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

0.6
0.5
0.4
0.3
η
0.2
0.1
0
−0.1
0 10 20 30 40 50 60
ξ
Figure 4.6: Fission of the wave. Dotted line: numerical solution for the nondispersive
LFM using RK4 for t=50.2655 and N= 512,∆ξ=2l/N= 0.098175,
∆t=∆ξ=0.098175, dashed line: initial condition, solid line: exact solution.
ξ ∈ Π[0, 2l],
⎧
η t − u 1ξ = 0,
⎪⎨
u 1t −η ξ = √ β ρ 2
ρ 1
T [0,2l]
[
u1
]
ξt ,
η(ξ, 0)=η 0 (ξ),
⎪⎩ u 1 (ξ, 0)=u 10 (ξ).
(4.9)
First, let us perform the change of variablesξ=πξ/l, t=πt/l to the standard
periodic domainξ ∈ Π[0, 2π]. The time variable is modified in order to maintain
the wave velocity as one for the hyperbolic regime (β=0). In these coordinates
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