Note: Intro -- Preface -- Fluid and Thermodynamics -- Fluid and Thermodynamics -- Contents -- 1 Introduction -- 1.1 Historical Notes and Definition of the Subject Field -- 1.2 Properties of Liquids -- References -- 2 Hydrostatics -- 2.1 Some Basic Concepts -- 2.2 Fluid Pressure -- 2.3 Fundamental Equation of Hydrostatics -- 2.4 Pressure Distribution in a Density Preserving Heavy Fluid -- 2.5 Hydrostatic Buoyancy of Floating Bodies -- 2.6 Hydrostatics in an Accelerated Reference System -- 2.7 Pressure Distribution in the Still Atmosphere -- Reference -- 3 Hydrodynamics of Ideal Liquids -- 3.1 Basic Kinematic Concepts -- 3.1.1 Motion, Velocity -- 3.1.2 Streamlines, Trajectories, Streaklines -- 3.2 Mass Balance, Continuity -- 3.3 Balance of Linear Momentum -- 3.4 Bernoulli's Equation -- 3.5 Simple Applications of the Bernoulli Equation -- 3.6 Global Formulation of the Momentum Equation -- 3.7 Applications of the Balance Law of Momentum in Integrated Form -- 3.7.1 Reaction Forces Due to Fluid Flow Through Pipes -- 3.7.2 Borda Exit Orifice -- 3.7.3 Impact of a Free Jet on a Wall -- 3.7.4 Mixing Processes -- 3.7.5 Hydraulic Jump -- 3.8 Plane Flow Around Infinitely Long Wings -- 3.8.1 Flow Through a Periodic Grid of Wings -- 3.8.2 Flow Around a Single Wing -- 3.9 Balance of Moment of Momentum -- 3.10 Applications of the Balance of Angular Momentum -- 3.10.1 Segner's Water Wheel -- 3.10.2 Euler's Turbine Equation -- References -- 4 Conservation of Angular Momentum---Vorticity -- 4.1 Circulation -- 4.2 Simple Vorticity Theorems -- 4.3 Helmholtz Vorticity Theorem -- 4.4 Potential Vorticity Theorem -- References -- 5 An Almanac of Simple Flow Problems of Ideal Fluids -- 5.1 General Concepts -- 5.1.1 A Primer on Vector Analysis -- 5.1.2 Determination of a Vector Field from Its Sources and Vortices -- 5.2 Vortex-Free Flow Fields. , 5.2.1 Mathematical Preliminaries -- 5.2.2 Potential Fields -- 5.3 Motion-Induced Force on a Body in Potential Flow. The Virtual Mass Concept -- 5.3.1 Force on a Sphere -- 5.3.2 Force on a Body of Arbitrary Geometry -- 5.4 Plane Flow Configuration -- 5.4.1 Stream Function -- 5.4.2 Simple Plane Flows of Ideal Fluids -- References -- 6 Function-Theoretical Methods Applied to Plane Potential Flows -- 6.1 General Principles -- 6.1.1 Some Notation and Mathematical Properties of Complex Functions -- 6.1.2 Examples -- 6.1.3 Steady Flow Around an Arbitrary Cylinder at Rest -- 6.1.4 The Kutta-Joukowski Mapping -- 6.2 Applications -- 6.2.1 Flow Over a Plane Plate -- 6.2.2 Potential Flow Over a Circular Segment -- 6.2.3 Realistic Air-Wings with Finite Thickness -- 6.3 The Circle Theorem of Milne-Thomson -- 6.4 Laminar Free Jets -- 6.4.1 Flow Through a Slit Orifice in a Vertical Wall -- 6.4.2 Potential Flow Through a Periodic Arrangement of Slits -- 6.5 Schwarz-Christoffel Transformation -- 6.5.1 Build-up of the General Schwarz-Christoffel Transformation -- 6.5.2 Examples of Schwarz-Christoffel Transformations -- References -- 7 Viscous Fluids -- 7.1 Fundamental