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Pulsatile jets

  • RICHARD E. HEWITT (a1) and PETER W. DUCK (a1)


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.


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Ackerberg, R. C. & Phillips, J. H. 1972 The unsteady laminar boundary layer on a semi-infinite plate due to small fluctuations in the magnitude of the free-stream velocity. J. Fluid Mech. 51, 137157.
Akatnov, N. I. 1953 Propagation of planar laminar fluid jet along rigid wall. Proc. LPI 5, 2431.
Bickley, W. G. 1937 The plane jet. Phil. Mag. 23, 727731.
Cowley, S. J., Hocking, L. M. & Tutty, O. R. 1985 The stability of solutions of the classical unsteady boundary-layer equation. Phys. Fluids 28, 441443.
Garg, V. K. 1981 Spatial stability of the non-parallel Bickley jet. J. Fluid Mech. 102, 127140.
Glauert, M. B. 1956 The wall jet. J. Fluid Mech. 1, 625643.
Goldstein, M. E. 1983 The evolution of Tollmien–Schlichting waves near a leading edge. J. Fluid Mech. 127, 5981.
Keller, H. B. 1978 Numerical methods in boundary-layer theory. Annu. Rev. Fluid Mech. 10, 417433.
Lam, S. H. & Rott, N. 1993 Eigenfunctions of linearized unsteady boundary layer equations. J. Fluid Engng 115, 597602.
Marzouk, S., Mhiri, H., El Golli, S., Le Palec, G. & Bournot, P. 2006 a Numerical study of momentum and heat transfer in a pulsed plane laminar jet. Intl J. Heat Mass Transfer 46, 43194334.
Marzouk, S., Mhiri, H., El Golli, S., Le Palec, G. & Bournot, P. 2006 b Numerical study of a heated pulsed axisymmetric jet in laminar mode. Numer. Heat Transfer A Appl. 43, 409429.
Riley, N., Sánchez-Sans, M. & Watson, E. J. 2009 A planar pulsating jet. J. Fluid Mech. 638, 161172.
Ruban, A. I. & Vonatsos, K. N. 2008 Discontinuous solutions of the boundary-layer equations. J. Fluid Mech. 614, 407424.
Sato, H. 1960 The stability and transition of a two-dimensional jet. J. Fluid Mech 7, 5381.
Schlichting, H. 1933 Laminare Strahlausbreitung. Z. Angew Math. Mech. 13, 260263.
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Pulsatile jets

  • RICHARD E. HEWITT (a1) and PETER W. DUCK (a1)


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