Abstract
Two-dimensional free surface flows generated by a moving distribution of pressure are considered. The bottom is assumed to be covered by a thin layer of mud. The mud is modelled as a viscous fluid. The problem is solved numerically by a boundary integral equation method. It is shown that the layer of mud produces a damping of the waves in the far field. Profiles of the free surface and of the surface of the mud are presented.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
H. Lamb,Hydrodynamics, 6th edn. Cambridge: University Press (1932).
L.W. Schwartz, Non-linear solution for an applied over-pressure on a moving stream,J. Eng. Math., 15 (1981) 147–156.
J.-M. Vanden-Broeck and F. Dias, Solitary waves in water of infinite depth and related free surface flows,J. Fluid Mech., 240 (1992) 549–557.
G. Gade, Effects of nonrigid, impermeable bottom on plane surface waves in shallow water,J. Marine Research, 16 (1958) 61–81.
H. MacPherson, The attenuation of water waves over a nonrigid bed,J. Fluid Mech., 97 (1980) 721–742.
G. Zilman, T. Miloh and L. Kagan, Hydrodynamics of a body moving over a mud layer,20th Symposium on Naval Hydrodynamics, Santa Barbara, U.S.A. (1994).
G. Zilman and T. Miloh, Hydrodynamics of a body moving over a mud layer, Part 1: Wave resistance,J. Ship. Res., 39 (1995) 194–201.
A.C. King, E.O. Tuck and J.-M. Vanden-Broeck, Air-blown waves on thin viscous sheets,Phys. Fluids A, 5 (1993) 973–978.
J.-M. Vanden-Broeck and E.O. Tuck, Computation of near-bow or stern flows, using series expansion in the Froude number, Proceedings,2nd International Conference on Numerical Ship Hydrodynamics, Berkeley, Calif., (1977).
L.K. Forbes and L.W. Schwartz, Free-surface flow over a semicircular obstruction,J. Fluid Mech., 114 (1982) 299–314.
E. Kit and L. Shemer, On dissipation coefficients in a rectangular wave tank,Acta Mechanics, 77 (1980) 171–180.
A. Cameron,Principles of Lubrication, Longmans, London (1966).
W.E. Olmstead and S. Raynor, Depression of an infinite liquid surface by an incompressible gas jet,J. Fluid Mech., 19 (1964) 561–576.
E.O. Tuck, On air flow over free surfaces of stationary water,J. Austral. Math. Soc., Ser. B, 19 (1975) 66–80.
J.-M. Vanden-Broeck, Deformation of a liquid surface by an impinging gas jet,SIAM J. Appl. Math., 41 (1981) 306–309.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Vanden-Broeck, JM., Miloh, T. The influence of a layer of mud on the train of waves generated by a moving pressure distribution. J Eng Math 30, 387–400 (1996). https://doi.org/10.1007/BF00042758
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00042758