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The spatial viscous instability of axisymmetric jets

  • Philip J. Morris (a1)

The stability of three axisymmetric jet profiles is reviewed. These profiles represent the development of an incompressible jet from a nearly top-hat profile to a fully developed jet profile. The disturbance equations for arbitrary mode number in a region of zero shear, which provide the boundary conditions for the numerical solution, are solved analytically through use of the disturbance vorticity equations. Numerical solutions for the spatial stability for the axisymmetric (n = 0) disturbance and the asymmetric n = l disturbance are presented. Previously published calculations of least stable modes are shown to be incorrectly interpreted and their actual mode types are given. The critical Reynolds number is found to increase as the profile varies from a top-hat to a fully developed jet form. Closed contours of constant amplification, which are unusual in free shear flows, are shown to exist for the n = 1 disturbance in the fully developed jet region. A fluctuation energy balance is used to justify the occurrence of this destabilizing effect of decreasing Reynolds number.

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Andbade, E. N. D. & Tsien, L. C. 1937 The velocity distribution in a liquid-into-liquid jet. Proc. Phys. Soc. Lond. 49, 381.
Batchelob, G. K. & Gill, A. E. 1962 Analysis of the stability of axisymmetric jets. J. Fluid Mech. 14, 529.
Bellman, R. E. & Kalaba, R. E. 1965 Quosi-linearizotion and Non-linear Boundary-value Problems. Elsevier.
Bubbidgb, D. M. 1968 The stability of round jets. Ph.D. thesis, Bristol University.
Conte, S. D. 1966 The numerical solution of linear boundary-value problems. Siam Rev. 8, 309.
Ceighton, D. G. 1973 Instability of an elliptic jet. J. Fluid Mech. 59, 665.
Crow, S. C. & Champagne, F. M. 1971 Orderly structure in jet turbulence. J. Fluid Mech. 48, 547.
Davey, A. 1973 A simple numerical method for solving Orr-Sommerfeld problems. Quart. J. Mech. Appl. Math. 26, 401.
Davey, A. & Nguyen, H. P. F. 1971 Finite-amplitude stability of pipe flow. J. Fluid Mech. 45, 701.
Fbeymuth, P. 1966 On transition in a separated laminar boundary layer. J. Fluid Mech. 25, 683.
Fyfe, D. J. 1966 Economical evaluation of Runge-Kutta formulae. Math. Comp. 20, 392.
Gabg, V. K. 1971 Stability of pipe Poiseuille flow to infinitesimal disturbances. Ph.D. thesis, Carnegie-Mellon University Pittsburgh.
Gabg, V. K. & Rouleau, W. T. 1972 Linear spatial stability of pipe Poiseuille flow. J. Fluid Mech. 54, 113.
Gasteb, M. 1962 A note on the relation between temporally-increasing and spatially-increasing disturbances in hydrodynamic stability. J. Fluid Mech. 14, 222.
Gill, A. E. 1962 On the occurrence of condensations in steady axisymmetric jets. J. Fluid Mech. 14, 557.
Gill, A. E. 1965 On the behaviour of small disturbances to Poiseuille flow in a circular pipe. J. Fluid Mech. 21, 145.
Kambe, T. 1969 The stability of an axisymmetric jet with a parabolic profile. J. Phys. Soc. Japan, 26, 566.
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics. Pergamon.
Lessen, M., Sadleb, S. G. & Liu, T.-Y. 1968 Stability of pipe Poiseuille flow, Phys. Fluids, 11, 1404.
Lessen, M. & Singh, P. J. 1973 The stability of axisymmetric free shear layers. J. Fluid Mech. 60, 443.
Mattingly, G. E. & Chang, C. C. 1974 Unstable waves on an axisymmetric jet column. J. Fluid Mech. 65, 541.
Michalke, A. 1965 On spatially growing disturbances in an inviscid shear layer. J. Fluid Mech. 23, 521.
Michalke, A. 1971 Instabilität eines kompressiblen runden Freistrahls unter Berück-sichtigung des Einflusses der Strahlgrenzschichtdicke. Z. Flugwiss. 19, 319.
Mollendobf, J. C. & Gebhart, B. 1973 An experimental and numerical study of the viscous stability of a round laminar vertical jet with and without thermal buoyancy for symmetric and asymmetric disturbances. J. Fluid Mech. 61, 367.
Morris, P. J. 1971 The structure of turbulent shear flow. Ph.D. thesis, Southampton University.
Obszag, S. A. & Cbow, S. C. 1970 Instability of a vortex sheet leaving a semi-infinite plate. Stud. Appl. Math. 49. 167.
Pai, S. I. & Hsieh, T. 1972 Numerical solution of laminar jet mixing with and without free stream. Appl. Sci. Res. 27, 39.
Reynolds, A. J. 1962 Observations of a liquid-into-liquid jet. J. Fluid Mech. 14, 552.
Sharma, R. 1968 The structure of turbulent shear flow. Ph.D. thesis, Southampton University.
Viilu, A. 1962 An experimental determination of the minimum Reynolds number for instability in a free jet. J. Appl. Mech. 29, 506.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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