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Conservation Laws and Bounds on the Efficiency of Wind-Wave Growth

We examine two means by which wind can impart energy to waves: sheltering and deposition of material upwards from windward surface shear. The shear driven deposition is shown to be the more efficient process. Lengthening of waves to match the wind speed is shown to be very inefficient and consume a large fraction of the energy imparted by the wind. The surface shear provides a low energy sink that absorbs most of the momentum from the wind. These produce bounds on the efficiency of wave growth. The results here are computed in a model independent and perturbation free fashion by a careful consideration of conservation laws. By combining these effects we can place bounds on the rates waves can grow in a given fetch and the relative amount of shear flow versus the, relatively small, Stokes drift that must arise.