Stokes' expansion of internal deep water waves to the fifth order

Stokes' expansion is applied to the internal waves of finite amplitude, which propagate on the interface between two layers of infinite thickness. Stream function, wave profile, phase velocity and mass transport velocity are given in the fifth order approximation. It is shown that (a) phase velocity increases with increase of wave steepness, (b) mass transport appears in the direction of the wave propagation in both layers as in the case of the surface waves, and (c) when the density difference is very small, the wave profile is flattened not only at the troughs but also at the crests.