Abstract
It is shown that a weak time-dependent stretching might rapidly destabilise a vortex, thus providing a mechanism for vortex bursts observed in turbulent flows. This study addresses the three-dimensional stability of a stretched viscous Batchelor vortex. In a fashion quite similar to Lundgren’s transformation, the strain field is almost eliminated from the linear equations that govern three-dimensional perturbations. Such transformed equations, which are reminiscent of those for the swirling jet instability, are then numerically solved in the simple case of a compression phase followed by a stretching phase. Simulations qualitatively demonstrate how strain and azimuthal vorticity cooperate to destabilise the vortex.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abid, M., Andreotti, B., Douady, S. & Nore, C. 2002 Oscillating structures in a stretched-compressed vortex. J.Fluid Mech.450, 207–233.
Cadot, O., Douady, S. & Couder, Y. 1995 Characterization of the low pressure filaments in three-dimensional turbulent shear flow. Phys. Fluids7(3), 630–646.
Delbende, I., Rossi. M. & Le dizès, S. 2002 Stretching effects on the three-dimensional stability of vortices with axial flow J. Fluid Mech.454, 419–442.
Gibbon, J.D., Fokas, A.S. & Doering, C.R. 1999 Dynamically stretched vortices as solution of the 3D Navier-Stokes equations. Physica D132, 497–510.
Lessen, M., Singh, P.J. & Paillet, P. 1974 The stability of a trailing line vortex. Part 1. Inviscid theory. J. Fluid Mech.63, 753–763.
Lundgren, T.S. 1982 Strained spiral vortex model for turbulent fine structure. Phys. Fluids, 25(12), 2193–2203.
Mayer, E.W. & Powell, K.G. 1992 Viscous and inviscid instabilities of a trailing line vortex, J. Fluid Mech.245, 91–114.
Verzicco, R. & Jiménez, J. 1999 On the survival of strong vortex filaments in ‘model’ turbulence. J.Fluid Mech.394, 261–279.
Verzicco, R., Jiménez, J. & Orlandi, P. 1995 On steady columnar vortices under local compression. J. Fluid Mech.299, 367–388.
Vincent, A. & Meneguzzi, M. 1991 The spatial structure and statistical properties of homogeneous turbulence. J. Fluid Mech.225, 1–20.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Kluwer Academic Publishers
About this paper
Cite this paper
Rossi, M., Delbende, I., Stéphane, L.D. (2002). Effect of stretching on vortices with axial flow. In: Bajer, K., Moffatt, H.K. (eds) Tubes, Sheets and Singularities in Fluid Dynamics. Fluid Mechanics and Its Applications, vol 71. Springer, Dordrecht. https://doi.org/10.1007/0-306-48420-X_3
Download citation
DOI: https://doi.org/10.1007/0-306-48420-X_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-0980-8
Online ISBN: 978-0-306-48420-9
eBook Packages: Springer Book Archive