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

Linear Weakly nonlinear
Strongly nonlinear
Flat bottom LFM WNFM SNFM
Rough
bottom
LCM WNCM SNCM
Table 4.1: Abbreviations for the six different models.
In order to use the method of lines to solve numerically the systems of equations
(4.1, 4.2, 4.3) and their flat bottom versions, let us rewrite them in a more
convenient way,
η t = E(η, u 1 ),
⎧⎪⎨⎪⎩ V t = F(η, u 1 ),
(4.4)
where V is an auxiliary variable defined for each model in Table 4.2. The corresponding
vector field (E, F) is defined in Table 4.3. The mean-layer horizontal
upper velocity u 1 can be recovered fromηand V by inverting the relations in Table
4.2 in a way to be specified later on for each case. For the time being, let us
assume that u 1 =Ψ(η, V), given a certain operatorΨ.
According to the method of lines, we can discretize in space and solve a coupled
system of ODEs by a finite difference formula in t like, for example, a Runge-
Kutta integration scheme or a predictor-corrector solver with an Adams-Bashforth
predictor and an Adams-Moulton corrector.
First, an approximation scheme for theξ-derivatives involved in the right-hand
side of the systems above must be used for the discretization in space. A choice
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