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

0.4
0.3
0.2
0.1
η
0
−0.1
−0.2
−0.3
0 10 20 30 40 50 60
ξ
Figure 4.12: Pulse propagating over a synthetic periodic slowly-varying topography.
Dotted line: numerical solution for the WNCM using RK4 for t=32.3977
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.
now the Gaussian function
η 0 (ξ)=0.5e −a(ξ−2π)2 /64
with a = 50, therefore its effective width is L = 4.8 and the ratio inhomogeneities/wavelength
is about 0.0873. For the mean velocity u 1 we choose the
corresponding initial condition to ensure one propagation direction for the LFM
withβ=0.0001,α=0, as done in Section 4.3. See Fig. 4.13 where the numerical
solution for t=35.3429 is depicted together with the solution for the flat bottom
and the initial condition. The other parameters areρ 1 = 1,ρ 2 = 2, N= 1024,
∆ξ=2l/N = 0.049087,∆t=∆ξ=0.049087. Note that the solution is very
similar to that of the flat bottom case. The wave is not modified by the rapidlyvarying
topography and no reflections are generated. Only the propagation speed
79