Numerical study of the effect of wind above irregular waves on the wave-induced load statistics

A wind-forcing model is implemented into a fully nonlinear potential flow solver for water wave propagation. The model is suited for simulations of a large number of waves and for generation of fully nonlinear wave kinematics. The direct effect of wind is achieved through Jeffreys sheltering mechanism, which models the form drag on steep waves by a varying surface pressure.

We detail the implementation and examine the effect of the model parameters, which consist of a sheltering coefficient and a threshold of the spatial slope of the wave for activation of the wind model. Next, we present the calibration and application of the model for reproduction of a test campaign for the effect of wind over waves on the wave-induced loads on a vertical surface piercing cylinder.

The experimental study has been reported in (Kristoffersen et al., 2021) and consisted of four storm sea states, each run with a duration equivalent to 30 h (full scale), with and without a simultaneous scaled wind field above the waves in the flume. After calibration, the numerical model is able to reproduce many of the findings from the experimental study.

When wind forcing is added and the significant wave height is kept fixed, the crest statistics are slightly suppressed in the tail by the presence of wind. The wind, however, leads to a pronounced increase in the wave steepness and to a larger number of breaking waves. Despite the increased number of breaking waves, the depth integrated inline force was only found to increase slightly for the most extreme events at small exceedance probabilities.

In contrast, the local force in the vicinity of the free surface was found to increase significantly, at short term exceedance probabilities up to 10−2, which is consistent with the measured pressures. For the numerical force profile along the vertical direction of the pile, we found that the altitude of maximum wave force is lowered with the introduction of wind.

All of these findings are consistent with the experimental observations. Further for the numerical wave-induced local force at short term exceedance probability of 10−4, an increase by a factor of 1.8 was found from the introduction of wind. Although the effect on the global inline force was less strong, this local effect is important for design.

The present numerical approach offers a direct way to establish such design loads.