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Stretching and compression of fluid elements is key for the understanding and quantification mixing and reaction in heterogeneous porous media. We quantify the evolution of the deformation tensor in 2 and 3 dimensional Darcy-scale porous media flows using streamline coordinates. Thus, we derive a stochastic process for the stretching of a material strip in terms of a coupled continuous
time...
Small-scale heterogeneity of permeability plays a major role in the spreading and mixing of contaminant plumes in groundwater systems. Spreading and mixing are interrelated because heterogeneity-induced spreading leads to the stretching of interfaces of the contaminant plume, while mixing across the interfaces is governed by local hydrodynamic dispersion. In many practical problems, mixing is...
Two approaches based on Lagrangian statistics of turbulent flow in porous media are investigated. In the first approach, usage of Lagrangian coherent structures (LCS) to understand barriers in transport and mixing in turbulent flows is studied. The computation of LCS typically involves post processing of experimentally or numerically obtained fluid velocity fields to obtain the finite time...
The fact that examining Eulerian entities in unsteady velocity fields gives misleading information on Lagrangian coherence is now well-established. In this talk, I will review a range of techniques which have been proposed to extract coherent structures from given velocity data. These include the commonly used finite-time Lyapunov exponents, as well as methods such as curves/surfaces to...
Subsurface scalar transport of e.g. heat or chemicals by fluid flow is key to problems as enhanced oil recovery, enhanced geothermal systems, carbon sequestration or in situ minerals mining. The Lagrangian transport properties of the subsurface flow are crucial in such processes. For example, recent studies in the literature on a two-dimensional (2D) unsteady Darcy flow in a circular reservoir...