Dynamical Equations of Viscous Fluids -- 7.1.1 Newtonian Fluids -- 7.1.2 Dilatant and Pseudoplastic Density Preserving Fluids -- 7.2 Plane Wall Bounded Shear Flows -- 7.3 Applications -- 7.3.1 Couette Viscometer -- 7.3.2 Cone Plate Viscometer -- 7.3.3 Hover Craft or Oil Pressure Cushion -- 7.3.4 Flows of Liquid Films -- 7.3.5 Influence of the Weight of a Fluid in Plane Poiseuille Flow -- 7.3.6 Slide Bearing Theory -- 7.4 Three-Dimensional Creeping Flow of a Pseudoplastic Fluid with Free Surface -- References -- 8 Simple Two- and Three-Dimensional Flow Problems of the Navier-Stokes Equations -- 8.1 Introductory Review -- 8.2 Steady State Layer Flows -- 8.2.1 Hagen-Poiseuille Flow. , 8.2.2 Ekman Theory and Its Extensions -- 8.3 Simple Unsteady Flows -- 8.3.1 Oscillating Wall -- 8.3.2 Adjustment of a Velocity Jump -- 8.4 Stationary Axisymmetric Laminar Jet -- 8.5 Viscous Flow in a Converging Two-Dimensional Channel -- 8.6 Closing Remarks -- References -- 9 Simple Solutions of Boundary Layer Equations -- 9.1 Preview -- 9.2 Two-Dimensional Boundary Layer Flow in the Vicinity of a Stagnation Point -- 9.3 Three-Dimensional Boundary Layer Flow in the Vicinity of a Stagnation Point -- 9.4 Boundary Layer Flows Around Wedges -- 9.4.1 Boundary Layer Equations -- 9.4.2 Flow Along Sidewalls of Wedges -- 9.4.3 Rotating Disk of Infinite Extent -- 9.5 The Blasius Boundary Layer -- 9.6 Round Laminar Jet---A Not So Simple Boundary Layer Problem -- 9.7 Boundary Layers of theaut]Navier Navier-Stokes aut]Stokes Equations Treated by Matched Asymptotic Expansions -- 9.7.1 A Simple Introductory Example -- 9.7.2 The Blasius Boundary Layer -- 9.8 Global Laws of the Steady Boundary Layer Theory -- 9.8.1 Global Mass and Momentum Balances -- 9.8.2 Holstein-Bohlen Procedure -- 9.9 Non-stationary Boundary Layers -- 9.9.1 Impulsive Start from Rest -- 9.9.2 Boundary Layer Formed at the Boundary of an Oscillating Body -- 9.9.3 Oscillation-Induced Drift Current -- 9.9.4 Non-Stationary Plate Boundary Layer -- References -- 10 Pipe Flows -- 10.1 Introductory Remarks -- 10.2 Laminar Pipe Flow -- 10.2.1 The Law of Hagen-Poiseuille -- 10.2.2 Laminar Flow in Cylindrical Pipes of Arbitrary Cross-Section -- 10.2.3 Flow Out of a Vessel -- 10.2.4 Influence of the Wall Drag of a Pipe to the Exit Flow from a Vessel -- 10.3 Turbulent Flows in Pipes -- 10.3.1 Coefficient of Resistance -- 10.3.2 Plane Turbulent Flow According to Prandtl and von Kármán. , 10.3.3 Calculation of Pressure Loss in Pipe FlowsThis subsection illustrates how pressure losses in a sequential arrangement of pipe segments are technically performed in the context of the Prandtl-von Kármán turbulence model. Conceptual thoughts on its theoretical limitation are given in the subsequent subsection. -- 10.3.4 Questioning the Prandtl-von Kármán Logarithmic Velocity ProfileWe follow in this subsection closely Chap. 30 in Physics of Lakes, Vol. 3 [9]. -- 10.4 Concluding Remarks -- References -- List of Biographies -- Name Index -- Subject Index.

