scholarly journals The Linear Shallow Water Theory: A Mathematical Justification

1993 ◽  
Vol 24 (4) ◽  
pp. 892-910
Author(s):  
James A. Donaldson ◽  
Daniel A. Williams
Keyword(s):  
Shallow Water ◽  
Shallow Water Theory ◽  
Mathematical Justification ◽  
Linear Shallow Water Theory

Trapping of water waves above a round sill

1983 ◽  
Vol 132 ◽  
pp. 105-118 ◽  
Author(s):  
Yuriko Renardy
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Small Amplitude ◽  
Three Dimensional ◽  
Substantial Effect ◽  
Dimensional Problem ◽  
Shallow Water Theory ◽  
Resonant Frequencies ◽  
Wave Trapping ◽  
Linear Shallow Water Theory

The three-dimensional problem of wave trapping above a submerged round sill was first analysed by Longuet-Higgins on the basis of a linear shallow-water theory. The large responses predicted by the theory were, however, not well borne out by the experiments of Barnard, Pritchard & Provis, and this has motivated a more detailed study of the problem. A full linear theory for both inviscid and weakly viscous fluid, without any shallow-water assumptions, is presented here. It reveals important limitations on the use of shallow-water theory and the reasons for them. In particular, while the qualitative features of wave trapping are similar to those of shallow-water theory, the nearly resonant frequencies differ significantly, and, since the resonances are narrow, the observed amplitudes at a given frequency differ greatly. The geometry is strongly indicative of long waves, and the dispersion relation appears quite consistent with that, but the part of the motion at wavenumbers that are not small has, despite the small amplitude, a substantial effect on the response to excitation.

scholarly journals A Shallow-Water Theory for the Sun's Active Longitudes

2005 ◽  
Vol 635 (2) ◽  
pp. L193-L196 ◽  
Author(s):  
Mausumi Dikpati ◽  
Peter A. Gilman
Keyword(s):  
Shallow Water ◽  
Shallow Water Theory

Water waves of finite amplitude on a sloping beach

1958 ◽  
Vol 4 (1) ◽  
pp. 97-109 ◽  
Author(s):  
G. F. Carrier ◽  
H. P. Greenspan
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Finite Amplitude ◽  
Explicit Solutions ◽  
Shallow Water Theory ◽  
Non Linear ◽  
Wave Forms ◽  
Time Histories ◽  
Sloping Beach

In this paper, we investigate the behaviour of a wave as it climbs a sloping beach. Explicit solutions of the equations of the non-linear inviscid shallow-water theory are obtained for several physically interesting wave-forms. In particular it is shown that waves can climb a sloping beach without breaking. Formulae for the motions of the instantaneous shoreline as well as the time histories of specific wave-forms are presented.

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