Wave-by-wave prediction in weakly nonlinear and narrowly spread seas using fixed-point surface-elevation time histories

The development of accurate, real-time predictive models for weakly nonlinear multidirectional wave fields would enable a significant reduction in the cost of wave energy, when combined with control strategies which use the prediction to increase power absorbed. An existing phase-resolved model for predicting weakly nonlinear long-crested wave fields is extended to sea-states with small spreading. When numerically advancing long-crested waves for prediction in spread seas, optimum prediction with the model is obtained when the waves are propagated at an offset angle (shown to be equal to the standard deviation of the component headings in the underlying sea) to the true mean wave direction. The model further exploits concurrent surface-elevation records from multiple adjacent fixed-point locations to obtain a prediction which is shown to be significantly more accurate than using individual input records. Furthermore, the prediction is unaffected by changes in mean wave direction up to a range of 30 degrees, for a prediction using measurements from three points. The model is tested on both synthetic linear and second-order nonlinear wave fields where the directional and bulk wave statistics are assumed to be known. In the nonlinear case, bound harmonics are first estimated using narrow-band approximations and removed. The resulting linear records are then padded at both ends with half a NewWave-type extension to eliminate the step discontinuity in the records before advancing them in both space and time. The bound harmonics are re-calculated and re-inserted into the prediction signal as a final step, if required. The overall computational cost is very small.