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H 1 / 4 . The relationship obtained is termed
the Green's law or the 'one quarter' rule. This law, for instance, explains why
the tsunami amplitude increases as it approaches the coast. Owing to a decrease in
depth and, consequently, in propagation velocity, the wave packet shrinks in space,
but boosts its amplitude.
Another 'classical' effect of the interaction of long waves with the relief con-
sists in their transformation in the region of abrupt changes in the ocean depth.
In those cases, when the ocean depth changes over distances much shorter than
the wavelength, the distribution of depths is expediently represented in the form
of a step (Fig. 5.4a). Such a situation is dealt with in many sectors of classical
wave theory (optics, acoustics), and it is known as wave refraction and reflection
at the boundary of two media. We shall only consider normal incidence of waves
(the one-dimensional problem). We shall determine the amplitude coefficients for
reflection, R , and transmission, T . To this end, following the classical topic [Lamb
(1932)], we take advantage of the continuity conditions for the free-surface displace-
ment,
amplitude will increase by the law
ξ 0
, and the water release ( Hu ) at the depth jump point. The resulting reflection
and transmission coefficients R and T , respectively, are
R = H 1 / H 2
ξ
1
H 1 / H 2 + 1 ,
(5.7)
2 H 1 / H 2
H 1 / H 2 + 1
T =
.
(5.8)
(a)
(b)
Fig. 5.4 Ocean bottom geometry in problem of long-wave transformation on irregularities of
the bottom relief: step (a); rectangular obstacle (b)
 
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