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(a)
(b)
(c)
(d)
−80
−40
0
40
80
Fig. 2.21 Profiles of waves formed by running (thin line) and piston-like (thick line) displacements
at time moment t = 50 for L = 10; (a-d) correspond to v = 0 . 2 , 0 . 5 , 1 and 10; τ = 50, 20, 10 and 1
Fig. 2.22 Energy of
waves excited by piston-
like displacement versus
displacement duration for
various linear dimensions of
the active region. Curves 1-4
correspond to L = 10, 5, 2
and 1
The quantity W equals twice the potential energy of the wave. The calculation
of energy was performed for the time moment t = 50( H / g ) 1 / 2 , when energy redis-
tribution between the potential and kinetic energies had been totally completed and
the value of W no longer depended on time.
The results of calculations are presented in Fig. 2.22 as dependences of the en-
ergy of a wave excited by a piston-like displacement of the basin bottom, W 1 ,
upon the displacement duration
τ
. The energy values are normalized to the quan-
2
0 / 2, representing the specific potential energy of a rectangular
elevation of height
tity W 0 =
ρ
gb
η
η 0 and length b of the free surface of a liquid. As the duration of
a piston-like displacement increases the wave energy undergoes a monotonous de-
crease. Moreover, the energy depends essentially on the size of the generation area.
Curves 1-4 in Fig. 2.22 correspond to values of parameter b / H = 10, 5, 2 and 1.
Note that these results, naturally, do not contradict the data presented in Fig. 2.14.
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