Note: Cover -- Half-title -- Title -- Copyright -- Dedication -- Contents -- Tables -- Preface -- Acknowledgements -- Symbols -- Abbreviations -- Preamble -- 1 General background -- 1.1 Introduction -- 1.2 Governing equations: basic assumptions and hypotheses -- Nonadiabatic processes -- Equations for wave disturbances -- Boussinesq approximation -- Approximation of the Coriolis acceleration -- Reynolds equations -- 1.3 Problem formulation: boundary and initial conditions -- Problem formulation -- Boundary and initial conditions -- 1.4 Linear wave equation -- 1.5 Linear boundary value problem and dispersion relation -- 1.5.1 Formulation of the boundary value problem -- 1.5.2 Linear vertical mode analysis -- 1.6 Nonlinear wave problem -- 2 Linear baroclinic tides over variable bottom topography -- 2.1 Analytical solution for "small" bottom features -- 2.1.1 Generation of internal waves by an oscillating tidal flux -- Zeroth-order solution -- First-order solution -- 2.1.2 Scattering of internal waves by a bottom obstacle -- 2.2 Numerical model for large bottom obstacles -- Step 1: Introduction of the grid -- Step 2: Finding the recurrence relation -- Step 3: Upstream procedure -- Step 4: Orthogonalization -- Step 5: Downstream procedure and orthogonalization -- Step 6: Truncation -- 2.3 Wave dynamics over oceanic ridges: applicability of the perturbation method -- 2.3.1 Generation of internal waves -- 2.3.2 Internal wave scattering -- 2.4 Wave dynamics in slope-shelf regions -- 2.4.1 Generation of baroclinic tides -- 2.4.2 Transformation of baroclinic tides -- 2.5 Internal waves near steep bottom topography -- 2.6 Internal waves near the critical latitude -- 3 Combined effect of horizontal density gradient and bottom topography on the dynamics of linear baroclinic tides -- 3.1 Semianalytical two-layer model. , 3.2 Wave characteristics derived from the two-layer model -- 3.2.1 Generation of internal waves -- 3.2.2 Internal wave scattering -- 3.3 Applicability of layer models -- 3.4 Riemann method for a continuously stratified fluid -- 3.5 Propagation of internal waves through a frontal zone -- 3.6 Generation of baroclinic tides in the presence of a frontal zone -- 4 Topographic generation of nonlinear baroclinic tides -- 4.1 Experimental evidence for nonlinear baroclinic tides -- 4.2 Numerical model for the description of nonlinear waves -- First semistep -- Second semistep -- 4.3 Qualitative analysis of the excitation mechanism -- 4.4 Generation mechanism at low Froude numbers: baroclinic tides -- 4.5 Influence of the intensity of the tidal forcing and dissipation -- 4.6 Critical Froude numbers: excitement of unsteady lee waves -- 5 Evolutionary stages of baroclinic tides -- 5.1 Analytical models for the evolution of baroclinic tides -- 5.2 Solitary internal waves as manifestations of the coherent structure of baroclinic tides -- 5.2.1 Long's equation -- 5.2.2 First-order weakly nonlinear theory -- 5.2.3 Second-order weakly nonlinear theory -- 5.3 Structure of large-amplitude solitary internal waves -- 5.3.1 Numerical model for stationary wave solutions -- 5.3.2 Characteristics of large waves -- 5.3.3 Observational evidence of large waves -- 5.4 Interaction of large-amplitude SIWs with bottom topography -- 5.4.1 Scenarios of wave-topography interaction -- Scenario 1: Wave adjustment when aξ /(H . Hξ ) 1 -- Scenario 2: Wave transformation at aξ /(H . Hξ ) 1 -- Scenario 3: Wave breaking at aξ /(H . Hξ ) > -- 1 -- 5.4.2 Strong wave-topography interaction: breaking criterion -- Kinematics of wave breaking -- Breaking criterion -- 5.4.3 Generation of high baroclinic modes by wave-topography interaction -- Experimental setup and measuring technique. , The experiments -- Typical experimental data -- Results of the numerical modeling -- 6 Generation mechanism for different background conditions -- 6.1 Effects related to the rotation of the Earth -- 6.1.1 Barents Sea Polar Front experiment -- 6.1.2 Baroclinic tides -- 6.1.3 Short internal waves -- 6.1.4 Dependence on the rotation of the Earth -- 6.2 Influence of the fluid stratification -- 6.2.1 Variation of the vertical position of the pycnocline -- 6.2.2 Effect of horizontal density gradients -- 6.3 Baroclinic tides over steep bottom features: "mode" and "beam" approaches -- 6.4 Strong high-mode baroclinic response over steep bottom topography -- 6.5 Generation mechanism at large Froude numbers -- 6.6 Summary of generation mechanism -- 7 Three-dimensional effects of baroclinic tides -- 7.1 Influence of wave refraction -- 7.1.1 Observations of SIWs on the Portuguese Shelf -- 7.1.2 Generation of waves at the Oporto Seamount -- 7.1.3 Far-field generation from a shelf edge -- 7.2 Baroclinic tides in narrow channels and straits -- 7.2.1 Modification of the model for straits -- 7.2.2 Dynamics of internal waves in the Skarnsund Strait -- 7.2.3 Residual currents produced by nonlinear waves -- 7.2.4 Experiments on the dynamics of a passive admixture -- References -- Index.

