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

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0.6<br />

0.4<br />

0.2<br />

η<br />

0<br />

−0.2<br />

40<br />

35<br />

30<br />

25<br />

20<br />

15<br />

10<br />

t<br />

5<br />

0<br />

0 5 10 15 20 25 30 35 40 45 50<br />

ξ<br />

Figure 4.3: Travelling wave on a periodic domainΠ[0, 16π]. The numerical<br />

solution was obtained using AM4 <strong>with</strong> N = 512,∆ξ = 2π/N = 0.098175,<br />

∆t=∆ξ=0.098175.<br />

0.6<br />

0.5<br />

0.4<br />

0.3<br />

η<br />

0.2<br />

0.1<br />

0<br />

−0.1<br />

0 10 20 30 40 50 60<br />

ξ<br />

Figure 4.4: Travelling wave. Dotted line: numerical solution <strong>for</strong> the nondispersive<br />

LFM using AM4 <strong>for</strong> t=39.2699 and N= 512,∆ξ=2l/N= 0.098175,∆t=<br />

∆ξ=0.098175, dashed line: initial condition, solid line: exact solution.<br />

68

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