Calculations of the stability of some axisymmetric flows proposed as a model of vortex breakdown
type: Item
instance of: scholarly article
title: Calculations of the stability of some axisymmetric flows proposed as a model of vortex breakdown
zbMATH Open document ID: 0611.76058
DOI: 10.1016/0168-9274(86)90033-4
author: Nessan Mac Giolla Mhuiris
published in: Applied Numerical Mathematics
publication date: 1986-01-01T00:00:00Z
review text: We investigate the stability of some axisymmetric wavy flows, which model vortex breakdown, to three-dimensional disturbances viewing the amplitude of the wave as a bifurcation parameter. We will also look at the stability of a set of related, columnar vortex flows which are constructed by taking the two-dimensional flow at a single axial location and extending it throughout the domain without variation. The method of our investigation will be to expand the perturbation velocity in a series of divergence free vectors which ensures that the continuity equation for the incompressible fluid is satisfied exactly by the computed velocity field. Projections of the stability equation onto the space of inviscid vector fields eliminates the pressure term from the equation and reduces the differential eigen problem to a generalized matrix eigen problem. Results are presented both for the one-dimensional, columnar vortex flows and also for the wavy 'bubble' flows.
Mathematics Subject Classification ID: 76E05
Mathematics Subject Classification ID: 76B47
Mathematics Subject Classification ID: 76M99
Mathematics Subject Classification ID: 35B32
zbMATH DE Number: 3988953
zbMATH Keywords: stability
zbMATH Keywords: axisymmetric wavy flows
zbMATH Keywords: vortex breakdown
zbMATH Keywords: three-dimensional disturbances
zbMATH Keywords: bifurcation parameter
zbMATH Keywords: columnar vortex flows
zbMATH Keywords: two- dimensional flow
zbMATH Keywords: single axial location
zbMATH Keywords: perturbation velocity
zbMATH Keywords: divergence free vectors
zbMATH Keywords: continuity equation
zbMATH Keywords: stability equation
zbMATH Keywords: inviscid vector fields
zbMATH Keywords: differential eigen problem
zbMATH Keywords: generalized matrix eigen problem
zbMATH Keywords: one-dimensional, columnar vortex flows
MaRDI profile type: Publication
full work available at URL: 0168-9274(86)90033-4
OpenAlex ID: W2012508779
cites work: Theory of the vortex breakdown phenomenon
cites work: Spectral Methods
cites work: Q3896709
cites work: Vortex Breakdown
cites work: On the hydrodynamic and hydromagnetic stability of swirling flows
cites work: Q4114880
cites work: The life and scientific work of Vladimir Ivanovich Smirnov
cites work: Weakly non-linear waves in rotating fluids
cites work: A sufficient condition for the instability of columnar vortices
cites work: Q3219047
cites work: Q3746543
cites work: The critical state: a trapped wave model of vortex breakdown
cites work: Linear stability of Poiseuille flow in a circular pipe
cites work: Q4151274
Wikidata QID: Q126819929
description: scientific article; zbMATH DE number 3988953