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Nonlinear spatial evolution of helical disturbances to an axial jet

Published online by Cambridge University Press:  26 April 2006

S. M. Churilov  and
I. G. Shukhman
S. M. Churilov
Affiliation:
Institute of Solar-Terrestrial Physics, Irkutsk, 664033, PO Box 4026, Russia
I. G. Shukhman
Affiliation:
Institute of Solar-Terrestrial Physics, Irkutsk, 664033, PO Box 4026, Russia
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Abstract

We investigate the weakly nonlinear spatial evolution of helical disturbances of an axisymmetrical jet which are the analogue of three-dimensional disturbances, such as a single oblique wave (the wave vector is directed at an angle to the main flow velocity) in plane-parallel flows. It is shown that when a supercriticality is large enough, the perturbation amplitude A grows in the streamwise direction (along z) explosively: A ∼ (z0 — z)−5/2, though more slowly than in the case of essentially three-dimensional disturbances in the form of a pair of oblique waves (A ∼ (z0 — z)−3; Goldstein & Choi 1989). The nonlinearity needed for such a growth, is due equally to the cylindricity of shear layer and to the spatial character of the evolution (in the temporal problem the ‘evolution’ contribution is absent). At a smaller supercriticality, the evolution equation has a non-local (integral in z) nonlinearity, unusual for the regime of a viscous critical layer. Scenarios of disturbance development for different levels of supercriticality are studied, with proper account taken of viscous broadening of the flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 281 , 25 December 1994 , pp. 371 - 402
Copyright
© 1994 Cambridge University Press

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