Hydrodynamics ― Mathematical Approach to Time-periodic Flows
Hydrodynamics ― Mathematical Approach to Time-periodic Flows
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  • This book proposes to introduce the fundamental theory of time-periodic groundwater flow, which is essential for those who seek a comprehensive knowledge of groundwater hydrology and hydraulics. While there are many publications that focus on steady flow and some aspects of transient flow, our goal is to introduce the under-explored topic of periodic flow. Periodic flow results from many natural sources, such as ocean, earth, and atmospheric tides, as well as from human sources, such as groundwater pumping and recharge. The mathematical framework for time-periodic groundwater flow is structurally equivalent to that of time-periodic diffusion. Therefore, some of the theory presented in this book may be relevant to time-periodic phenomena encountered in fields other than groundwater flow, like electronics, heat transport, and chemical diffusion. Consequently, we expect that students and professionals in these other fields will also find this book useful.

    Readers who have knowledge of multivariable calculus, linear algebra, and subsurface fluid dynamics (e.g., groundwater hydraulics), and who have a basic familiarity with complex variables, Fourier series, and partial differential equations, would be potential readers of this volume. Knowledge of Greens' functions and contour integration in the complex plane is not required.

    Authors follow a quantitative but mathematically nonrigorous approach, and emphasize on problem definition and problem understanding, rather than problem solution techniques, because they believe the former are fundamental prerequisites of the latter, and because solution techniques have been described exhaustively by other authors (e.g., Carslaw and Jaeger [1986], Ozisik [1989], Hermance [1998], Bruggeman [1999], Mandelis [2001]), the need for understanding the problems in depth is encessary. Much of the information presented here could be gleaned from reading articles in peerreviewed scientic publications such as those listed in the References section. However, one would have to read many such articles, which typically present only terse descriptions of the mathematical development. This volume is more explicit to accommodate the needs of beginners. Beginners often need to see more intermediate steps in order to follow the development, and to see more of the details in order to understand the mathematical context and to recognize the limitations of the approach.



  • Todd Rasmussen is a Professor of Hydrology and Water Resources at the University of Georgia (UGA). He is a member of the Faculty of Water Resources, the Faculty of Engineering, and the Academy of the Environment at UGA. He is an associate editor for the Journal of Hydrology, and has been an associate editor for Water Resources Research and Hydrogeology Journal. He received his PhD from the Department of Hydrology and Water Resources, College of Engineering and Mines, at the University of Arizona in 1988. His publications focus on uid ow and contaminant transport through surface and subsurface environments, including the physical, chemical, mathematical, and statistical description and quantification of hydrologic processes. He was a co-author of the AGU Geophysical Monograph 42 (Evans et al., 2001) as well as multiple journal articles specifically related to subsurface periodic behavior (Toll and Rasmussen, 2007; Rasmussen and Mote, 2007; Rasmussen et al., 2003).

    Joe Depner graduated with an M.S. from the Department of Hydrology and Water Resources at the University of Arizona in 1985. His thesis topic was Estimation of the three-dimensional anisotropic spatial covariance of log permeability using single-hole and cross-hole packer test data from fractured granites, under the direction of Professor Shlomo P. Neuman, which was subsequently published (Neuman and Depner, 1988). He has also published on the topic of periodic flow in groundwater (Depner, 2000). He has worked professionally for multiple private consulting services and for Pacific Northwest National Laboratory in Hanford, WA.


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