Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-18T22:09:43.376Z Has data issue: false hasContentIssue false
  • English
  • Français

The laminar interactions of a pair of vortex tubes with a free surface

Published online by Cambridge University Press:  26 April 2006

Douglas G. Dommermuth
Douglas G. Dommermuth
Affiliation:
Naval Hydrodynamics Division, Science Applications International Corporation, 10260 Campus Point Dr., MS C4, San Diego, CA 92121, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

A fully nonlinear numerical method is developed to study the viscous interactions of a pair of vortex tubes rising toward a free surface. The numerical theory uses Helmholtz's decomposition to treat the irrotational and vortical components of the flow as separate nonlinearly coupled equations. The laminar interactions of a pair of vortex tubes with a clean free surface at intermediate Froude and Weber numbers and a low Reynolds number show two distinct phases. During the rise phase of the vortex pairs, instabilities lead to the formation of helical vorticity. The rotation of the helical vorticity around the primary vortex tubes causes an unsteady oscillation in the free-surface elevation. During the reconnection phase, the helical vortex sheets get narrower and attach themselves to the free surface. The normal connections of cross-axis vorticity with the free surface give whirls. The free-surface elevation is well correlated with the vortical pressure. The numerical results agree qualitatively with experimental measurements.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 246 , January 1993 , pp. 91 - 115
Copyright
© 1993 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Baer, F. & Tribbia, J. J. 1977 On complete filtering of gravity modes through nonlinear initialization. Mon. Wea. Rev. 12, 1536– 1539.Google Scholar
Crow, S. 1970 Stability theory for a pair of trailing vortices. AIAA J. 8, 2172– 2179.Google Scholar
Dommermuth, D. G. 1991 The viscous interactions of a pair of vortex tubes with a free surface. Science Applications International Corporation, Tech. Rep. SAIC-91/1326.Google Scholar
Dommermuth, D. G. 1992 The formation of U-shaped vortices on vortex tubes impinging on a wall with applications to free surface. Phys. Fluids A 4, 757– 769.Google Scholar
Dommermuth, D. G. & Yue, D. K. P. 1990 A numerical study of three-dimensional viscous interactions of vortices with a free surface. In Proc. 18th-Syrup. on Naval Hydrodyn., Ann Arbor pp. 727– 788. National Academy of Sciences, Washington, DC.
Hirsa, A. 1990 An experimental investigation of vortex pair interaction with a clean or contaminated free surface. Ph.D. thesis, University of Michigan, Dept. of Aero. Engng.
Hirsa, A., Tryggvasson, G., Abdollahi-Alibeik, J. & Willmarth, W. W. 1990 Measurement and computations of vortex pair interaction with a clean or contaminated free surface. In Proc. 18th Symp. on Naval Hydrodyn., Ann Arbor, pp. 521– 532. National Academy of Sciences, Washington, DC.
Hirt, C. W., Nichols, B. D. & Romero, N. C. 1975 SOLA-A numerical solution algorithm for transient fluid flows. Los Alamos Scientific Lab. Rep. LA–5852.
Hunt, J. C. R. 1984 Turbulence structure and turbulent diffusion near gas-liquid interfaces. In Gas Transfer at Water Interfaces (ed. W. Brutsaert & G. H. Jirka), pp. 67– 82. D. Reidel.
Leighton, R. I., Swean, T. F., Handler, R. A. & Swearingen, J. D. 1991 Interaction of vorticity with a free surface in turbulent open channel flow. In Proc. 29th Aerospace Sciences Meeting, Reno, NV, AIAA 91– 0236.
Lugt, H. J. & Ohring, S. 1992 The oblique ascent of a viscous vortex pair toward a free surface. J. Fluid Mech. 236, 461– 476.Google Scholar
Melander, M. V. & Hussain, F. 1988 Cut-and-connect of two antiparallel vortex tubes. In Studying Turbulence using Numerical Databases - II, Proc. 1988 Summer Program Rep. CTR-S88, pp. 257– 286. NASA Ames Research Center & Stanford University.
Ohring, S. & Lugt, H. J. 1991 Interaction of a viscous vortex pair with a free surface. J. Fluid Mech. 227, 47– 70.Google Scholar
Orszag, S. A. & Pao, Y. H. 1974 Numerical computation of turbulent shear flows. In Proc. Symp. on Turbulent Diffusion in Environmental Pollution (ed. F. N. Frenkiel & R. E. Mann), pp. 225– 236. Academic.
Rai, M. M. & Moin, P. 1991 Direct simulations of turbulent flow using finite-difference schemes. J. Comput. Phys. 96, 15– 53.Google Scholar
Rogers, M. M. & Moser, R. D. 1991 The three-dimensional evolution of a plane mixing layer. Part 1: The Kelvin-Helmholtz rollup. NASA Ames Research Center, NASA Tech. Memo 103856.
Saffman, P. G. 1990 A model of vortex reconnection. J. Fluid Mech. 212, 395– 402.Google Scholar
Sarpkaya, T. 1985 Surface signatures of trailing vortices and large scale instabilities. In Proc. Colloq. on Vortex Breakdown (Sonderforschungsbereich, 25), pp. 145– 187. University of Aachen.
Sarpkaya, T. 1986 Trailing-vortex wakes on the free surface. In Proc. 16th Symp. on Naval Hydrodyn. pp. 38– 50. National Academy of Sciences, Washington, DC.
Sarpkaya, T. & Henderson, D. O. 1984 Surface disturbances due to trailing vortices. Naval Postgraduate School Tech. Rep. NPS-69-84-004.Google Scholar
Sarpkaya, T. 1992 Three-dimensional interactions of vortices with a free surface. In Proc. 30th Aerospace Sciences Meeting & Exhibit, Reno, NV, AIAA 92-0059.
Sarpkaya, T. & Suthon, P. 1990 Scarred and striated signature of a vortex pair on the free surface. In Proc. 18th Symp. on Naval Hydrodyn., Ann Arbor, pp. 503– 520. National Academy of Sciences, Washington, DC.
Sarpkaya, T. & Suthon, P. 1991 Interaction of a vortex couple with a free surface. Exps. Fluids 11, 205– 217.Google Scholar
Spreiter, J. R. & Sacks, A. H. 1951 The rolling up of the trailing vortex sheet and its effect on the downwash behind wings. J. Aero. Sci. 18, 21– 32.Google Scholar
Zakharov, V. E. 1968 Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. Appl. Mech. Tech. Phys. 9, 190– 194. (English transl.)Google Scholar