Numerical Study on the Motion of Azimuthal Vortices in Axisymmetric Rotating Flows

  • Suh, Yong-Kweon (Division of Mechanical and Industrial System Engineering, Dong-A University)
  • 발행 : 2004.02.01

초록

A rich phenomenon in the dynamics of azimuthal vortices in a circular cylinder caused by the inertial oscillation is investigated numerically at high Reynolds numbers and moderate Rossby numbers. In the actual spin-up flow where both the Ekman circulation and the bottom friction effects are included, the first appearance of a seed vortex is generated by the Ekman boundary-layer on the bottom wall and the subsequent roll-up near the corner bounded by the side wall. The existence of the small vortex then rapidly propagates toward the inviscid region and induces a complicated pattern in the distribution of azimuthal vorticity, i.e. inertial oscillation. The inertial oscillation however does not deteriorate the classical Ekman-pumping model in the time scale larger than that of the oscillatory motion. Motions of single vortex and a pair of vortices are further investigated under a slip boundary-condition on the solid walls. For the case of single vortex, repeated change of the vorticity sign is observed together with typical propagation of inertial waves. For the case of a pair of vortices with a two-step profile in the initial azimuthal velocity, the vortices' movement toward the outer region is resisted by the crescent-shape vortices surrounding the pair. After touching the border between the core and outer regions, the pair vortices weaken very fast.

키워드

참고문헌

  1. Cederlof, U., 1988, 'Free-Surface Effects on Spin-up,' J. Fluid Mech., Vol. 187, pp. 395-407 https://doi.org/10.1017/S0022112088000485
  2. Dolzhanskii, F. V., Krymov, V. A. and Manin, D. Y., 1992, 'Self-Similar Spin-up and Spin-down in a Circular Cylinder of Small Ratio of Height to Diameter,' J. Fluid Mech., Vol. 234, pp. 473-486 https://doi.org/10.1017/S0022112092000879
  3. Greenspan, H. P., 1968, The Theory of Rotating Fluids, Cambridge University Press
  4. Greenspan, H. P. and Howard, L. N., 1963, 'On a Time Dependent Motion of a Rotating Fluid,' J. Fluid Mech., Vol. 17, pp. 385-404 https://doi.org/10.1017/S0022112063001415
  5. Hart, J. E., 1995, 'Nonlinear Ekman Suction and Ageostrophic Effects in Rapidly Rotating Flows,' Geophys. Astrophys. Fluid Dynamics, Vol. 79, pp. 201-222 https://doi.org/10.1080/03091929508228997
  6. Hart, J. E., 2000, 'A Note on Nonlinear Correction to the Ekman Layer Pumping Velocity,' Phys. Fluids, Vol. 12, No. 1, pp. 131-135 https://doi.org/10.1063/1.870300
  7. Hyun, J. M., Fowlis, W. W. and Warn-Varnas, A., 1982, 'Numerical Solutions for the Spin-up of a Strafied Fluid,' J. Fluid Mech., Vol. 117, pp. 71-90 https://doi.org/10.1017/S0022112082001529
  8. Mass, L. R. M., 1993, 'Nonlinear and Free-Surface Effects on the Spin-down of Barotropic Axisymmetric Vortices,' J. Fluid Mech., Vol. 246, pp. 117-141 https://doi.org/10.1017/S0022112093000060
  9. Suh, Y. K. and Choi, Y. H., 2002, 'Study on the Spin-up of Fluid in a Rectangular Container Using Ekman Pumping Models,' J. Fluid Mech., Vol. 458, pp. 103-132 https://doi.org/10.1017/S0022112002007826
  10. van de Konijnenberg, J. A. and van Heijst, G. J. F., 1995, 'Nonlinear Spin-up in a Circular Cylinder,' Phys. Fluids, Vol. 7, No. 12, pp. 2989-2999 https://doi.org/10.1063/1.868676
  11. Wedemeyer, E. H., 1964, 'The Unsteady Flow within a Spinning Cylinder,' J. Fluid Mech., Vol. 20, pp. 383-399 https://doi.org/10.1017/S002211206400129X
  12. Zavala Sanson, L. and van Heijst, G. J. F., 2000, 'Nonlinear Ekman Effects in Rotating Barotropic Flows,' J. Fluid Mech., Vol. 412, pp. 75-91 https://doi.org/10.1017/S0022112000008193