A Regime-Switching Diffusion Process Model for Advection-Dispersion Phenomena in Open Channels with Aquatic Vegetation

Abstract

Advection-dispersion phenomena in 1-D open channels are described with a diffusion process model governing Lagrangian particle dynamics. The objective of this paper is to propose a new diffusion process model for analysing advection-dispersion phenomena in open channels with aquatic vegetation, which serves as a physically more appropriate alternative to the conventional models. The concept of regime-switching diffusion process is utilized in formulating the problem so that the physical effects of aquatic vegetation in the advection-dispersion phenomena are described in a consistent manner. The linearity of the system of extended Kolmogorov’s backward equations associated with the model leads to the governing equations of the spatially-distributed statistics, which are key indicators in analytically assessing purification ability of water bodies. Numerical analysis on the deposition probability of suspended sediment particles is performed as an application example of the model. Qualitative and quantitative differences between the proposed and conventional models are also investigated.