Accurate Prediction of Nonlinear Wave Forces: Part I (Fixed Cylinder)

A new equation structure is proposed as an alternative to the Morison equation for the prediction of wave forces. Initially, nonlinear parametric continuous time differential equation models were estimated from wave force data for a variety of flow situations by adopting a new approach which avoids direct differentiation of the input-output data. The method consists of two stages. The first stage involves estimation of a discrete time model (polynomial NARMAX) from sampled input-output data and computation of the linear and higher order frequency response functions. The second stage involves identifying continuous time models by curve fitting to the complex frequency response data using a weighted complex orthogonal estimator. The orthogonal property of the estimator helps in identifying the correct model structure or which terms to include in the model and the weighting property provides an additional degree of freedom to control the properties of the estimator with respect to the selection of the frequency range and number of data points. Morison equation models were initially fitted to the data but were shown to simply curve fit to the data without capturing the underlying dynamics. The frequency domain characteristics of the Morison equation models were also analysed and shown to be structurally deficient in representing certain dynamic features of the force. However, it is shown that the new equation structure is capable of emulating all the relevant features of the wave force mechanics. The paper is organised in two parts. Part I is concerned with the modelling of wave forces on a fixed cylinder and Part II deals with a responding cylinder. Extensive simulations on a variety of experimental data show that models based on the new structure perform remarkably well compared with the Morison equation. For each flow situation, in addition to the drag and inertia coefficients of the Morison equation, there are two non-dimensional coefficients defining history effects, which show some consistency between widely different flow situations.