Modulation of short waves by long waves

The amplitude, wavelength, and frequency of short waves in the presence of waves of a longer scale vary in a manner that is related in phase to the long-wave profile. The purpose of this study is to observe and quantify the change in the variance of short-wave slope that occurs as a result of the change in short-wave position along a coincident long wave, during the active generation of the short-wave field by wind. To this end, measurements of wave-slope time series are made in a laboratory environment where the long-scale waves are generated mechanically and the short scale are generated primarily by air flow. The frequency variation of the short waves, as measured along the long-wave profile, is described by considering the waves to be linearly advected by the longer waves. The peak-to-peak variation along the long-wave profile of the short-wave slope variance for a given frequency band is commonly found to be 10% of its mean value. The magnitude of the excursions become smaller as short-wave frequency increases, and larger as wind speed increases. The maximum value of the short-wave slope variance generally leads the long-wave profile curve by 45 ° to 180 °.