Modelling Flow Trajectories Using Fractional Brownian Motion

Abstract

An improved fractional Brownian motion (fBm) model using fractal geometry is outlined Brownian motion. It produces more realistic flow trajectories than traditional Brownian motion does. The fBm model is used for producing both super diffusive and sub diffusive particle paths, therefore, the non-Fickian diffusion of particle clouds can be modelled. The particle trajectories and clouds are released in an idealised coastal bay and the fBm particle tracking method is used for simulation the particle cloud spreading in the bay. There is a noticeable increase in the spreading rate of the cloud. The variation of the Hurst exponent can lead to an area of the flow being affected by a contaminant cloud which is not picked up by the regular Brownian motion models. Using the fBm particle tracking model allows more flexibility in simulation of diffusion in fluids.