In this IGMS project, PI Aleksey Telyakovskiy will spend a year working with scientists in the Interdisciplinary Graduate Program of Hydrologic Sciences and the Department of Geological Sciences. Under the guidance of Dr. Stephen Wheatcraft, he will be studying various aspects of variable density flows. A common example of such flows is salt water intrusion into coastal aquifers, although it may be encountered in inland aquifers. For example, halite (salt in mineral form) is prevalent in aquifers beneath Kansas.
A few classical problems are known in the theory of variable density flows: Henry's, Elder's and Yusa's problems. A very limited number of analytical solutions are known for these problems. The goal of this work is to obtain new analytical/semi-analytical solutions that would provide insights into the nature of these problems. Also, it would allow more efficient testing of numerical codes that can be used for many applications. Today these codes are tested only against an extremely limited number of known solutions. So such solutions will be extremely useful to the groundwater hydrology community. Sea water intrusion, the most important of variable density flow problems, is a very big problem in the world today, with a significant portion of the world's population living within 50 km of the world's oceans. To summarize, the PI will develop a set of skills in hydrology that would allow him to continue interdisciplinary work. This IGMS project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS).