Simplified Models for Equatorial Waves with Vertical Structure

Explicitly solvable models have recently been developed for the interaction of waves with the Equatorial Undercurrent in an f-plane approximation. We observe that these analyses can be dramatically simplified by a Boussinesq-type approximation, and that the additional errors introduced are for the most part negligible. The approximate formulas are easier to interpret and show that critical layers occur if and only if the disturbances of the thermocline and free surface are in phase