Effects of nonlinear waves on prediction of dynamic responses of floating offshore wind turbines

Pan Jia, Ishihara Takeshi
The University of Tokyo, Tokyo, Japan


Nonlinear waves will lead to increased motions of Floating Offshore Wind Turbines (FOWTs) in shallow water and in intermediate depth, so that effects of nonlinear waves should be taken into consideration in the design of FOWT. The use of nonlinear irregular waves generated by constrained wave theory is investigated for predicting dynamic responses of a floater based on Morison’s equation in this study. Firstly, a real scale model of a FOWT in Fukushima FORWARD project is developed, and comparison of response amplitude operators (RAOs), predicted from numerical model and estimated from experiment, respectively, is performed for validation. Secondly, RAOs of the numerical model in airy waves, and nonlinear regular waves generated by stream function are compared, and effects of nonlinearity in waves relating with water depth and wave height, have been investigated. Finally, constrained nonlinear irregular waves are employed for estimating motions of the FOWT, where motions are brought by stepper waves with higher velocities and accelerations. It is found that in water depth of 50m, the maximum displacements of the floater in nonlinear irregular waves increase by 6.4% and 18% in surge and pith directions, respectively, compare to the traditional linear wave model. Therefore, it is safer to use nonlinear irregular waves into the design of FOWT in water depth of 50m.

Keyword: Floating Offshore Wind Turbines, constrained wave, nonlinear irregular wave, dynamic response


A fully coupled nonlinear simulation tool based on Morison’s equation is developed to study dynamic responses of a real scale model, and numerical verification is completed and compared with measured RAOs from a water tank test. In order to investigate the effects of nonlinear waves, RAOs in linear and nonlinear regular waves, and also displacements of the FOWT in linear and nonlinear irregular waves, are compared in different water depths, respectively.

Stream function is employed to generate nonlinear regular waves, while irregular waves for simulating stochastic waves in natural are based on constrained wave theory. The constrained nonlinear irregular wave theory means embedding one period of nonlinear regular wave into linear irregular wave.


RAOs in airy waves with wave height of 3m and periods from 7.07s to 21.3s, predicted by numerical model and obtained from experiment show good agreement.

In regular waves, the floater enduring waves with small wave height is not obviously influenced by nonlinearity, and differences of RAOs in linear and nonlinear waves are less than 1% in the water depth of 120m. In water depth of 50m, RAOs in pitch motion according to nonlinear waves is almost 27% larger than that based on linear waves. Constrained nonlinear irregular waves are generated, and maximum displacements of the FOWT by nonlinear irregular wave decrease in water depth of 120m, but increase in water depth of 50m by about 6% and 18% in surge and pitch motions, respectively.


In this study, effects of nonlinear regular and irregular waves on prediction of FOWTs are investigated, and conclusions are as follows:

1) Nonlinearity of waves increasing motions of floater has relation with large wave height and shallow water depth. Nonlinear waves hardly increase heave motion, but will increase pitch motion.

2) Constrained nonlinear irregular waves are generated to predict dynamic responses of FOWTs, and it is suggested that for designing FOWT, it is proper to use linear irregular waves in water depth of 120m, but in water depth of 50m, nonlinearity of waves should be taken into consideration in predicting motions of FOWTs.


This research endeavors to investigate the effects of nonlinear waves on predicting dynamic responses of FOWTs, and provides a reference of using constrained nonlinear irregular waves to predict dynamic responses of FOWTs. Results show that nonlinear irregular waves will increase dynamic motions and should be considered even in intermediate water depth of 50m.