One-dimensional fractalmodel of the sea surface

Abstract

A one-dimensional fractal model of the sea surface based on the band-limited Weierstrass–Mandelbrot fractal functions is proposed. The model accounts for the geometry and time dependence of the sea-surface shape and is in agreement with the solution of the sea hydrodynamic differential equations obtained in a linear regime. A statistical analysis of the electromagnetic field scattered from the sea fractal surface is performed to validate the model from the scattering phenomenon point of view. The results are in good agreement with experimental results presented in the literature.