On the onset of wave-breaking and the time evolution of the maximum of horizontal velocity in rotational equatorial waves

We are concerned here with the time evolution of the maximal (modified) surface velocity for a rotational wave in the f -plane approximation. Using a parametric description of the wave surface, we show that the appearance of asymmetry in the wave profile is a necessary condition for the occurrence of a fluid velocity that exceeds the wave crest celerity, the latter occurence characterizing the inception of the wave-breaking phenomenon. This is achieved by means of an equation relating the time evolution of the maximum of the (modified) horizontal velocity to the horizontal component of the pressure gradient. Our analysis extends previous results concerning irrotational flows to the rotational situation of constant vorticity.