Dispersion Tensor in Rotating Flows

Abstract

Many environmental flow problems involve mixing and transport of substances in a non-uniform rotating ambient. Dispersion should be treated as a second order tensor in such flows since the principal directon of motion changes continuously. Secondary flows in open channels have been investigated and modeled by various researchers. These flows have been shown to influence the transport of pollutants in rivers and streams. In some studies, dispersion has been represented by a tensor. In practice, simplifying assumptions are made to make the tensor symmetric and, consequently, the mixing coefficient scalar. The general equation governing transport of mass with dispersion treated as a second-order tensor in Cartesian coordinates is considered here. Components of the dispersion tensor are given in terms of dispersion along and snormal to the flow, scaled by the local velocity vector. Simulation results are given for mass transport in two-dimensional rotating flows. The role of cross-variant components of the dispersiosn tensor in the transport process is also examined