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

So the numerical velocity equals the theoretical one in the LFM above and the
Courant numberσ=1×∆t/∆ξ equals one. This choice is maintained throughout
the numerical experiments with the different systems.
The time evolution step forηand V using RK4 is
η n+1 =η n + ∆t ( )
K1+2K2+2K3+ K4
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V n+1 = V n + ∆t ( ) KK1+2KK2+2KK3+ KK4 ,
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whereη n and V n are N× 1 vectors with componentsη n j=η( j∆ξ, n∆t) and V n =
V( j∆ξ, n∆t) respectively. After each evolution step the N× 1 vector u 1 n with
components u 1
n
j = u 1 ( j∆ξ, n∆t) must be recovered fromη n and V n via u 1 n =
Ψ(η n , V n ).
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