This paper explores a new horizontal dispersion mechanism due to recurrent changes of the depth of the wind drift. In the shallow mode, the wind drift moves the upper part of the surface layer relative to the lower part, giving an increased horizontal area being covered by a tracer present in the layer. When returning to the deep mode, the accompanying vertical mixing increases the volume of the cloud. The rate of increase of the tracer cloud area is proportional to the wind drift velocity in the shallow mode and the area itself, and therefore proportional to the elapsed time squared t2. The t2-law is demonstrated by a numerical experiment and supported by published experimental results. The quadratic dependence is explained by the larger and larger exposure to wind driven advection and not by larger and larger scales of motions taking part in the process known from eddy dispersion.