Wave Phase/Amplitude Effects on Force Coefficients

Estimating the force coefficients $C_d$ and $C_m$ for the two‐term Morison equation for a cylinder in waves depends on accurately measuring the amplitudes and phase shifts between the kinematics of the ambient wave and the wave‐induced force. A regression analysis is used to develop an algorithm that illustrates both the parametric dependency of the data on the Dean eccentricity parameter and the variability of these force coefficients if incorrect amplitudes or phase shifts are introduced into the analysis. The algorithm assumes that the two‐term Morison equation represents the “true” forces exactly and that linear wave theory represents the wave kinematics exactly. A least‐squares analysis of the time‐averaged, mean‐squared error between a “true” and a “computed” force is used. Dimensionless variations in the coefficients depend on two parameters: (1) A dimensionless force amplitude ratio W (proportional to the Dean eccentricity parahieter E); and (2) a dimensionless velocity amplitude ratio V, which is a function of the vertical elevation in the water column z. A new way to illustrate the importance of data conditioning is presented that combines the parametric dependency of the Dean eccentricity parameter with the wave phase/amplitude dependency. Good agreement is obtained with laboratory data of wave forces on a vertical, sand‐roughened cylinder wherein the force measurements were synthetically phase shifted with respect to the wave phase in small increments, up to $\pm 33.8$ degrees $(\pm 3\pi /16\mathrm{radians})\text{.}$