Fluid mixing processes in enclosed shallow water flows and applications

Abstract

This work develops a numerical modelling tool to investigate and better understand the fluid mixing processes in enclosed or semi-closed shallow water flows. The integrated fluid mixing modelling framework consists of two components, i.e. a shallow flow model for predicting hydrodynamics and a particle-tracking model for calculating the trajectories of passive particles released in the water bodies. The well-defined analysis method in dynamical system theory, Finite Time Lyapunov Exponent (FTLE), is used to extract the Lagrangian Coherent Structures (LCSs) to provide insight of the nonlinear particle dynamics in the time-dependant environmental shallow water flows under consideration. The fluid mixing modelling and analysis framework is firstly used to study the mixing properties of an oscillating environmental flow driven by two inflows and one outflow in an idealised shallow basin. The Eulerian velocity field of the flow is first predicted using the shallow flow model, which is then used by the particle-tracking model to calculate the particle trajectories and describe the transport and mixing properties of the inflows/outflow driven shallow water flow. The particle dynamics is found to be controlled by a dimensionless parameter and fluid mixing changes from regular to chaotic when the magnitude of the parameter increases. The integrated numerical modelling framework is then applied to reproduce the wind-driven flow hydrodynamics and investigate the corresponding fluid mixing in Taihu, one of the largest fresh water lakes in China, for continuous 12 months. The predicted flow field, which is used to drive the particle dynamics, compares favourably with the field measurements. The transport and mixing properties of the lake are analysed by calculating the FTLE and identifying the LCSs, clearly revealing the stagnant and well-mixing zones of the water body. The understanding of the underlying fluid mixing mechanism of the lake is also improved. Through successful application to one idealised and one realistic case studies, the potential of the current integrated numerical modelling framework is confirmed for analysing fluid mixing in (semi-)enclosed water bodies.