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Pulsatile jets

Published online by Cambridge University Press:  12 January 2011

RICHARD E. HEWITT  and
PETER W. DUCK
RICHARD E. HEWITT
Affiliation:
School of Mathematics, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
PETER W. DUCK*
Affiliation:
School of Mathematics, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
*
†Email address for correspondence: duck@ma.man.ac.uk
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Abstract

We consider the evolution of high-Reynolds-number, planar, pulsatile jets in an incompressible viscous fluid. The source of the jet flow comprises a mean-flow component with a superposed temporally periodic pulsation, and we address the spatiotemporal evolution of the resulting system. The analysis is presented for both a free symmetric jet and a wall jet. In both cases, pulsation of the source flow leads to a downstream short-wave linear instability, which triggers a breakdown of the boundary-layer structure in the nonlinear regime. We extend the work of Riley, Sánchez-Sans & Watson (J. Fluid Mech., vol. 638, 2009, p. 161) to show that the linear instability takes the form of a wave that propagates with the underlying jet flow, and may be viewed as a (spatially growing) weakly non-parallel analogue of the (temporally growing) short-wave modes identified by Cowley, Hocking & Tutty (Phys. Fluids, vol. 28, 1985, p. 441). The nonlinear evolution of the instability leads to wave steepening, and ultimately a singular breakdown of the jet is obtained at a critical downstream position. We speculate that the form of the breakdown is associated with the formation of a ‘pseudo-shock’ in the jet, indicating a failure of the (long-length scale) boundary-layer scaling. The numerical results that we present disagree with the recent results of Riley et al. (2009) in the case of a free jet, together with other previously published works in this area.

JFM classification

Boundary Layers: Boundary layer control Boundary Layers: Boundary layer stability Instability: Instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 670 , 10 March 2011 , pp. 240 - 259
Copyright
Copyright © Cambridge University Press 2011

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References

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