Hydrodynamics of Time-Periodic Groundwater Flow Diffusion Waves in Porous Media

Hydrodynamics of Time-Periodic Groundwater Flow introduces the emerging topic of periodic fluctuations in groundwater. While classical hydrology has often focused on steady flow conditions, many systems display periodic behavior due to tidal, seasonal, annual, and human influences. Describing and quantifying subsurface hydraulic responses to these influences may be challenging to those who are unfamiliar with periodically forced groundwater systems. The goal of this volume is to present a clear and accessible mathematical introduction to the basic and advanced theory of time-periodic groundwater flow, which is essential for developing a comprehensive knowledge of groundwater hydraulics and groundwater hydrology.

Volume highlights include:

• Overview of time-periodic forcing of groundwater systems
• Definition of the Boundary Value Problem for harmonic systems in space and time
• Examples of 1-, 2-, and 3-dimensional flow in various media
• Attenuation, delay, and gradients, stationary points and flow stagnation
• Wave propagation and energy transport

Hydrodynamics of Time-Periodic Groundwater Flow presents numerous examples and exercises to reinforce the essential elements of the theoretical development, and thus is eminently well suited for self-directed study by undergraduate and graduate students. This volume will be a valuable resource for professionals in Earth and environmental sciences who develop groundwater models., including in the fields of groundwater hydrology, soil physics, hydrogeology, geoscience, geophysics, and geochemistry. Time-periodic phenomena are also encountered in fields other than groundwater flow, such as electronics, heat transport, and chemical diffusion. Thus, students and professionals in the field of chemistry, electronic engineering, and physics will also find this book useful.

Read an interview with the editors to find out more:
https://eos.org/editors-vox/a-foundation-for-modeling-time-periodic-groundwater-flow

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

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