DIMENSIONAL INVISCID FLOWS. In R. W. Miksad, T. R. Akylas, & T. Herbert (Eds.), American Society of Mechanical Engineers, Applied Mechanics Division, AMD (Vol. 87, pp. 71-77). ASME.

THREE-DIMENSIONAL INSTABILITIES IN QUASI-TWO DIMENSIONAL INVISCID FLOWS. / Bayly, Bruce J.

American Society of Mechanical Engineers, Applied Mechanics Division, AMD. ed. / R.W. Miksad; T.R. Akylas; T. Herbert. Vol. 87 ASME, 1987. p. 71-77.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Bayly, BJ 1987, THREE-DIMENSIONAL INSTABILITIES IN QUASI-TWO DIMENSIONAL INVISCID FLOWS. in RW Miksad, TR Akylas & T Herbert (eds), American Society of Mechanical Engineers, Applied Mechanics Division, AMD. vol. 87, ASME, pp. 71-77.
Bayly BJ. THREE-DIMENSIONAL INSTABILITIES IN QUASI-TWO DIMENSIONAL INVISCID FLOWS. In Miksad RW, Akylas TR, Herbert T, editors, American Society of Mechanical Engineers, Applied Mechanics Division, AMD. Vol. 87. ASME. 1987. p. 71-77
Bayly, Bruce J. / THREE-DIMENSIONAL INSTABILITIES IN QUASI-TWO DIMENSIONAL INVISCID FLOWS. American Society of Mechanical Engineers, Applied Mechanics Division, AMD. editor / R.W. Miksad ; T.R. Akylas ; T. Herbert. Vol. 87 ASME, 1987. pp. 71-77
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