Time-Varying Kelvin Wake Model and Microwave Velocity Observation

In the synthetic aperture radar (SAR) imaging of ship-induced wakes, it is difficult to obtain the Doppler velocity of a Kelvin wake due to the lack of time-varying wake models and suitable radar equipment. The conventional Kelvin wake investigation based on the static Kelvin wake model failed to reflect time-varying characteristics, which are significant in the application of the Kelvin wake model. Therefore, a time-varying Kelvin wake model with consideration of geometric time-varying characteristics and the hydrodynamic equation is proposed in this paper, which reflects the wake's time-varying change lacking in the conventional Kelvin wake investigation. The Doppler velocity measurement, measured by a specially designed radar, can be exploited to verify the time-varying model by the comparison of velocity fields. Ground-based multi-input multi-output (MIMO) millimeter wave radar imaging through the simultaneous switching of transceiver channels was used to obtain the Doppler velocity for the first time. Finally, promising results have been achieved, which are in good agreement with our proposed model in consideration of the experimental scene. The proposed time-varying model and radar equipment provide velocity measurements for the Kelvin wake observation, which contains huge application potential.