Contents -- Preface -- Menu -- Acknowledgments -- 1. Introduction -- 1.1 Topics and Strategies in the Study of Fluid Physics -- 1.2 Units and Mathematical Conventions -- 1.3 Scope of Mathematics Used in This Text -- 1.3.1 Analytical solutions, vectors, and tensors -- 1.3.2 Partial differential notation -- 1.4 Example Problems -- 1.4.1 Steady one-dimensional heat and water flows: a structural homology -- 1.4.2 Sediment particles, vesicles, and olivine crystals: a case of geometric similitude -- 1.4.3 Series, averages, covariances, and autocovariances of physical quantities -- 1.5 Reading -- 2. Fluids and Porous Media as Continua -- 2.1 Mean Free Path -- 2.2 Mathematical and Physical Points -- 2.3 Representative Elementary Volume -- 2.4 Example Problems -- 2.4.1 Shear of thin liquid films: behavior below the continuum scale -- 2.4.2 Fractal pore geometry -- 2.4.3 Porosity estimates of regularly and randomly packed particles -- 2.4.4 Covariance of porosity -- 2.5 Reading -- 3. Mechanical Properties of Fluids and Porous Media -- 3.1 Body and Surface Forces -- 3.2 Ideal versus Real Fluids -- 3.3 Density -- 3.3.1 Fluids -- 3.3.2 Porous media -- 3.4 Fluid Rheology and Shear Viscosity -- 3.4.1 Newtonian fluids -- 3.4.2 Non-Newtonian fluids -- 3.5 Compressibility -- 3.5.1 Fluids -- 3.5.2 Porous media -- 3.6 Surface Tension -- 3.6.1 Surface tension as a potential energy -- 3.6.2 Bubble pressure and capillarity -- 3.7 Example Problems -- 3.7.1 Velocity distributions in viscous fluids: Couette, conduit, and free-surface flows -- 3.7.2 Free-surface flow of a Bingham plastic: nonturbulent lava streams and debris flows -- 3.7.3 Surface tension in unsaturated flow: bubbling pressure -- 3.8 Reading -- 4. Thermodynamic Properties of Fluids -- 4.1 Specific Heat -- 4.2 Heat Conduction -- 4.3 Fluid Phases -- 4.4 Equations of State -- 4.4.1 Ideal gases.

4.4.2 Real gases -- 4.4.3 Liquids -- 4.5 Thermodynamic State and the First Law of Thermodynamics -- 4.6 Isobaric and Isothermal Processes -- 4.6.1 Specific heat of an ideal gas -- 4.6.2 Phase transitions -- 4.7 Adiabatic Processes -- 4.8 Compressibility and Thermal Expansion -- 4.9 Bulk Viscosity -- 4.10 Example Problems -- 4.10.1 Change in ice temperature with steady heat inflow -- 4.10.2 An empirical equation of state for water -- 4.10.3 Water loss from a geyser: thermal effects -- 4.10.4 Ice regelation and glacier movement -- 4.10.5 Growth of carbon dioxide bubbles in a liquid -- 4.11 Reading -- 5. Dimensional Analysis and Similitude -- 5.1 Dimensional Homogeneity -- 5.2 Dimensional Quantities -- 5.2.1 Viscosity of a gas -- 5.2.2 Average velocity in conduit flow -- 5.2.3 Drag on a spherical particle: the Reynolds number -- 5.3 Buckingham Pi Theorem -- 5.4 Geometrical Similitude -- 5.4.1 Exact -- 5.4.2 Statistical -- 5.5 Dynamical Similitude -- 5.6 Characteristic Dimensionless Quantities -- 5.7 Example Problems -- 5.7.1 Drag on a spherical particle using Buckingham Pi theorem -- 5.7.2 Drag on spinose foraminifera -- 5.7.3 Geometrical similitude of randomly packed, unconsolidated sand grains -- 5.8 Reading -- 6. Fluid Statics and Buoyancy -- 6.1 Static Pressure -- 6.2 Equation of Fluid Statics -- 6.3 Hydrostatic Equation -- 6.4 Hypsometric Equations -- 6.5 Buoyancy -- 6.6 Stability of a Thermally Stratified Fluid -- 6.6.1 Liquids -- 6.6.2 Gases -- 6.7 Example Problems -- 6.7.1 Buoyant force on a sediment particle: coordinate position of action -- 6.7.2 Buoyant ascent of magma within a vertical dike -- 6.7.3 Growth and ascent of carbon dioxide bubbles in a liquid -- 6.7.4 Advective overpressure within a magma chamber -- 6.8 Reading -- 7. Fluid Kinematics -- 7.1 Qualitative Descriptions of Motion -- 7.2 Substantive Derivative.

