On the basis of the wave energy balance equation, the response model of mean directions of locally wind-generated waves in slowly turning wind fields has been derived. The results show that in a homogeneous field, the time scale of the response is not only related to the rate of wave growth, but also to the directional energy distribution and the angle between the wind direction and the mean wave direction. Furthermore, the law of change in the mean wave direction has been derived. The numerical computations show that the response of wave directions to slowly turning wind directions can be treated as the superposition of the responses of wave directions to a series of sudden small-angle changes of wind directions and the turning rate of the mean wave direction depends on the turning rate and the total turning angles of the wind direction. The response of wave directions is in agreement with the response for a sudden change of wind directions if the change in wind directions is very fast. Based on the normalized rates of wave growth under local winds presented by Wen et al. (1989),a quantitative estimate of the time scale of the response shows that the relationships between the dimensionless time scale and both the dimensionleas total wave energy and the dimensionless peak frequency agree fairly well with the observations in comparison with other models.
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