The effect of capillarity and resonant interactions on the second-order Doppler spectrum of radar sea echo

Previous work on the second-order contributions of radar sea echo by Hasselmann and Barrick is generalized to include the effect of capillarity (i.e., surface tension) in the hydrodynamic part of the transfer coefficient, the lossy dielectric properties of the sea, and the angle of incidence and the polarization of the electromagnetic radiation. The present theoretical results apply to the backscattering of electromagnetic radiation from water waves that are gravity or gravity capillary waves. The introduction of surface tension in the analysis allows for second-order resonant interactions of the gravity capillary wave components. To include resonant interactions of gravity waves, the analysis must be extended to higher order. In general, resonant interactions produce higher-order contributions in the Doppler spectrum at the frequency of the first-order Bragg line that represent the nonstationary and non-Gaussian properties of the water surface. Furthermore, because of the different dispersion relation of gravity capillary water waves, the secondary lines of the second-order Doppler spectrum now are shifted toward the Bragg frequency and 2½ times the Bragg frequency. Numerical results are presented from our generalized theory for various radar and sea (water surface) parameters.