It is suggested that a possible mechanism for the formation of the thermocline step structure is a sporadic overturning by rotors associated with finite-amplitude internal waves. A criterion for the required critical amplitude of an internal wave is derived, and good agreement is found with numerical experiments illustrating the mechanism. A scale analysis for the ocean shows that downward-propagating waves with a vertical wavelength of 10–20 meters would be most favored to ‘break’ by the convective instability mechanism. Examination of velocity spectra measured in the North Atlantic shows that more than enough energy exists in the internal wave frequency range for this type of instability to occur.