An Euler Poincaré framework for the multilayer Green Nagdhi equations

The Green Nagdhi equations are frequently used as a model of the wave-like behaviour of the free surface of a uid, or the interface between two homogeneous uids of di ering densities. Here we show that their multilayer extension arises naturally from a framework based on the Euler Poincaré 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 ow regimes. We nd that the free surface and multilayer waves can exhibit intriguing di erences compared to the results of single layer or rigid lid models. ar X iv :0 80 7. 03 58 v1 [ ph ys ic s. fl udy n] 2 J ul 2 00 8 An Euler Poincaré framework for the multilayer Green Nagdhi equations 2