A Temporal SSA-Based Mesh-Free Analytical Solution of Dynamic CWM Sea Surfaces

In this paper, a temporal mesh-free analytical solution by using the first-order small-slope approximation (SSA-1) method (TSSA-MF) is firstly proposed to analyze the scattering characteristics of the dynamic nonlinear sea surface. The choppy wave model (CWM) is employed to perform the 2-D nonlinear waves. The algorithm starts with incorporating the expression of the nonlinear sea surface fluctuation into the scattering amplitude of the traditional SSA. Then, the TSSA-MF is established to characterize the dynamic nonlinear sea surface by averaging the random time-dependent non-Gaussian surface. The normalized radar scattering cross section (NRCS) can be predicted quickly and accurately by the proposed TSSA-MF. And, comparing with the scattering amplitude of traditional SSA in the statistical sense, the proposed TSSA-MF includes the time variable. Therefore, the time auto-correlation function (TACF) and the Doppler spectrum of nonlinear and linear sea surfaces are analyzed. The simulation results show that the double-peak phenomenon of the CWM is not obvious in the crosswind compared to linear sea surfaces. It should be noted that, mesh generation and averaging a large number of samples can be avoided for the proposed TSSA-MF, so that the calculation time is substantially reduced with encouraging accuracy.