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

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η
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ξ
Figure 4.13: Pulse propagating over a synthetic periodic rapid-varying topography.
Dotted line: numerical solution for the LCM using RK4 with N= 1024 for
t=35.3429, dashed line: initial condition, solid line: flat bottom exact solution.
should be slightly decreased as predicted in Rosales and Papanicolaou [26]. But
this change is only noticeable over very large distances.
Example 4.7. Let us add the nonlinearity ingredient (α=0.005) to the previous
example. We consider again the periodic rapidly-varying topography defined in
Example 4.6, together with the same Gaussian shape of effective width L=4.8.
Therefore the ratio inhomogeneities/wavelength is kept at 0.0873. In Fig. 4.14 the
numerical solution for t=35.3429 is depicted together with the exact solution for
the LFM and the initial condition. The other parameters areβ=0.0001,ρ 1 = 1,
ρ 2
= 2, N = 1024,∆ξ = 2l/N = 0.049087,∆t = ∆ξ = 0.049087. Again,
the solution is very similar to that of the LFM. The wave is not modified by the
rapidly-varying topography and no reflections are generated.
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