Directional Response of Ocean Waves to Changing Wind Direction

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  • 1 KNMI, De Bilt, the Netherlands
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Abstract

When analysing wave measurements in turning winds, one usually assumes that the rate of change of mean wave direction is determined by the angle between θw, the wind direction, and θo, the mean wave direction; however, it is well known that this is an approximation. The correct quantity is the angle between θF/∂t, the mean direction of the rate of change of the spectrum, and θo. The approximation is made because it is not easy to measure the correct angle θF/∂t. In this note a new approximation for calculating this angle and the directional relaxation time scale τ is derived. To test the approximation, a third-generation wave model is used as a numerical laboratory. The full two-dimensional spectra are known in the model. Therefore, time scales can be evaluated exactly and the accuracy of the approximation can be checked explicitly.

The new scheme is then used to reanalyze observations made by Holthuijsen et al. The results show an improved correlation of the dimensionless directional time scale τ* with the dimensionless wave age. This correlation has been compared with the one found in the model and is in good agreement.

Abstract

When analysing wave measurements in turning winds, one usually assumes that the rate of change of mean wave direction is determined by the angle between θw, the wind direction, and θo, the mean wave direction; however, it is well known that this is an approximation. The correct quantity is the angle between θF/∂t, the mean direction of the rate of change of the spectrum, and θo. The approximation is made because it is not easy to measure the correct angle θF/∂t. In this note a new approximation for calculating this angle and the directional relaxation time scale τ is derived. To test the approximation, a third-generation wave model is used as a numerical laboratory. The full two-dimensional spectra are known in the model. Therefore, time scales can be evaluated exactly and the accuracy of the approximation can be checked explicitly.

The new scheme is then used to reanalyze observations made by Holthuijsen et al. The results show an improved correlation of the dimensionless directional time scale τ* with the dimensionless wave age. This correlation has been compared with the one found in the model and is in good agreement.

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