An axisymmetric boundary layer solution for an unsteady vortex above a plane

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Bellamy-Knights, Peter G. (2011)
  • Publisher: Co-Action Publishing
  • Journal: Tellus A (issn: 1600-0870, eissn: 0280-6495)
  • Related identifiers: doi: 10.3402/tellusa.v26i3.9837
  • Subject:
    arxiv: Physics::Fluid Dynamics

A given axisymmetric potential swirling flow is bounded by a plane perpendicular to the axis of symmetry. By the no slip condition, viscous effects will be important over the plane and since the circumferential velocity must be zero on the axis of symmetry, viscous effects will also be important in the core of the vortex. These two viscous regions will overlap near the intersection of the axis of symmetry with the plane. Thus the flow field can be divided into four regimes, the viscous core, the boundary layer on the plane, a ‘stagnation point’ regime and the given potential flow which provides the outer boundary conditions for each of the first two regimes. Such a model could be useful for studying meteorological flow systems such as tornadoes. The viscous core regime has already been studied (Rott, 1958, 1959; Bellamy-Knights, 1970, 1971).DOI: 10.1111/j.2153-3490.1974.tb01609.x
  • References (12)
    12 references, page 1 of 2

    Bellamy-Knights, P G. 1970. An unsteady two-cell vortex solution of the Navier-Stokes equations. J. Fluid Mech. 41, 673-687.

    Bellamy-Knights, P. G. 1971. Unsteady multicellular viscous vortices. J . Fluid Mech. 50, 1-16.

    Burgers, J. M. 1940. Application of a model system to illustrate some points of the statistical theory of free turbulence. Proc. Acad. Sci. Amst. 43,2-12.

    Burgers, J. M. 1948. A mathematical model illustrating the theory of turbulence. Adv. AppZ. Mech. 1, 197-199.

    Hartree, D. R. 1937. On a n equation occurring in Falkner and Skan's approximate treatment of the equations of the boundary layer. Proc. Camb. phil. SOC3.3, 223-239.

    Lighthill, M. J. 1958. On displacement thickness. J . FZuid Mech. 4, 383-392.

    Morse, P. M. & Feshbach, H. 1953. Methods of theoretical physics. McGraw-Hill, New York.

    Morton, B. R. 1966. Geophysical vortices. Progress in Aeronautical Sciences 7, 145-194.

    Oseen, C. W. 1911. Ark. Mat. Astr. Fys. 7.

    Rott, N. 1958. On the viscous core of a line vortex. 2. angew. Math. Phys. 96, 543-553.

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