Theory and Application of the Cubic Approximation of Random Drag Forces

The cubic approximation of random wave drag forces is studied in this paper to simplify the applications of nonlinear wave drag forces in spectral analysis. Nonlinear spectral analysis and numerical simulations are used in the study. The drag force expression is approximated by a cubic function whose coefficients are determined by equating the corresponding autocorrelation function with that associated with the original bilinear form of Morison's equation. Numerical verification indicates that the cubic approximation approaches the original expression satisfactory for engineering applications. Application examples indicate that the spectral densities of wave forces per unit pile length and total wave forces on vertical cylinders, as well as the root mean squares (RMSs) of wave forces, can be easily obtained using cubic approximations.