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Structure of a linear array of hollow vortices of finite cross-section

  • G. R. Baker (a1), P. G. Saffman (a1) and J. S. Sheffield (a1)
Abstract

Free-streamline theory is employed to construct an exact steady solution for a linear array of hollow, or stagnant cored, vortices in an inviscid incompressible fluid. If each vortex has area A and the separation is L, there are two possible shapes if A½/L is less than a critical value 0.38 and none if it is larger. The stability of the shapes to two-dimensional, periodic and symmetric disturbances is considered for hollow vortices. The more deformed of the two possible shapes is found to be unstable while the less deformed shape is stable.

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Brown, G. L. & Roshko, A.1974 On density effects and large structure in turbulent mixing layers J. Fluid Mech. 64, 775.
Hill, F. M.1975 Ph.D. thesis, Imperial College, London.
Jeffreys, H. & Jeffreys, B. S.1950 Methods of Mathematical Physics.Cambridge University Press.
Lamb, H.1932 Hydrodynamics.Cambridge University Press.
Moore, D. W. & Saffman, P. G.1971 Structure of a line vortex in an imposed strain. In Aircraft Wake Turbulence and its Detection (ed. Olsen, Goldberg & Rogers), p. 339. Plenum.
Moore, D. W. & Saffman, P. G.1975 The density of organized vortices in a turbulent mixing layer J. Fluid Mech. 69, 465.
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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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