Wave radiation stress ($S_{xx}=\mathcal{E}(2c_g/c_p-1/2)$)

The excess depth-integrated, time-averaged momentum flux of a surface gravity wave is its radiation stress. In deep water $c_g/c_p=1/2$, so $S_{xx}=\mathcal{E}/2={\rho }_{w}g{a}^2/4$. The force per transverse width on a reflecting object is the incident plus reflected minus transmitted radiation stress. Reflection increases force because the reflected wave carries momentum in the opposite direction.