Geoscience Reference
In-Depth Information
where
T
min
=
2
H
1
/
H
2
=
k
2
D
is the phase difference between the boundaries
of the obstacle,
k
2
is the wave number over the obstacle. In the case of transforma-
tion of a long wave on a step the transmission and reflection coefficients were only
determined by the depth ratio and did not depend on any parameters of the wave. In
the case of wave transformation above the rectangular obstacle the transmission co-
efficient turns out to depend on the wave frequency. The phase difference
1 +
H
1
/
H
2
,
β
β
i
s rela
ted
D
/
√
g
H
2
.
The dependence (5.9) is presented in Fig. 5.6. Its important peculiarity consists
in the existence of a minimum transmission coefficient
T
min
, the value of which is
only determined by the depth ratio
H
1
/
H
2
, but does not depend on the width of
the obstacle or the wavelength. The transmission coefficient is quite weakly related
to the quantity
H
1
/
H
2
. The less the width of the obstacle, i.e. the smaller the ratio
D
/
β
ω
to the wave number and, consequently, to the wave frequency,
=
, the weaker this relationship happens to be.
If the width of the obstacle is small as compared to the tsunami wavelength
(
D
/
λ
<
0
.
2), then an increase in the dimensions (width and height) of the obstacle
unambiguously results in a decrease of the transmission coefficient. As soon as
λ
(a)
1,000
(b)
Fig. 5.6 Amplitude transmission coefficient for a long wave on a rectangular obstacle versus
the depth ratio (a) and versus the phase difference between the edges of the obstacle (b)
