An empirical examination of the use of non-dimensional wave parameters

A number of datasets from wave tank and field measurements have been assembled from published data. For fixed wind speed, the peak frequency has F∝x−1/3 and the significant wave height has H∝x1/2. It has been confirmed following earlier work that wind speed should not be used to non-dimensionalise wave parameters, such as the frequency or the significant wave height because the wind-speed dependence is stronger than expected for the assembled data sets. New parameters have recently been proposed that use fetch, x, and the number of waves to create non-dimensional wave height and wave period, H~ and T~. The applicability of these quantities to the assembled datasets has also been investigated. A new non-dimensional relationship has been found empirically that relates the wave steepness, ak to the dimensionless fetch, ν, of the waves, (ak)2ν=130 (or H2k3x=260), which has the property of being wind-speed invariant. The estimated wind-speed dependence varied with fetch, although the ratio between the wind-speed exponents for H and F remained constant at −1/3 for all fetches.