Laboratory observations of the modulation of centimetric waves

The modulation of short wind-generated waves by long waves or swell is a critical aspect of the mechanics of water waves vis-a-vis the remote detection of long waves using real or synthetic aperture radars, of wind speed and direction using scatterometers, inter alia. Consequently, much effort has been devoted to the measurement of and parameterization of the modulation in terms of the complex modulation transfer function. Generally, the modulation is detected by radar and related to a particular wave number on the assumption that the dominant radar interaction with the surface is first order Bragg scattering. The use of radar in this application has the significant advantage that radars are wavelength selective and so the Doppler shifting of the frequencies does not compound the measurement as it does when waves are observed as time series of elevation at a point and interpreted as frequency spectra. On the other hand, a single radar can be used only in a narrow wavenumber range dependent on the sine of the angle of incidence between about 25 degrees and 70 degrees. Donelan et al. (1996) developed a method of analysis using wavelets that allows one to examine the wavenumber structure of the surface from arrays of wave staffs. Here we employ a similar approach using simultaneous point measurements of elevation and slopes in a wind-wave tank. This paper introduces the method and applies it to an exploration of the modulation of centimetric wind-generated waves by the passage of paddle generated swell