EM 1110-2-1100 (Part II)
30 Apr 02
Figure II-5-2.
Variation of particle velocity with depth (Ippen 1966)
(6) Certain simplifications to Equations II-5-1 through II-5-4 result from the asymptotic values of the
hyperbolic functions. For example, Table II-5-2 (Ippen 1966) presents the hyperbolic functions contained
in the long- and short-wave representations, as well as their asymptotes. No simplification results for
intermediate waves.
Table II-5-2
Hyperbolic Function Asymptotes
Asymptotes
Function
Long waves
Short waves
ekh/2
sinh kh
kh
ekh/2
cosh kh
1
tanh kh
kh
1
(7) The resulting long wave simplification for celerities and wave lengths is shown below.
C ' gh
(II-5-5)
L ' T gh
(II-5-6)
(8) Therefore, long waves propagate as the square root of gh. This relationship will be shown to be
useful in analyzing and interpreting long-wave phase propagation data, because wave celerity is predictable
for a given depth.
II-5-4
Water Levels and Long Waves
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