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The effect of axial stretching on the three-dimensional stability of a vortex pair

Published online by Cambridge University Press:  26 April 2006

J. S. Marshall
J. S. Marshall
Affiliation:
Department of Ocean Engineering, Florida Atlantic University, Boca Raton. FL 33431. USA
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Abstract

The stability of a pair of counter-rotating vortices to three-dimensional disturbances in the presence of a stretching flow is studied for vortices of small circular cross-section. The problem is reduced to a system of two first-order, linear ordinary differential equations, which can be integrated numerically to obtain the change in the perturbation of the vortex pair with time. The stability of the vortex pair depends upon four dimensionless constants, two of which characterize the stretching flow. Computations indicate that stretching usually exerts a stabilizing influence on the vortex pair, although in many cases the perturbation amplitude may initially increase and then decrease at some later time due to the effects of stretching. The results of the study are applied to investigate stability of hairpin vortices that are typically observed in turbulent shear flows. An estimate of the percentage increase in perturbation amplitude of a hairpin vortex in a homogeneous turbulent shear flow is given as a function of the stretch of the hairpin for different values of the dimensionless perturbation wavenumber and the microscale Reynolds number Reλ = λq/ν (based on the Taylor microscale λ and the turbulent kinetic energy ½q2). The maximum percentage growth of a perturbation of the legs of a hairpin vortex in a turbulent shear flow is found to decrease with increase in Reλ.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 241 , August 1992 , pp. 403 - 419
Copyright
© 1992 Cambridge University Press

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