Intrinsic frequency spectra of short gravity-capillary waves obtained from temporal measurements of wave height on a lake

Intrinsic frequency spectra of water waves in the range of 6-17 Hz were obtained as a function of both wind speed and wind stress from point measurements of wave height. In a lake with a limited fetch, there are two types of surface motions causing Doppler shift in the frequencies of short waves: orbital velocity of long waves and surface wind drift. The former was estimated from long-wave amplitude by using a linear wave theory. The error in this estimate is of the order of the long-wave slope, and for this work it is typically 10 percent. The latter was approximated by the friction velocity. The friction velocity could be either taken as 3 percent of the mean wind speed measured at a height of 10 m or obtained from direct measurements of the wind stress. The surface drift velocities obtained by these two approaches were found to be in close agreement. Doppler frequency shift can be corrected in either the frequency or the equivalent spatial domain. The two techniques were found to produce comparable results. Experimental results showed that the spectral energy of short waves rapidly increased in response to increasing winds and jumped up by an order of magnitude when wave breaking occurred.