MS Thesis R. Hager - Hawaii National Marine Renewable Energy ...

gKE 22A k2022de kz dzH 2 gKE (65)16The average potential and kinetic energy are equal, following the principle of equipartition ofenergy. Thus, the total energy per unit surface area is:H 2 gTE (66)83.6 Power FluxPower flux is the time derivative of the energy flux. The power flux of the incident wave is:PwdEdtddt 1 V 2 1 gzd V t 2 1 gzd V 2222 gzUndS(67)S where, U n is the normal velocity of the vertical surface of the water column (Newman, 1977).If the column moves at a constant velocity then the energy entering and leaving the columnis equal, and thus the last term of Eq. (67) is null (Newman, 1977). The vertical position istime independent, thus the latter term in the final volume integrand of Eq. (67) is also null.where,Pw 1 1 V 2 d I I d(68)tt 2tt 2 1 I I 2I I 2 I I II I I I I I2t 2tt t tI2The last term vanishes due to Laplace’s equation, I 0 . Thus, Eq. (68) is: I Pw d(69)I tApplying Gauss’s divergence theorem to Eq. (69) results in:51