from the shorter waves generated by the Miles mechanism to those that have slightly lower frequencies than at the peak wave magnitudes. Ultimately, the wave speed becomes higher than that of the cross wind (Pierson & Moskowitz). (Note: Most of the wave speeds calculated from the wavelength divided by the period are proportional to the square root of the length. Thus, except for the shortest wavelength, the waves follow the deep water theory described in the next section. The 8.5 m long wave must be either in shallow water or between deep and shallow.) Development Long swell waves develop from and take energy from the shorter wind waves. The process was first described by Klaus Hasselmann (2021 Nobel prize winner) after investigating the non-linear effects that are most pronounced near the peaks of the highest waves. He showed that, through these non-linearities, two wave trains in deep water can interact to generate two new sets of waves, one generally of longer and the other of shorter wavelength. The equation that Hasselmann developed to described this process is now used in the sea state models (for example Wavewatch III) used by all the major weather and climate forecasting centres. This is because both the wind sea and the swell have significant effects on the transfer of heat from the ocean to atmosphere. This affects both large scale climate systems, like the El Niño, and smaller scale systems, such as the atmospheric depressions that develop near the edges of the Gulf Stream. A good physical description of the Hasselmann process is hard to explain, but the non-linear effects are largest near the peaks of the highest waves and the short waves, which often break near the same position, can be used as an analogy. This is because each small breaking wave gives a small push to the longer wave on which it is breaking. From the point of view of the long wave, it is receiving a small push on each of its crests just like a swing being given a small push at just the right time. There is also no comparable effect in the wave's trough - a term which would tend to reduce the size of the long wave. From the point of view of a physicist this effect is of extra interest because it shows how, what starts as a random wave field, can generate the order of