Water Waves in a Nonhomogeneous Incompressible Fluid

[+] Author and Article Information
A. E. Green

Mathematical Institute, University of Oxford, Oxford, England

P. M. Naghdi

Department of Mechanical Engineering, University of California, Berkeley, Calif.

J. Appl. Mech 44(4), 523-528 (Dec 01, 1977) (6 pages) doi:10.1115/1.3424129 History: Received March 01, 1977; Online July 12, 2010


After a brief discussion of some undesirable features of a number of different partial differential equations often employed in the existing literature on water waves, a relatively simple restricted theory is constructed by a direct approach which is particularly suited for applications to problems of fluid sheets. The rest of the paper is concerned with a derivation of a system of nonlinear differential equations (which may include the effects of gravity and surface tension) governing the two-dimensional motion of incompressible in-viscid fluids for propagation of fairly long waves in a nonhomogeneous stream of water of variable initial depth, as well as some new results pertaining to hydraulic jumps. The latter includes an additional class of possible solutions not noted previously.

Copyright © 1977 by ASME
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