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.
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December 1977
Research Papers
Water Waves in a Nonhomogeneous Incompressible Fluid
A. E. Green,
A. E. Green
Mathematical Institute, University of Oxford, Oxford, England
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P. M. Naghdi
P. M. Naghdi
Department of Mechanical Engineering, University of California, Berkeley, Calif.
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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. Dec 1977, 44(4): 523-528 (6 pages)
Published Online: December 1, 1977
Article history
Received:
March 1, 1977
Online:
July 12, 2010
Citation
Green, A. E., and Naghdi, P. M. (December 1, 1977). "Water Waves in a Nonhomogeneous Incompressible Fluid." ASME. J. Appl. Mech. December 1977; 44(4): 523–528. https://doi.org/10.1115/1.3424129
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