# Numerical calculations of the stability of some axisymmetric flows proposed as a model for vortex breakdown

## Abstract

This thesis is concerned with a model that has been proposed for the so-called axisymmetric or bubble-type breakdown. It has been conjectured (Leibovich (1984)) that this form of breakdown can be viewed as a growing axisymmetric wave travelling upstream in a primarily columnar flow whose progress is impeded only when it reaches a critical amplitude and which is then destabilized by some nonaxisymmetric disturbance. The growth of this asymmetric mode at the expense of the axisymmetric wave causes it to equilibrate at some point along the axis as is observed in experiments. Leibovich (1970) showed that columnar flows can support (weakly nonlinear) axisymmetric, dispersive waves, and this thesis studies the linear, temporal stability of such flows to three-dimensional disturbances, viewing the amplitude of the wave as a bifurcation parameter. The stability equations are solved numerically by a vector spectral method due to Leonard and Wray (1984). In this method the disturbance velocity field is expanded in terms of divergence-free basis vectors that satisfy appropriate (viscous or inviscid) boundary conditions.

- Authors:

- Publication Date:

- Research Org.:
- Cornell Univ., Ithaca, NY (USA)

- OSTI Identifier:
- 6534283

- Resource Type:
- Thesis/Dissertation

- Resource Relation:
- Other Information: Thesis (Ph. D.)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING; FLOW MODELS; VORTEX FLOW; AXIAL SYMMETRY; BOUNDARY CONDITIONS; DISTURBANCES; STABILITY; THREE-DIMENSIONAL CALCULATIONS; TRAVELLING WAVES; FLUID FLOW; MATHEMATICAL MODELS; SYMMETRY; 420400* - Engineering- Heat Transfer & Fluid Flow

### Citation Formats

```
MacGiolla Mhuiris, N.
```*Numerical calculations of the stability of some axisymmetric flows proposed as a model for vortex breakdown*. United States: N. p., 1986.
Web.

```
MacGiolla Mhuiris, N.
```*Numerical calculations of the stability of some axisymmetric flows proposed as a model for vortex breakdown*. United States.

```
MacGiolla Mhuiris, N. Wed .
"Numerical calculations of the stability of some axisymmetric flows proposed as a model for vortex breakdown". United States.
```

```
@article{osti_6534283,
```

title = {Numerical calculations of the stability of some axisymmetric flows proposed as a model for vortex breakdown},

author = {MacGiolla Mhuiris, N},

abstractNote = {This thesis is concerned with a model that has been proposed for the so-called axisymmetric or bubble-type breakdown. It has been conjectured (Leibovich (1984)) that this form of breakdown can be viewed as a growing axisymmetric wave travelling upstream in a primarily columnar flow whose progress is impeded only when it reaches a critical amplitude and which is then destabilized by some nonaxisymmetric disturbance. The growth of this asymmetric mode at the expense of the axisymmetric wave causes it to equilibrate at some point along the axis as is observed in experiments. Leibovich (1970) showed that columnar flows can support (weakly nonlinear) axisymmetric, dispersive waves, and this thesis studies the linear, temporal stability of such flows to three-dimensional disturbances, viewing the amplitude of the wave as a bifurcation parameter. The stability equations are solved numerically by a vector spectral method due to Leonard and Wray (1984). In this method the disturbance velocity field is expanded in terms of divergence-free basis vectors that satisfy appropriate (viscous or inviscid) boundary conditions.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {1986},

month = {1}

}