  We propose a simple model for the evolution of an inviscid vortex sheet in a
potential flow in a channel with parallel walls. This model is obtained by
augmenting the Birkhoff-Rott equation with a potential field representing the
effect of the solid boundaries. Analysis of the stability of equilibria
corresponding to flat sheets demonstrates that in this new model the growth
rates of the unstable modes remain unchanged as compared to the case with no
confinement. Thus, in the presence of solid boundaries the equilibrium solution
of the Birkhoff-Rott equation retains its extreme form of instability with the
growth rates of the unstable modes increasing in proportion to their
wavenumbers. This linear stability analysis is complemented with numerical
computations performed for the nonlinear problem which show that confinement
tends to accelerate the growth of instabilities in the nonlinear regime.