Note: Intro -- Preface to the Book Series -- VOLUME 1: Physics of Lakes - Formulation of the Mathematical and Physical Background -- VOLUME 2: Physics of Lakes - Lakes as Oscillators -- VOLUME 3: Physics of Lakes - Methods of Understanding Lakes as Components of the Geophysical Environment -- Vorwort zur Buchreihe -- BAND 1: Physik der Seen - Formulierung des mathematischen und physikalischen Hintergrundes -- BAND 2: Physik der Seen - Seen als Oszillatoren -- BAND 3: Physik der Seen - Methoden, die Seen als Komponenten des geophysikalischen Umfeldes verstehen -- Пpeдиcлoвиe к cepии -- 本书系列序 -- Acknowledgements -- References -- Books, Reports -- Diploma (M. Sc.) Theses -- Doctoral Dissertations -- Habilitation Theses -- Preface to Volume I -- Acknowledgements for Copyright Permission -- Contents -- Notations -- Roman Symbols -- Greek Symbols -- Miscellaneous Symbols -- 1 Introduction -- 1.1 Motivation -- 1.2 Lakes on Earth -- 1.3 Lakes Characterised by Their Response to the Driving Environment -- 1.3.1 Seasonal Characteristics -- 1.3.2 Characteristics by Mixing -- 1.3.3 Boundary-Related Processes -- 1.3.4 Characterisation by Typical Scales -- References -- 2 Mathematical Prerequisites -- 2.1 Scalars and Vectors -- 2.2 Tensors -- 2.3 Fields and Their Differentiation -- 2.4 Gradient, Divergence and Rotation of Vector and Tensor Fields -- 2.5 Integral Theorems of Vector Analysis -- 2.5.1 Gauss Theorems -- 2.5.2 Stokes Theorems -- References -- 3 A Brief Review of the Basic Thermomechanical Laws of Classical Physics -- 3.1 Underlying Fundamentals -- General Balance Laws -- 3.2 Physical Balance Laws -- 3.2.1 Balance of Mass -- 3.2.2 Balance of Linear Momentum -- 3.2.3 Balance of Moment of Momentum -- 3.2.4 Balance of Energy -- 3.2.5 Second Law of Thermodynamics -- References -- 4 Fundamental Equations of Lake Hydrodynamics. , 4.1 Kinematics -- 4.2 Balance of Mass -- 4.3 Balances of Momentum and Moment of Momentum, Concept of Stress, Hydrostatics -- 4.3.1 Stress Tensor -- 4.3.2 Local Balance Law of Momentum or Newton's Second Law -- 4.3.3 Material Behaviour -- 4.3.4 Hydrostatics -- 4.4 Balance of Energy: First Law of Thermodynamics -- 4.5 Diffusion of Suspended Substances -- 4.6 Summary of Equations -- 4.7 A First Look at the Boussinesq and Shallow-Water Equations -- References -- 5 Conservation of Angular Momentum--Vorticity -- 5.1 Circulation -- 5.2 Simple Vorticity Theorems -- 5.3 Helmholtz Vorticity Theorem -- 5.4 Potential Vorticity Theorem -- References -- 6 Turbulence Modelling -- 6.1 A Primer on Turbulent Motions -- 6.1.1 Averages and Fluctuations -- 6.1.2 Filters -- 6.1.3 Isotropic Turbulence -- 6.1.4 Reynolds Versus Favre Averages -- 6.2 Balance Equations for the Averaged Fields -- 6.2.1 Motivation -- 6.2.2 Averaging Procedure -- 6.2.3 Averaged Density Field < -- ρ> -- -- 6.2.4 Dissipation Rate Density < -- φ> -- -- 6.2.5 Reynolds Stress Hypothesis -- 6.2.6 One- and Two-Equation Models -- 6.3 k-ε Model for Density-Preserving and Boussinesq Fluids -- 6.3.1 The Balance Equations -- 6.3.2 Closure Relations -- 6.3.3 Summary