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Problem definition


 
Table 1: Standard parameters. Note that the equations have been non-dimensionalized, leading to ``odd'' values for some parameters.
width $-24.\leq x \leq 24.$
height $-8.0\leq y \leq 8.0$
dx,dy 0.5,0.5
depth 1
f $f_o + \beta y$
fo 0
$\beta$ 1
g 1
horizontal viscosity 0
horizontal diffusivity --
vertical viscosity --
vertical diffusivity --
bottom drag 0
dt 0.02
duration 40
equations shallow water
forcing none
initial conditions see below
boundary conditions no-slip walls
 

Initial conditions:

\begin{eqnarray*}u & = & \phi(x) ({{-9+6 y^2}\over{4}}) e^{-y^2/2} \\
v & = & ...
... \frac{\partial\phi}{\partial x} & = & -2B~\tanh(Bx) \; \phi ~~.
\end{eqnarray*}


The only free parameter in the problem is the amplitude of the soliton B which should be kept smaller than 0.6 in order not to affect the accuracy of the asymptotic expansion. The value used here is B=0.395.



Kate Hedstrom
2000-01-27