Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-18T18:52:19.691Z Has data issue: false hasContentIssue false
  • English
  • Français

Interaction of a viscous vortex pair with a free surface

Published online by Cambridge University Press:  26 April 2006

Samuel Ohring  and
Hans J. Lugt
Samuel Ohring
Affiliation:
David Taylor Research Center, Bethesda, MD 20084-5000, USA
Hans J. Lugt
Affiliation:
David Taylor Research Center, Bethesda, MD 20084-5000, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

A vortex pair in a viscous, incompressible fluid rises vertically toward a deformable free surface. The mathematical, description of this flow situation is a time-dependent nonlinear free-surface problem that has been solved numerically for a two-dimensional laminar flow with the aid of the Navier-Stokes equations by using boundary-fitted coordinates. For a number of selected flow parameters, results are presented on the decay of the primary vortices and their paths, the generation of surface vorticity and secondary vortices, the development and final stage of the disturbed free surface, and the influence of surface tension. High and low Froude numbers represent the two extremes of free-surface yielding and stiffness, respectively. For an intermediate Froude number, a special rebounding due to the presence of secondary vortices has been observed: the path of the primary vortex centre portrays a complete loop.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 227 , June 1991 , pp. 47 - 70
Copyright
© 1991 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

Barker, S. J. & Crow, S. C. 1977 The motion of two-dimensional vortex pairs in a ground effect. J. Fluid Mech. 82, 659–671.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics, pp. 366. Cambridge University Press.
Bernal, L. P., Hirsa, A., Kwon, J. T. & Willmarth, W. W. 1989 On the interaction of vortex rings and pairs with a free surface for varying amounts of surface active agent.. Phys. Fluids A 1, 2001–2004.Google Scholar
Couder, Y. & Basdevant, C. 1986 Experimental and numerical study of vortex couples in two-dimensional flows. J. Fluid Mech. 173, 225–251.Google Scholar
Dagan, A. 1989 Pseudo-spectral and asymptotic sensitivity investigation of counter-rotating vortices. Computers & Fluids 17, 509–525.Google Scholar
Fish, S. 1990 Ambient free surface wave modification by a submerged vortex pair. David Taylor Research Center Rep. DTRC-90/004.
Floryan, J. M. & Rasmussen, H. 1989 Numerical methods for viscous flows with moving boundaries. Appl. Mech. Rev. 42, 323–341.Google Scholar
Harvey, J. K. & Perry, F. J. 1971 Flowfield produced by trailing vortices in the vicinity of the ground. AIAA J. 9, 1659–1660.Google Scholar
Kochin, N. E., Kibel, I. A. & Roze, N. V. 1964 Theoretical Hydromechanics. Wiley.
Lamb, H. 1932 Hydrodynamics. Dover.
Lugt, H. J. 1983 Vortex Flow in Nature and Technology. Wiley-Interscience.
Lugt, H. J. & Haussling, H. J. 1974 Laminar flow past an abruptly accelerated elliptic cylinder at 45 incidence. J. Fluid Mech. 65, 711–734.Google Scholar
Marcus, D. L. 1988 The interaction between a pair of counter-rotating vortices and a free boundary. Ph.D. thesis, University of California at Berkeley.
Nguyen Duc, J. & Sommeria, J. 1988 Experimental characterization of steady two-dimensional vortex couples. J. Fluid Mech. 192, 175–192.Google Scholar
Novikov, Y. A. 1981 Generation of surface waves by discrete vortices. Izv. Akad. Nauk. SSSR Atmos. Ocean. Phys. 92, 497–503.Google Scholar
Ohring, S. & Lugt, H. J. 1989 Two counter-rotating vortices approaching a free surface in a viscous fluid. David Taylor Research Center Rep. DTRC-89/013 (referred to herein as I).Google Scholar
Orlandi, P. 1990 Vortex dipole rebound from a wall.. Phys. Fluids A 2, 1429–1436.Google Scholar
Peace, A. J. & Riley, N. 1983 A viscous vortex pair in ground effect. J. Fluid Mech. 129, 409–426.Google Scholar
Saffman, P. G. 1979 The approach of a vortex pair to a plane surface in inviscid fluid. J. Fluid Mech. 92, 497–503.Google Scholar
Salvesen, N. & Kerczek, C. von 1976 Comparison of numerical and perturbation solutions of two-dimensional nonlinear water-wave problems. J. Ship Res. 20, 160–170.Google Scholar
Sarpkaya, T. 1986 Trailing-vortex wakes on the free surface In Proc. 16th Symp. on Naval Hydrodynamics, Berkeley, pp. 38–50.
Sarpkaya, T., Elnitsky, J. & Leeker, R. E. 1988 Wake of a vortex pair on the free surface In Proc. 17th Symp. on Naval Hydrodynamics, pp. 47–54. Washington: Naval Studies Board.
Sarpkaya, T. & Henderson, D. O. 1984 Surface disturbances due to trailing vortices. Naval Postgraduate School, Monterey, California, Rep. NPS-69–84–004.Google Scholar
Sarpkaya, T. & Suthon, P. B. 1990 Scarred and striated signature of a vortex pair on the free surface. Proc. 18th Symp. on Naval Hydrodynamics. National Academy Press (to appear).
Telste, J. G. 1989 Potential flow about two counter-rotating vortices approaching a free surface. J. Fluid Mech. 201, 259–278.Google Scholar
Thompson, J. F. & Shanks, S. P. 1977 Numerical solution of the Navier-Stokes equations for 2d surface hydrofoils. Mississippi State University Rep. MSSU-EIRS-ASE-77–4.Google Scholar
Tryggvason, G. 1988 Deformation of a free surface as a result of vortical flows. Phys. Fluids 31, 955–957.Google Scholar
Walker, J. D. A., Smith, C. R., Cerra, A. W. & Doligalski, T. L. 1987 The impact of a vortex ring on a wall. J. Fluid Mech. 181, 99–140.Google Scholar
Wehausen, J. V. & Laitone, E. V. 1960 Surface waves In Handbuch der Physik, Vol. ix, pp. 446–778 Springer.
Willmarth, W. W., Tryggvason, G., Hirsa, A. & Yu, D. 1989 Vortex pair generation and interaction with a free surface.. Phys. Fluids A 1, 170–172.Google Scholar
Yeung, R. W. 1982 Numerical methods in free-surface flows. Ann. Rev. Fluid Mech. 14, 395–442.Google Scholar