DIRECTIONAL RESPONSE OF OCEAN WAVES TO CHANGING WIND DIRECTION

When analyzing wave measurements in turning winds, one usually assumes that the rate of change of mean wave direction is determined by the a ngle between theta(w), the wind direction, and theta(o), the mean wave direction; however, it is well known that this is an approximation. T he correct quantity is the angle between theta(partial derivative F/pa rtial derivative t), the mean direction of the rate of change of the s pectrum, and theta(o). The approximation is made because it is not eas y to measure the correct angle theta(partial derivative F/partial deri vative t). In this note a new approximation for calculating this angle and the directional relaxation time scale tau is derived. To test the approximation, a third-generation wave model is used as a numerical l aboratory. The full two-dimensional spectra are known in the model. Th erefore, time scales can be evaluated exactly and the accuracy of the approximation can be checked explicitly. The new scheme is then used t o reanalyze observations made by Holthuijsen et al. The results show a n improved correlation of the dimensionless directional time scale tau with the dimensionless wave age. This correlation has been compared with the one found in the model and is in good agreement.