How to find work done by wave?

How would you describe the work done on a boat in the ocean by the waves that hit the boat?





Do you know of any websites that can explain this problem better?





Any help is welcomed!

How to find work done by wave?
Divide the wave action into two parts: translational (up/down) and longitudinal (fore/aft). The work done by the translational action is simply W(T) = Fs = F A sin(wt) = INT(mg A sin(wt)dt) = Amg INT(sin(wt)dt) over t = 0 to T. F = mg; where m is the mass of the boat and g = 9.81 m/sec^2 on Earth's surface. w is the angular velocity of the waves in cycles per sec. T is the total time span over which the work is done and A is the amplitude of the wave. I've used INT to indicate integration over time dt.





INT(mg A sin(wt))dt represents the work done by continually raising and lowering the boat over the distance 2A. The force F = mg is simply the weight of the boat that is lifted and lowered by the translational wave action. The wave shape is assumed a sine function, which is idealized and not a real world shape. But a real world shape is not well defined.





The other work done by the wave would come from its longitudinal action as the wave advances along the surface of the water. We can assume this is continual all other things remaining the same. Therefore, W(L) = FL = kmg L is the longitudinal work as the wave moves the boat a distance L = vT. The T is the same timeframe as before; the v is the linear velocity of the boat as it moves across the surface. kmg represents the drag force on the boat as it moves across the surface of the water.





This is only a rough approximation. There are a lot of unknown and/or unrealistic variables here. For example, what's k? Well, that's a representation of how "sticky" the boat is in the water. k is higher when the boat is harder to move along the surface. It's something like a coefficient of friction only this time its a coefficient of drag.





And as mentioned earlier, the sine wave assumption is idealized. In reality, waves are typically skewed by the winds and the dynamics of the ocean bottom etc. But in any case, you can see from W(T) + W(L) = total work how one can get an order of magnitude answer on the work done on a boat by wave action.
Reply:Ocean Waves-Their Energy and Power, Ned Mayo, Physics Teacher 35, September 1997 p352