| Contents |
| We shall discuss aspects of the theory of incompressible stratified Euler fluids in a $2D$ channel.
In particular, our focus will be on conserved quantities, both for continuous and sharp (two-layer)
stratification. We shall analytically show the existence of classes of initial data for which total horizontal momentum is not conserved,
and briefly compare these results with long-wave asymptotic models.
Hamiltonian pictures (both in the full $2D$ case and in the $1D$ long wave limit(s))
will then be discussed in order to illustrate these results. |
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