### 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 language | English (US) |
---|---|

Title of host publication | American Society of Mechanical Engineers, Applied Mechanics Division, AMD |

Editors | R.W. Miksad, T.R. Akylas, T. Herbert |

Publisher | ASME |

Pages | 71-77 |

Number of pages | 7 |

Volume | 87 |

State | Published - 1987 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mechanical Engineering

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*American Society of Mechanical Engineers, Applied Mechanics Division, AMD.*vol. 87, ASME, pp. 71-77.

}

TY - GEN

T1 - THREE-DIMENSIONAL INSTABILITIES IN QUASI-TWO DIMENSIONAL INVISCID FLOWS.

AU - Bayly, Bruce J

PY - 1987

Y1 - 1987

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0023597086&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0023597086&partnerID=8YFLogxK

M3 - Conference contribution

VL - 87

SP - 71

EP - 77

BT - American Society of Mechanical Engineers, Applied Mechanics Division, AMD

A2 - Miksad, R.W.

A2 - Akylas, T.R.

A2 - Herbert, T.

PB - ASME

ER -