Surface gravity waves impacting still water

摘要

When plane surface gravity waves move into still deep water and there are no torques available to change the magnitude of the orbital angular momentum, then the angular momentum of the waves is conserved, meaning that the square of the amplitude divided by the frequency is constant at a fixed location as the waves pass by. Linear momentum is not conserved because the still environment exerts a reaction force on the advancing waves. From the balances of linear and orbital angular momentum come the conclusion that both the amplitude and the frequency must change as the waves travel into still water. Some ocean wave data agree qualitatively with the conservation of angular momentum. Quantitative comparisons between theory and measurement are left for the future.