Note on the directional properties of meter-scale gravity waves

Abstract

The directional distribution of the energy of young waves is bimodal for frequencies above twice the peak frequency; i.e., their directional distribution exhibits two peaks in different directions and a minimum between. Here we analyze in detail a typical case measured with a peak frequency fp = 0.18 Hz and a wind speed of 10.7 m s−1 using a stereo-video system. This technique allows for the separation of free waves from the spectrum of the sea-surface elevation. The latter indeed tend to reduce the contrast between the two peaks and the background. The directional distribution for a given wavenumber is nearly symmetric, with the angle distance between the two peaks growing with frequency, reaching 150° at 35 times the peak wavenumber kp and increasing up to 45 kp. When considering only free waves, the lobe ratio, the ratio of oblique peak energy density over energy in the wind direction, increases linearly with the non-dimensional wavenumber k∕kp, up to a value of 6 at k∕kp ≃ 22, and possibly more for shorter components. These observations extend to shorter components' previous measurements, and have important consequences for wave properties sensitive to the directional distribution, such as surface slopes, Stokes drift or microseism sources.