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1
A L η 0 = v max τ
C 1 ,
C 1 =
η
(
α
)d
α
0 . 7 ,
(3.80)
0
and the energy as the potential energy of the initial elevation
+
2 L C 1 C 2
2
ρ
g
2
2 ( x ,
g v 2 max τ
ξ
τ
ρ
,
W L
)d x =
(3.81)
1
2 (
C 2 =
η
α
)d
α
0 . 65 .
0
Applying formulae (3.80) and (3.81), we obtain relationships permitting to calcu-
late the relative contributions of the non-linear and the linear mechanisms to the am-
plitude and energy of tsunami waves:
= η
g H 2 A (
0 c 2
τ , L )
C 1 τ 2
A N
A L
,
(3.82)
= η 0 c 2
g H 2 2 2 W (
τ , L )
C 1 C 2 τ 4 L
W N
W L
,
(3.83)
where
η 0 is the amplitude of the vertical ocean bottom deformation. From formulae
(3.82) and (3.83) the quantities A N / A L and W N / W L are seen to be determined to
a large extent by the dimensionless combination
η 0 c 2 g 1 H 2 .
Figures 3.28 and 3.29 present the dependences of quantities A N / A L and W N / W L
upon the piston-like displacement duration. The calculation is performed for three
different relationships between the source size and the ocean depth. The curves be-
ing non-monotonous for
τ > 1 is due to the modal structure of elastic oscillations
of the water column (the minimum normal frequency corresponds to
τ = 4). When
τ < 1, the dependences investigated behave approximately like the power func-
tions
τ ∗− 2 . An increase in the horizontal size of the source leads to an
insignificant enhancement of the role of the non-linear mechanism.
τ ∗− 1
and
Fig. 3.28 Ratio between am-
plitudes of tsunami waves
formed by the non-linear ( A N )
and the linear ( A L ) mecha-
nisms versus the displacement
duration. Curves 1-3 are
drawn for L / H = 20, 10 and 5
 
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