Wind Wave Growth at Short Fetch

Abstract

Wave wire data from the large wind wave tank of the Ocean Engineering Laboratory at the University of California, Santa Barbara, are analyzed, and comparisons are made with published data collected in four other wave tanks. The behavior of wind waves at various fetches (7?80 m) is very similar to the behavior observed in the other tanks. When the nondimensional frequency F* or nondimensional significant wave height H* is plotted against nondimensional fetch x*, a large scatter in the data points is found. Multivariate regression to the dimensional parameters shows that significant wave height Hsig is a function of U2x and frequency F is a function of U1.25x, where U is the wind speed and x is the horizontal distance, with the result that in general for wind waves at a particular fetch in a wave tank, approximately speaking, the wave frequency is inversely proportional to the square root of the wind speed and the wavelength is proportional to the wind speed. Similarly, the wave height is proportional to U1.5 and the orbital velocity is proportional to U. Comparison with field data indicates a transition from this fetch law to the conventional one [the Joint North Sea Wave Project (JONSWAP)] for longer fetch. Despite differences in the fetch relationship for the wave tank and the field data, the wave height and wave period satisfy Toba?s 3/2 power law. This law imposes a strong constraint on the evolution of wind wave energy and frequency; consequently, the energy and momentum retention rate are not independent. Both retention rates grow with wind speed and fetch at the short fetches present in the wave tank. The observed retention rates are completely different from those typically observed in the field, but the same constraint (Toba?s 3/2 law) holds true.