The growth rate of finite depth wind-generated waves

Abstract

Fetch limited wind wave experiments traditionally investigate the growth of wave energy with distance from shore. [Donelan, M., Skafel, M., Graber, H., Liu, P., Schwab, D., Venkatesh, S., 1992. On the growth rate of wind-generated waves, Atmos.-Ocean 30, 457–478], have, however, shown that for deep water conditions it is advantageous to investigate the differential growth between points located along the fetch. Based on the extensive data set collected by [Young I.R., Verhagen, L.A., 1996a. The growth of fetch limited waves in water of finite depth, Part I: Total energy and peak frequency, Coastal Eng. 28, 47–78], this approach has been extended to finite depth conditions. The data clearly show that at short fetches the growth rate is comparable to deep water conditions. At longer fetches the finite depth influences increase and the growth rate decreases compared to deep water. Finally the waves approach a depth limited state where the growth rate becomes zero. Based on the observed differential growth between measurement stations, a relationship is developed which can be integrated to yield the development of the total energy with fetch. This relationship is significantly more flexible than previous finite depth growth relationships. Cases in which the water depth and/or wind speed vary with fetch can be investigated. In particular, it is shown that the development of the atmospheric boundary layer with fetch has a significant influence on the observed wave growth. By the inclusion of a realistic relationship for the boundary layer development it is shown that apparently anomalous features of the [Young, I.R., Verhagen, L.A., 1996a. The growth of fetch limited waves in water of finite depth, Part I: Total energy and peak frequency, Coastal Eng. 28, 47–78] data set can be explained.