基于改进二维分形模型的海面模拟方法

Simulation Method of Sea Surface Based on Improved Two-Dimensional Fractal Model

针对粗糙海面的非线性和自相似性特点,在带限Weierstrass分形函数的基础上,建立了改进二维分形模型,描述了表面谱与空间波数之间的正幂率和负幂率关系,针对P-M海谱给出了分形参数的定量描述,实现了对粗糙海面的模拟。仿真结果表明,模型能够生成不同风速下的海面模型,反映了小尺度波浪的细微结构和大尺度波浪的浪涌特性,不同尺度的组成波之间具有较好的自相似性,可以较好地模拟粗糙海面背景。

According to the nonlinear and self-similarity characteristics of rough surface, based on the band-limited Weierstrass fractal function, the improved two-dimensional fractal model was set up, and the relationship between the positive power and negative power of surface spectrum and space wave number was described. According to that P-M sea spectrum the quantitative description of fraetal parameters was given, the simulation of rough sea surface was realized. Simulation results indicated that the model can generate the surface of the model under different wind speed, and the fine structure of small scale waves and the surge characteristics of large scale waves were showed, and the composition of the different scale had a good self-similarity between wave, which could better simulate the rough sea surface background.