A parametric model linking the free-surface elevations with the fluid acceleration field under an irregular wave is developed. In order to estimate the parameters of the model, system identification procedures are applied based on data recorded in a wave tank. The free-surface time series are taken as input data and the output data are components of the particle acceleration vector. The particle acceleration time series were obtained by taking the numerical derivative of the measured orbital velocity time series. A simple algorithm of numerical diffrentiation is proposed. This algorithm gives very accurate values of the particle acceleration and is quite straightforward as the derivative is computed directly in time domain. A linear time-invariant model with the static nonlinearities incorporated at the input side is assumed. This paper demonstrates the results of modelling the horizontal component of the particle acceleration in comparison with the time series calculated from wave kinematics data taken in a wave flume during an earlier experiment using Laser Doppler Velocimetry. The modelled particle acceleration time series compare well with those calculated from the observed velocity time series. This proves the effectiveness of the applied approach. The system identification techniques allow for preparing the model which constructs the wave kinematics (both velocities and accelerations) using the measured time series of only the free-surface elevation. This feature of the proposed approach may be very useful in maritime engineering and oceanography.

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