SYMMETRY OF ROTATIONAL EQUATORIAL INTERNAL WAVES

The aim of this paper is to study the symmetry of the equatorial internal waves, which propagate above the thermocline and beneath the upper flat boundary. For general vorticity distributions, we prove that a steady periodic internal wave with a monotone profile between crests and troughs must be symmetric. Moreover, for the flows with constant vorticity, we show that the symmetric periodic internal waves must be traveling waves.