Viscosity and Surface-Tension Effects on Wave Generation by a Translating Body
Purchase on Springer.com
$39.95 / €34.95 / £29.95*
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.
Various theoretical and experimental studies have been carried out to examine the generation of waves ahead of a translating body. Not all issues pertaining to this wave-motion problem are, however, fully resolved. In particular, mechanisms pertaining to generation of white-water instability and inception of vortices in the bow region are not fully understood. In this paper, the two-dimensional, unsteady, nonlinear, viscous-flow problem associated with a translating surface-piercing body is solved by means of finite-difference algorithm based on boundary-fitted coordinates. Effects of surface tension and surfactants are examined. Results of this work resolve certain classic issues pertaining to bow flows. A continuous generation of short and steepening bow waves is observed at low (draft) Froude number, a nonlinear phenomenon uncovered recently in the case of inviscid fluid also. This indicates that, steady-state nonlinear bow-flow solution may not exist, even at low speed. It is postulated that these short bow waves are responsible for the white-water instability commonly observed ahead of a full-scale ship. The amplitudes of these short bow waves are suppressed by surface tension, which is, possibly, the reason why white-water instability is not distinctly observed in laboratory-scale experiments. The presence of surfactants on the free surface is found to intensify the generation of free-surface vorticity, thus resulting in the formation of bow vortices. The accumulation of surface-active contaminants at the bow is hence responsible for the generation of bow vortices observed in laboratory experiments at low Froude number. At high Froude number, an impulsive starting motion of the body results in the generation of a jet-like splash at the bow and a gentle start an overturning bow wave, as previously observed in the case of inviscid bow flow.
- E. Baba, A new component of viscous resistance of ships. J. Soc. Naval Arch. Japan 125 (1969) 23–34.
- K. Suzuki, On the drag of two-dimensional bodies semi-submerged in a surface flow. J. Soc. Naval Arch. Japan 137 (1975) 22–35.
- H. Honji, Observation of a vortex in front of a half-submerged circular cylinder. J. Phys. Soc. Japan 40 (1976) 1475–1478.
- K. Takekuma and K. Eggers, Effect of bow shape on free-surface shear flow. Proc. Fifteenth Symp. on Naval Hydrodyn., Hamburg, Germany (1984) pp. 387–405.
- Y. Osawa, Aufmessung des Geschwindigkeitsfeldes an und unter der freien Wasseroberfläche in der Bugumströmung eines stumpfen Körpers. Bericht 476, Institut für Schiffbau, Universität der Hamburg, Germany. (in German) (1987) 125 pp.
- V. C. Patel, L. Landweber, and C. J. Tang, Free-surface boundary layer and the origin of bow vortices. Report 284, Iowa Institute of Hydraulic Research, The University of Iowa. (1984 22 pp.
- M. A. Grosenbaugh and R. W. Yeung, Flow structure near the bow of a two-dimensional body. J. Ship Res. 33 (1989) 269–283.
- H. J. Lugt, Local flow properties at a viscous free surface. Phys. Fluids 30 (1987) 3647–3652.
- K. Mori, Necklace vortex and bow wave around blunt bodies. Proc. Fifteenth Symp on Naval Hydrodyn., Hamburg, Germany, (1984) pp. 9–20.
- H. Maruo and M. Ikehata, Some discussions on the free-surface flow around the bow. Proc. Sixteenth Symp. on Naval Hydrodyn. Berkeley, California (1986) pp. 65–77.
- G. Dagan and M. P. Tulin, Two-dimensional free-surface gravity flow past blunt bodies. J. Fluid Mech. 51 (1972) 529–543.
- J.-M. Vanden-Broeck and E. O. Tuck, Computation of near-bow and stern flows using series expansion in the Froude number. Proc. Second Int. Conf. Num. Ship Hydrodyn. Berkeley, California, (1977) pp. 377–387.
- E. O. Tuck and J.-M. Vanden-Broeck, Splashless bow flows in two dimensions? Fifteenth Symp. on Naval Hydrodyn. Hamburg, Germany (1984) pp. 293–301.
- M. A. D. Madurasinghe, Splashless ship bows with stagnant attachment. J. Ship Res. 32 (1988) 194–202.
- E. O. Tuck, Ship-hydrodynamic free-surface problems without waves. J. Ship Res. 35 (1991) 277–287.
