An asymptotic method based upon ray theory is developed for the study of surface waves on a viscous fluid of variable depth. An asymptotic solution involving a phase function and an amplitude function is constructed. Uniform asymptotic expansions at and away from caustics and shorelines are obtained. To illustrate the method, an example concerning the spreading of a bore over a sloping beach is considered.
REFERENCES
1.
2.
M. C.
Shen
, R. E.
Meyer
, and J. B.
Keller
, Phys. Fluids
11
, 2289
(1968
).3.
4.
5.
D.
Hector
, J.
Cohen
, and N.
Bleistein
, Stud. Appl. Math.
51
, 121
(1972
).6.
7.
8.
J. K.
Cohen
and R. M.
Lewis
, J. Inst. Math. Its Appl.
3
, 266
(1967
).9.
10.
11.
12.
13.
R. M. Lewis and J. B. Keller, New York University Report No. EM‐194 (1964).
14.
A. Erdelyi, Asymptotic Expansions (Dover, New York, 1956).
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© 1976 American Institute of Physics.
1976
American Institute of Physics
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