  The Green Nagdhi equations are frequently used as a model of the wave-like
behaviour of the free surface of a fluid, or the interface between two
homogeneous fluids of differing densities. Here we show that their multilayer
extension arises naturally from a framework based on the Euler Poincare theory
under an ansatz of columnar motion. The framework also extends to the
travelling wave solutions of the equations. We present numerical solutions of
the travelling wave problem in a number of flow regimes. We find that the free
surface and multilayer waves can exhibit intriguing differences compared to the
results of single layer or rigid lid models.
