Action of a Variable Stress at the Surface of Water Waves

A boundary-layer argument shows that, paradoxically, a variable tangential stress which is greatest at the wave crests and least in the wave troughs produces a thickening of the boundary layer on the rear slopes of the waves and a thinning on the forward slopes. In deep water, a variable tangential stress ⊥ is precisely equivalent to a normal stress i⊥ in quadrature with the tangential stress. The corresponding rate of growth of the waves is calculated.