Analysis of discontinuities across thin inhomogeneities, groundwater/surface water interactions in river networks, and circulation about slender bodies using slit elements in the Analytic Element Method. Issue 11 (2nd November 2015) - Steward, David R.
Abstract: Groundwater and surface water contain interfaces across which hydrologic functions are discontinuous. Thin elements with high hydraulic conductivity in a porous media focus groundwater, which flows through such inhomogeneities and causes an abrupt change in stream function across their interfaces, and elements with low conductivity retard flow with discontinuous head. Base flow interactions at the interface between groundwater and surface water transport water between these stores and generate a discontinuous normal component of flow. Thin objects in surface water with Kutta condition generate circulation by the discontinuous tangential component of flow across their interface. These discontinuities across hydrologic interfaces are quantified and visualized using the Analytic Element Method, where slit elements are formulated using the Joukowsky transformation with Laurent series and new influence functions to represent sinks and circulation, and methods are developed for these applications expressing discontinuities as Fourier series. The specific geometries illustrate solutions for a randomly generated heterogeneous porous media with nonintersecting inhomogeneities, for groundwater/surface water interaction in a synthetic river network, and for a slender body with geometry similar to the wings of the Wright Brothers. The mathematical details are reduced to series solutions and matrix multiplications, which are easily extensible to other geometries and applications. Key Points: Methods quantify abrupt change in flows Representative problems are studied Analysis reveals patterns of interactions