Wave Energy - Energy associated with wave motion.

For a single plane progressive wave:

• Potential energy PE (per unit surface area of wave)
  
  $$\begin{align}& \mbox{PE without wave } = \int\limits_{ - h}^0 {\rho gy dy} = - ... ...}\rho gA^2\mbox{ average over one period or one wavelength} \notag \end{align}$$
  
  
• Kinetic energy (per unit surface area of wave):
  
  $$\begin{align}& \mbox{KE}_{\mbox{wave}} = \int\limits_{ - h}^\eta {dy} \textstyl... ...1 \over 4}\rho gA^2\mbox{\ for\ }\mbox{\underline{any}\ } h \notag \end{align}$$
  
  
• Wave energy
  
  $$\mbox{E } = \mbox{ PE } + \mbox{ KE } = \textstyle{1 \over 2}... ...ft( {kx - \omega t} \right) + \textstyle{1 \over 2}} \right]$$
  
  

• Average wave energy E (over 1 period or 1 wavelength):
  
  $$\overline{ \mbox{E}} = \textstyle{1 \over 2}\rho gA^2[\textst... ...verline {KE} } } }}] = \textstyle{1 \over 2}\rho gA^2 = E_s,$$
  
  
  which is the Specific energy: total average wave energy per unit surface area.
• Linear waves: $\overline {\mbox{PE}} = \overline {\mbox{KE}} = \textstyle{\mbox{1} \over \mbox{2}}E_s$ (equipartition).
• Nonlinear waves: $\overline {\mbox{KE}} > \overline{\mbox{PE}}$. figure
  
  
  
  

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