Hydrodynamics of Time–Periodic Groundwater Flow: Diffusion Waves in Porous Media

Author Biography: 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.

Preface vii Notation xi Acknowledgments xvii Part I: Introduction 1 1 Introduction 3 Part II: Problem Definition 7 2 Initial Boundary Value Problem for Hydraulic Head 9 3 Hydraulic Head Components and Their IBVPs 13 4 Periodic Transient Components 15 5 BVP for Harmonic Constituents 21 6 Polar Form of Space BVP 29 7 Complex-Variable Form of Space BVP 37 8 Comparison of Space BVP Forms 43 Part III: Elementary Examples 45 9 Examples: 1D Flow in Ideal Media 47 10 Examples: 1D Flow in Exponential Media 63 11 Examples: 1D Flow in Power Law Media 89 12 Examples: 2D and 3D Flow in Ideal Media 95 13 Examples: Uniform-Gradient Flow 107 Part IV: Essential Concepts 121 14 Attenuation, Delay, and Gradient Collinearity 123 15 Time Variation of Specific-Discharge Constituent 131 Part V: Stationary Points 149 16 Stationary Points: Basic Concepts 151 17 Stationary Points: Amplitude and Phase 157 18 Flow Stagnation 171 Part VI: Wave Propagation 181 19 Harmonic, Hydraulic Head Waves 183 20 Wave Distortion 199 21 Waves in One Dimension 215 22 Wave Equation 225 Part VII: Energy Transport 231 23 Mechanical Energy of Groundwater 233 24 Mechanical Energy: Time Averages 239 25 Mechanical Energy of Single-Constituent Fields 249 Part VIII: Conclusion 261 26 Conclusion 263 Part IX: Appendices 269 A Hydraulic Head Components 271 B Useful Results from Trigonometry 273 C Linear Transformation of Space Coordinates 275 D Complex Variables 281 E Kelvin Functions 283 Bibliography 291 Index 295