Hostname: page-component-77c89778f8-cnmwb Total loading time: 0 Render date: 2024-07-21T10:18:37.881Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonlinear bow flows with spray

Published online by Cambridge University Press:  26 April 2006

Frédéric Dias  and
Jean-Marc Vanden-Broeck
Frédéric Dias
Affiliation:
Institut Non-Linéaire de Nice, UMR CNRS 129, Université de Nice Sophia-Antipolis, Faculté des Sciences, 06108 Nice, cedex 2, France
Jean-Marc Vanden-Broeck
Affiliation:
Department of Mathematics and Center for the Mathematical Sciences, University of Wisconsin-Madison, Madison, WI 53705, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The steady flow past the bow of a two-dimensional ship in water of infinite depth is considered. The ship is assumed to be a semi-infinite flat-bottomed body terminated by a face inclined at an angle β with the horizontal. The spray is modelled by a layer of water rising along the bow and falling back as a jet. A series truncation method is used to solve the fully nonlinear problem numerically. It is shown that for a prescribed value of β, there is a one-parameter family of solutions. Values of the drag and of the jet thickness are presented for different values of β.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 255 , October 1993 , pp. 91 - 102
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

Birkhoff, G. & Carter, D. 1957 J. Math. Mech. 6, 769.
Dagan, G. & Tulin, M. P. 1972 Two-dimensional free-surface gravity flow past blunt bodies. J. Fluid Mech. 51, 529–543.Google Scholar
Dias, F. & Christodoulides, P. 1991 Ideal jets falling under gravity. Phys. Fluids A 3, 1711–1717.Google Scholar
Dias, F. & Elcrat, A. R. 1992 Ideal jet flow with a stagnation streamline. Eur. J. Mech. B 11, 233–247.Google Scholar
Dias, F., Keller, J. B. & Vanden-Broeck, J.-M. 1988 Flow over rectangular weirs. Phys. Fluids 31, 2071–2076.Google Scholar
Dias, F. & Tuck, E. O. 1991 Weir flows and waterfalls. J. Fluid Mech. 230, 525–539.Google Scholar
Dias, F. & Tuck, E. O. 1993 A steady breaking wave. Phys. Fluids A 5, 277–279.Google Scholar
Fernandez, G. 1981 Nonlinearity of the three-dimensional flow past a flat blunt ship. J. Fluid Mech. 108, 345–361.Google Scholar
Grosenbaugh, M. A. & Yeung, R. W. 1989 Nonlinear free-surface flow at a two-dimensional bow. J. Fluid Mech. 209, 57–75.Google Scholar
Oertel, H. 1975 The steady motion of a flat ship including an investigation of local flow near the bow. Ph.D, thesis, University of Adelaide.
Ting, L. & Keller, J. B. 1974 Planing of a flat plate at high Froude number. Phys. Fluids 17, 1080–1086.Google Scholar
Tuck, E. O. & Vanden-Broeck, J.-M. 1985 Splashless bow flows in two dimensions? In Proc 15th Symp. Naval Hydrodynamics, Hamburg, 1984, pp. 293–300, National Academy Press, Washington, DC.
Vanden-Broeck, J.-M. 1985 Nonlinear free-surface flows past two-dimensional bodies. In Advances in Nonlinear Waves, vol. 2 (ed. L. Debnath). Pitman.
Vanden-Broeck, J.-M. 1989 Bow flows in water of finite depth. Phys. Fluids A 1, 1328–1330.Google Scholar
Vanden-Broeck, J.-M. 1993 Two-dimensional jet aimed vertically upwards. J. Austral. Math. Soc. B 34, 393–400.Google Scholar
Vanden-Broeck, J.-M. & Keller, J. B. 1986 Pouring flows. Phys. Fluids 29, 3958–3961.Google Scholar
Vanden-Broeck, J.-M. & Keller, J. B. 1987 Weir flows. J. Fluid Mech. 176, 283–293.Google Scholar
Vanden-Broeck, J.-M., Schwartz, L. W. & Tuck, E. O. 1978 Divergent low-Froude-number series expansion in nonlinear free-surface flow problems. Proc. R. Soc. Lond. A 361, 207–224.Google Scholar
Vanden-Broeck, J.-M. & Tuck, E. O. 1977 Computation of near-bow or stern flows, using series expansion in the Froude number. In Proc. 2nd Intl Conf. Numerical Ship Hydrodynamics. Berkeley, CA, pp. 371–381. University Extension Publications.
Wu, T. Y. T. 1967 Intl Shipbuild. Prog. vol. 14, p. 88.
Yeung, R. W. 1991 Nonlinear bow and stern waves - inviscid and viscous solutions, In Mathematical Approaches in Hydrodynamics (ed. T. Miloh), pp. 349–369. SIAM.