On the Relation between Wind Speed and Maximum or Mean Water Wave Height

Dimensional analysis shows that the relation between wind speed and maximum or mean water wave height takes the form H=cU02g, where H is the maximum or mean water wave height caused by wind of speed U0, g is the gravitational acceleration, and c is a dimensionless constant. This relation is important in predicting the maximum or mean water wave height caused by a tropical cyclone. Firstly, the mathematical and theoretical justification for determining c is presented. Verification is conducted using four tropical cyclones as case studies for determining c using significant wave heights rather than the overall maximum and mean. The observed values of c are analyzed statistically. On the days when the fixed buoy captured the highest wind speeds, the frequency distributions of the data for c are close to a bell shape with very small standard deviations in comparison with the mean values; thus, the mean values provide good predictions for c. In view of the fact that tropical cyclone waves are turbulent and the background waves caused by many other factors such as lunar tidal effect cannot be ignored, the obtained results for c are quite satisfactory. This method provides a direct approach in the prediction of the wave height or the wind speeds given the c value and can serve an interpolation methodology to increase the temporal resolution of the data.