A two-dimensional fractal model of the sea surface and sea spectrum evaluation

In this paper we propose a two-dimensional fractal model of the sea surface defined by means of the solution of the sea hydrodynamic differential equations and based on the band-limited Weierstrass-Mandelbrot (WM) fractal functions. Fractal geometry is used to take into account of the multiscale nature of the sea and to give a better description of the fine structure of the sea surface. We determine a closed form expression of the directional sea wave spectrum, we derive the omnidirectional wave spectrum, the angular distribution function and we compare the results with the typical models proposed in the literature. The main contribution of the work is the definition of a new model of the directional sea wave spectrum. This is of interest to SAR imaging studies