7.2.1 General expression -- 7.2.2 Convective accelerations -- 7.3 Example Problems -- 7.3.1 Local and convective temperature changes within a dike -- 7.3.2 Streamwise acceleration in a Venturi flow -- 7.4 Reading -- 8. Conservation of Mass -- 8.1 Continuity in Cartesian Coordinates -- 8.1.1 Purely fluid flow -- 8.1.2 Flow in porous media -- 8.2 Continuity of Solutes -- 8.2.1 Simple solvent-solute flow -- 8.2.2 Solutes in porous media flow -- 8.3 Continuity in Large Control Volumes -- 8.3.1 Saint-Venant equation of continuity -- 8.3.2 Dupuit flow -- 8.4 Example Problems -- 8.4.1 Steady conduit flow: inferences from continuity -- 8.4.2 Depth-integrated equation of continuity for open-channel flow -- 8.4.3 Continuity of radial flow at a well with steady pumping -- 8.4.4 Diffusion of carbon dioxide into a slowly ascending bubble -- 8.4.5 Lake mass balance -- 8.4.6 Flow within a two-dimensional fracture network -- 8.5 Reading -- 9. Conservation of Energy -- 9.1 Energy Equation -- 9.1.1 Conservation in absence of viscous dissipation -- 9.1.2 Mechanical energy and Euler's equation -- 9.1.3 Porous media -- 9.2 Hubbert's Potential -- 9.3 Example Problems -- 9.3.1 Velocity measurements in open channel flow using a meter stick -- 9.3.2 Heat flow within glacier ice -- 9.3.3 Solidification and melting along dikes with Newtonian magma flow -- 9.4 Reading -- 10. Inviscid Flows -- 10.1 Euler's Equations -- 10.2 Bernoulli's Equation -- 10.3 Example Problems -- 10.3.1 Pressure conditions in a Venturi flow -- 10.3.2 Near-vent velocity of a subsonic geyser eruption -- 10.3.3 Speed of shallow waves -- 10.4 Reading -- 11. Vorticity and Fluid Strain -- 11.1 Flow with Rotation -- 11.2 Vorticity -- 11.3 Fluid Strain -- 11.4 Example Problems -- 11.4.1 Local vorticity and grain rotation in a dike or sill.

11.4.2 Generation of vorticity in viscous boundary flow: precursor to turbulence -- 11.5 Reading -- 12. Viscous Flows -- 12.1 Viscous Forces -- 12.2 Newtonian Fluids -- 12.2.1 Constitutive equations -- 12.2.2 Navier-Stokes equations -- 12.2.3 Energy equation -- 12.3 Incompressible Newtonian Flows -- 12.4 Non-Newtonian Fluids: The Example of Glacier Ice -- 12.4.1 Constitutive equations -- 12.4.2 Equations of motion -- 12.4.3 Energy equation -- 12.5 Example Problems -- 12.5.1 Buoyant ascent of magma in a vertical dike -- 12.5.2 Steady free-surface flow down an inclined bed -- 12.5.3 Viscous generation of heat in the vertical dike problem -- 12.5.4 Extending and compressing glacier flow -- 12.5.5 Very viscous (Hele-Shaw) flow -- 12.5.6 Boundary-layer equations -- 12.5.7 Flow around a vortex in a liquid with free surface -- 12.6 Reading -- 13. Porous Media Flows -- 13.1 Hydraulic Conductivity and Darcy's Law -- 13.1.1 Saturated media -- 13.1.2 Unsaturated media -- 13.2 Equations of Motion -- 13.2.1 Saturated media -- 13.2.2 Unsaturated media: the Richards equation -- 13.3 Advection-Dispersion Equation -- 13.4 Energy Equation -- 13.5 Example Problems -- 13.5.1 Permeability and Hagen-Poiseuille flow -- 13.5.2 Propagation of pressure waves within a coastal aquifer -- 13.5.3 Excess-fluid pressure in thick sediments -- 13.5.4 Unsaturated flow as a diffusion phenomenon -- 13.5.5 Use of temperature and solute-concentration curves to estimate vertical flow within sediments -- 13.6 Reading -- 14. Turbulent Flows -- 14.1 Onset of Turbulence -- 14.2 Time-Averaged Velocities and Pressure -- 14.3 Reynolds Stresses -- 14.4 Time-Averaged Continuity and Navier-Stokes Equations -- 14.5 Fluctuating Velocity Components -- 14.6 Production and Dissipation of Turbulence Energy -- 14.7 Example Problems -- 14.7.1 A statistical measure of the scale of turbulence.

14.7.2 Turbulence kinetic energy in a boundary layer -- 14.8 Reading -- 15. Turbulent Boundary-Layer Shear Flows -- 15.1 Turbulent Boundary-Layer Development -- 15.2 Prandtl's Mixing-Length Hypothesis -- 15.3 Mixing-Length and Eddy Viscosity Distributions -- 15.4 Logarithmic Velocity Law -- 15.5 Turbulent Flow over Rough Boundaries -- 15.5.1 Nikuradse sand roughness -- 15.5.2 Natural roughness -- 15.6 Production and Dissipation of Turbulence Energy -- 15.7 Turbulent Flow and Darcy's Law -- 15.8 Example Problems -- 15.8.1 Turbulent magma flow in a dike -- 15.8.2 Turbulence field over two-dimensional dunes -- 15.8.3 Flow over a two-dimensional wavy bed -- 15.8.4 Similitude and the logarithmic velocity law -- 15.9 Reading -- 16. Thermally Driven Flows -- 16.1 Boussinesq Approximation -- 16.2 Dimensionless Quantities -- 16.3 Laboratory Experiments with Rayleigh-Bénard and Hele-Shaw Flows -- 16.4 Convection in Porous Media -- 16.5 Example Problems -- 16.5.1 The onset of Rayleigh-Bénard convection -- 16.5.2 Convection in a porous medium -- 16.6 Reading -- 17. Appendixes -- 17.1 Formulae in Vector Analysis -- 17.1.1 Basic definitions -- 17.1.2 Differential operations in Cartesian coordinates -- 17.2 Orthogonal Curvilinear Coordinates -- 17.2.1 Cylindrical coordinates -- 17.2.2 Spherical coordinates -- 17.2.3 Curvilinear coordinates -- 17.3 Notation -- References -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Y -- Z.