Talk:Linear Theory of Ocean Surface Waves

Equation for water energy incorrect

Hi, one thing that is stated in the article is that the energy of ocean waves in Joule per square meter is given by the equation

[math]\displaystyle{ E = p_w \ g \lt \zeta^2 \gt }[/math]

This is clearly wrong, considering that the ocean can contain standing waves (i.e. two waves with the same amplitude and wavelength moving in the opposite directions). There will be moments when the displacement for a standing wave is zero everywhere and the formula would evaluate to zero. However, the waves still contain energy because of the kinetic energy that now is because of the motion in the water. The formula does indeed calculate an energy, but it is only the potential energy of the waves and does not contain the kinetic energy. --Kri 22:11, 15 October 2010 (UTC)

Your point is not correct because for linear waves there is a change from potential to kinetic energy and there is a theory that states that these are equal over one period. The averaging is with respect to time. However, the point is very subtle because we have assumed some kind of stationarity. I have tried to include this in the explanation.