Hostname: page-component-7b7567c8c-2n9c9 Total loading time: 0 Render date: 2026-11-15T16:24:25.467Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonlinear free-surface flow at a two-dimensional bow

Published online by Cambridge University Press:  26 April 2006

Mark A. Grosenbaugh and
Ronald W. Yeung
Mark A. Grosenbaugh
Affiliation:
Department of Naval Architecture and Offshore Engineering, University of California, Berkeley, CA 94720, USAPresent address: Department of Ocean Engineering, Woods Hole Oceanographic Institution, Woods Hole, MA 02543, USA.
Ronald W. Yeung
Affiliation:
Department of Naval Architecture and Offshore Engineering, University of California, Berkeley, CA 94720, USA
Get accessRights & Permissions [Opens in a new window]

Abstract

Unsteady free-surface flow at the bow of a steadily moving, two-dimensional body is solved using a modified Eulerian-Lagrangian technique. Lagrangian marker particles are distributed on both the free surface and the far-field boundary. The flow field corresponding to an inviscid, double-body solution is used for the initial condition. Solutions are obtained over a range of Froude numbers for bodies of three different shapes: a vertical step, a faired profile, and a bulbous bow. A transition Froude number exists at which the bow wave begins to overturn and break. The value of the transition Froude number depends on the bow shape. A stagnation point is observed to be present below the free surface during the initial stage of the wave formation. For flows occurring above the transition Froude number, the stagnation point remains trapped below the free surface as the wave overturns. Below the transition Froude number, the stagnation point rises to the surface as the crest of the transient bow wave moves upstream and away from the body.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 209 , December 1989, pp. 57 - 75
Copyright
© 1989 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.)

Article purchase

Temporarily unavailable

References

Baba, E. 1969 A new component of viscous resistance of ships. J. Soc. Naval Archit. Japan 125, 23–34.Google Scholar
Baker, G. B., Meiron, D. I. & Orszag, S. A. 1982 Generalized vortex method for free-surface flow problems. J. Fluid Mech. 123, 477–501.Google Scholar
Dagan, G. & Tulin, M. P. 1972 Two-dimensional free-surface gravity flow past blunt bodies. J. Fluid Mech. 51, 529–543.Google Scholar
Dommermuth, D. G. & Yue, D. K. 1986 Study of nonlinear axisymmetric body-wave interactions. Proc. 16th Symp. on Naval Hydrodynamics, Berkeley, California, pp. 116–126.Google Scholar
Finkelstein, A. B. 1957 The initial value problem for transient water waves. Commun. Pure Appl. Maths 10, 511–522.Google Scholar
Fry, D. J. & Kim, Y. H. 1984 Bow flow field of surface ships. Proc. 15th Symp. on Naval Hydrodynamics, Hamburg, W. Germany, pp. 319–345.Google Scholar
Grosenbaugh, M. A. 1987 Nonlinear flow at the bow of a ship: an experimental and theoretical investigation. Ph.D. dissertation, Dept. of Naval Archit. and Offshore Engng, U. of California, Berkeley.
Hildebrand, F. B. 1976 Calculus for Applications. Prentice-Hall.
Hong, Y. S. 1977 Numerical calculation of second-order wave resistance. J. Ship Res. 21, no. 2, pp. 94–106.Google Scholar
John, F. 1949 On the motion of floating bodies - I. Commun. Pure Appl. Maths 2, 13–57.Google Scholar
Lin, W. M., Newman, J. N. & Yue, D. K. 1984 Nonlinear forced motion of floating bodies. Proc. 15th Symp. on Naval Hydrodynamics, Hamburg, W. Germany, pp. 33–47.Google Scholar
Longuet-Higgins, M. S. & Cokelet, E. D. 1976 The deformation of steep surface waves on water. I. A numerical method of computation. Proc. R. Soc. Lond. A 350, 1–26.Google Scholar
Miyata, H., Suzuki, A. & Kajitani, H. 1981 Numerical explanation of nonlinear nondispersive waves around bow. Proc. 3rd Intl Conf. Numerical Ship Hydrodynamics, Paris, France, pp. 37–54.Google Scholar
Mori, K. 1984 Necklace vortex and bow wave around blunt bodies. Proc. 15th Symp. on Naval Hydrodynamics, Hamburg, W. Germany, pp. 9–20.Google Scholar
Ogilvie, T. F. 1968 Wave resistance: the low speed limit. University of Mich., College of Engng Rep. 002, Dept. of Nav. Archit. and Marine Engng.
Roberts, A. J. 1987 Transient free-surface flows generated by a moving vertical plate. Q. J. Mech. Appl. Maths 40, 129–158.Google Scholar
Tuck, E. O. & Vanden-Broeck, J. M. 1984 Splashless bow flows in two dimensions. Proc. 15th Symp. on Naval Hydrodynamics, Hamburg, W. Germany, pp. 293–300.Google Scholar
Tulin, M. P. 1982 An exact theory of gravity wave generation by moving bodies, its approximation and its implications. Proc. 14th Symp. on Naval Hydrodynamics, Ann Arbor, Mich., pp. 19–48.Google Scholar
Vanden-Broeck, J.-M., Schwartz, L. W. & Tuck, E. O. 1978 Divergent low-Froude-number series expansions of nonlinear free-surface flow problems. Proc. R. Soc. Lond. A 361, 207–224.Google Scholar
Vanden-Broeck, J.-M. & Tuck, E. O. 1977 Computations of near-bow and stern flows using series expansions in the Froude number. Proc. 2nd Intl Conf. on Numerical Ship Hydrodynamics, Berkeley, California, pp. 377–387.Google Scholar
Vinje, T. & Brevig, P. 1981 Nonlinear ship motions. Proc. 3rd Intl Conf. Numerical Ship Hydrodynamics, Paris, France, pp. 257–268.Google Scholar
Wehausen, J. V. 1969 Use of Lagrangian coordinates for ship wave resistance (first- and second-order thin-ship theory). J. Ship Res. 12, 12–22.Google Scholar
Yeung, R. W. 1975 A hybrid integral-equation method for time-harmonic free-surface flows. Proc. 1st Intl Conf. Numerical Ship Hydrodynamics, Gaithersburg, Maryland, pp. 581–608.Google Scholar
Yeung, R. W. 1982 Numerical methods in free-surface flows. Ann. Rev. Fluid Mech. 14, 395–442.Google Scholar