Characterizing the internal wave wakes and synthetic aperture radar image features of underwater moving objects

In this study, a refined and improved theoretical model was proposed for calculating the synthetic aperture radar (SAR) images of internal wave wakes. This model was based on an equivalent source model of internal wave wakes and the velocity-bunching principle. Wake field, scattering field, and SAR image characteristics were systematically calculated for multiple scenarios. The model described the transfer and solution processes by inputting the background flow field temperature and salinity profiles to map the radar image intensity distribution. The physical mechanisms of the internal wave wake generation and its capture by SAR were comprehensively explained. The effects of various parameters on the internal wave wake SAR images were analyzed comprehensively. The SAR image features containing internal wave wakes were determined based on the graylevel co-occurrence matrix and image power spectrum, which revealed that the maximum surface current induced by the internal wave modes of the same amplitude was considerably larger than that induced by surfacewave mode. When traveling far from the water surface, the rate of change in the total scattering coefficient because of the Bragg effect was approximately 20 times that of the slope effect. In SAR images, the recognizability of wakes depends primarily on the maximum intensity rather than the average disturbance on the sea surface. Therefore, SAR images exhibit considerable differences during downwind radar observations, with the most prominent contrast differences occurring at the maximum spreading angle of wake scattering and 1500 m behind underwater objects. In the image power spectrum, the frequency range of the first modal internal waves was approximately 10-30 Hz, whereas the higher-order modal internal waves had frequencies lower than 10 Hz. Furthermore, the frequency range of the surface-wave mode was larger than that of internal-wave modes, approximately 50-60 Hz.