- M. A. Grosenbaugh and R. W. Yeung, Nonlinear free-surface flow at a two-dimensional bow. J. Fluid Mech. 209 (1989) 57–75.
- R. W. Yeung, Nonlinear bow and stern waves—inviscid and viscous solutions. In: T. Miloh (ed.) Mathematical Approaches in Hydrodynamics, Philadelphia: Society of Industrial and Applied Mathematics (1991) pp. 349–369.
- H. Miyata, Finite-difference simulation of breaking waves. J. Comp. Phys. 65 (1986) 179–214.
- P. Ananthakrishnan, Surface waves generated by a translating two-dimensional body: effects of viscosity. Ph.D. dissertation, Dept. Naval Arch. and Offshore Eng., University of California at Berkeley (1991) 155 pp.
- R. W. Yeung and P. Ananthakrishnan, Vortical flows with and without a surface-piercing body. Proc. Nineteenth Symp. on Naval Hydrodyn. Seoul, S. Korea, (1992) pp. 212–238.
- J. V. Wehausen and E. V. Laitone, Surface Waves. In: S. Flügge (ed.) Handbuch der Physik ix. Berlin: Springer-Verlag (1960) pp. 447–778.
- V. G. Levich, Physicochemical Hydrodynamics. Englewood Cliffs: Prentice-Hall Inc, (1962) 700 pp.
- H. W. Hoogstraten, H. C. J. Hoefsloot, and L. P. B. M. Janssen, Marangoni convection in V-shaped containers. J. Eng. Math. 26 (1992) 21–37.
- E. B. Dussan V. and S. H. Davis, On the motion of a fluid-fluid interface along a solid surface. J. Fluid Mech. 74 (1974) 71–95.
- É. É Marcovich, Effect of surface tension on the free outflow of a wetting fluid from a horizontal tube. Fluid Dyn. 23 (1988) 230–237.
- J. Koplik, J. R. Banavar, and J. F. Willemsen, Molecular dynamics of fluid flow at solid surfaces. Phys. Fluids, A5, (1989) 781–794.
- E. B. Dussan V., The moving contact line: the slip boundary condition. J. Fluid Mech. 77 (1976) 665–684.
- C. Huh and S. G. Mason, The steady movement of a liquid meniscus in a capillary tube. J. Phy. Soc. Japan 81 (1977) 401–419.
- R. W. Yeung and P. Ananthakrishnan, Oscillation of a floating body in a viscous fluid. J. Eng. Math. 26 (1992) 211–230.
- A. J. Chorin, Numerical solution of incompressible flow problems. Studies in Num. Anal. 2 (1968) 64–71.
- A. J. Chorin, Numerical solution of the Navier-Stokes equations. Math. Comp. 22 (1968) 745–762.
- J. Kim and P. Moin, Application of a fractional-step method to incompressible Navier-Stokes equations. J. Comp. Phys. 59 (1985) 308–323.
- R. W. Yeung and M. Vaidhyanathan, Non-linear interaction of water waves with submerged obstacles. Int. J. Num. Meth. Fluids 14 (1992) 1111–1130.
- C. Hirsch, Numerical Computation of Internal and External Flows: vol. 1 Fundamentals of Numerical Discretization. Wiley (1988) 515 pp.
- H. Lamb, Hydrodynamics. New York: Dover (1932) 738 pp.
- G. K. Batchelor, An Introduction to Fluid Mechanics. Cambridge: Cambridge University Press (1967) 615 pp.
- Y. J. Kim and J. H. Hwang, Two dimensional transient motions with large amplitude by time domain method. Proc. Sixteenth Symp. on Naval Hydrodyn. Berkeley, California (1986) pp. 415–426.
- M. Vaidhyanathan, Separated flows near a free surface. Ph.D. dissertation, Dept. Naval Arch. and Offshore Eng. University of California at Berkeley (1993) 197 pp.
- R. C. Y. Mui and D. G. Dommermuth, The vortical structure of parasitic capillary waves. J. Fluids Eng. 117 (1995) 355–361.
- J. H. Duncan, V. Philomin, M. Behres, and J. Kimmel, The formation of spilling breaking waves. Phys. Fluids 6 (1994) 2558–2560.
- Viscosity and Surface-Tension Effects on Wave Generation by a Translating Body
Journal of Engineering Mathematics
Volume 32, Issue 2-3 , pp 257-280
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- surface tension
- bow waves
- finite differences.