a reduced model for internal waves interacting with submarine ...

0.5
0.4
0.3
0.2
η
0.1
0
−0.1
−0.2
−0.3
0 10 20 30 40 50 60
ξ
Figure 4.10: Pulse propagating over a synthetic periodic slowly-varying topography.
Dashed line: initial condition. Dotted line: numerical solution for the LCM
using RK4 for t=36.3247 and N= 1024, vertical bars mark spatial intervals of
size 2.5133 that fall together with the end of each period of the reflected signal.
defined on the domain [0, 16π] as
⎧
⎪⎨ 1+0.5 sin(5ξ), for 6π≤ξ≤12π,
M(ξ)=
⎪⎩ 1, elsewhere.
The initial perturbation of the interface is the Gaussian function
η 0 (ξ)=0.5e −a(ξ−π)2 /64
with a=200 and effective width L=2.4. The ratio inhomogeneities/wavelength
is about 0.5236. The physical parameters areρ 1 = 1,ρ 2 = 2,β=0.0001,α=
0.01. We employ N= 1024,∆ξ=2l/N= 0.0491,∆t=∆ξ=0.0491. In Fig. 4.11
the numerical solution for t=32.3977 is depicted together with the exact solution
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