分数型布朗运动粒子追踪模型在沿海污染扩散中的应用

传统的Fickian扩散模型已经不再适用于模拟大规模水域表面污染物的扩散。研究人员已观测到了沿海水域地带的non-Fickian扩散现象。研究发现，沿海表层水域的Hurst指数H并不局限于0-1的范围。因此，在分数布朗运动的基础上，引进了加速分数型布朗运动来模拟non-Fickian扩散，从而使表面Hurst指数可以大于1。本文采用一种新型的加速分数型布朗运动的粒子追踪技术，并由此来模拟沿海水域中的non-Fickian传播。对用粒子云来模拟沿海水域中污染物的non-Fickian扩散方法成功地作了研究。比较实际观测的数据和英国HR Wallingford传统的用Fickian扩散模型计算出来的结果，其模拟的结果更胜一筹。

The application of Fractional Brownian Motion Particle Tracking Method on Coastal Contaminant Dispersion

Traditional Fickian diffusion model cannot be used in modelling pollutant diffusion in large scale water body. The non-Fickian diffusion dispersion in coastal water and open sea has been discovered by some researches. Research shows that, for coastal surface waters, the Hurst exponent H is not restricted to the range of 0-1. A new particle tracking technique is introduced in this paper where non-Fickian diffusion is generated by employing an accelerated fractional Brownian motion (AfBm) based on fractional Brownian motion (fBm). The methods of modeling the non-Fickian dye dispersion from observed real data have been developed and the simulation results are encouraging comparing with the real data and the Fickian modeling results from HR Wallingford Ltd in UK.