A Study of the Growth of the Wave Spectrum with Fetch

Abstract

The development of the wave spectrum with fetch in a steady wind has been studied with a line of consecutive wave buoys in the Bothnian Sea in 1976 and 1979. The relationship that was found between dimensionless peak frequency ?m (=?mU10/g) and dimensionless fetch X? (=gX/U102) was close to previous observations. The dimensionless energy ?σ2 (=g2?2/U104) was about twice that observed in the JONSWAP experiment. In the saturation range when ??>4 the frequency spectrum was found to have the form S(?) = αuU10g??4 where αu=4.5 ? 10?3, independent of the dimensionless fetch X?. The deviation from the Phillips ?5 power law could not be explained by the influence of currents or finite depth. Near the peak, the spectra were satisfactorily described by the JONSWAP spectrum; above frequencies twice the peak frequency the difference becomes significant. A qualitative explanation is proposed for the dependence of the spectrum on the wind speed in the saturation range. The semi-theoretical method of Longuet-Higgins (1969) to estimate the Phillips saturation-range constant is applied to estimate αu. The result (4.4?6.4) ? 10?1 agrees with the experimental value. The growth of a component of the dimensionless spectrum with the fetch was found to be exponential within the accuracy of the data. The exponential growth parameter agreed with previous observations. A simple model is proposed to predict the growth rate without assuming nonlinear transfer of energy by wave-wave interactions; the results agree well with observations.