of (k-ε)-Equations -- 6.3.4 Boundary Conditions -- 6.4 Final Remarks -- 6.4.1 Higher Order RANS Models -- 6.4.2 Large Eddy Simulation and Direct Numerical Simulation -- 6.4.3 Early Anisotropic Closure Schemes -- References -- 7 Introduction to Linear Waves -- 7.1 The Linear Wave Equation and Its Properties -- 7.2 Surface Gravity Waves Without Rotation -- 7.2.1 Short-Wave Approximation -- 7.2.2 Long-Wave Approximation -- 7.2.3 Standing Waves -- Reflection -- 7.3 Free Linear Oscillations in Rectangular Basins of Constant Depth -- 7.4 Concluding Remarks -- References. , 8 The Role of the Distribution of Mass Within Water Bodies on Earth -- 8.1 Motivation -- 8.2 Processes of Surface Water Penetration to Depth -- 8.3 Homogenisation of Water Masses Requires Energy -- 8.3.1 Constant Density Layers -- 8.3.2 Continuous Density Variation -- 8.3.3 Influence of the Thermal Expansion -- 8.4 Motion of Buoyant Bodies in a Stratified Still Lake -- 8.4.1 Influence of Friction -- 8.5 Internal Oscillations -- The Dynamical Imprintof the Density Structure -- 8.5.1 Fundamental Equations -- 8.5.2 Eigenvalue Problem for the Vertical Mode Structurein Constant Depth Basins -- 8.6 Closure -- References -- 9 Vertical Structure of Wind-Induced Currentsin Homogeneous and Stratified Waters -- 9.1 Preview and Scope of This Chapter -- 9.2 Hydrodynamic Equations Applied to a Narrow Lake Under Steady Wind -- 9.2.1 Wind-Induced Steady Circulation in a Narrow Homogeneous Lake of Constant Depth -- 9.2.2 Influence of Bottom Slip on the Wind-Induced Circulation -- 9.2.3 Wind-Induced Steady Circulation in a Narrow Lake Stratified in Two Layers -- 9.3 Ekman Theory and Some of Its Extensions -- 9.3.1 Ekman Spiral -- 9.3.2 Steady Wind-Induced Circulation in a Homogeneous Lake on the Rotating Earth -- 9.3.3 Wind-Driven Steady Currents in Lake Erie -- 9.3.4 Time-Dependent Wind-Induced Currents in Shallow Lakes on the Rotating Earth -- 9.3.5 The Dynamical Prediction of Wind Tides on Lake Erie -- 9.4 Final Remarks -- References -- 10 Phenomenological Coefficients of Water -- 10.1 Density of Water -- 10.1.1 Natural Water and Sea Water -- 10.1.2 Suspended Matter -- 10.2 Specific Heat of Water -- 10.2.1 Specific Heat of Salty Water -- 10.3 Viscosity of Water -- 10.3.1 Pure Water -- 10.3.2 Sea Water -- 10.3.3 Natural Water -- 10.3.4 Suspended Matter -- 10.4 Molecular Heat Conductivity of Water. , 10.4.1 Heat Conductivity of Salt Water -- 10.4.2 Impurities -- References -- Name Index -- Lake Index -- Subject Index.

Note: Intro -- Preface to the Book Series -- Vorwort zur Buchreihe -- Acknowledgments -- Preface to Volume III -- Acknowledgments for Copyright Permission -- Contents of Volume I -- Contents of Volume II -- Contents -- Part I Wind-Induced Three-Dimensional Currents: Numerical Models and Applications -- Part1 -- 23 Barotropic Wind-Induced Motions in a Shallow Lake -- 23.1 Introduction -- 23.2 Mathematical Prerequisites -- 23.2.1 Boundary Value Problem of the One-Layer Model for the Water Transport and the Free Surface Displacements -- 23.2.2 The Barotropic Multi-Layer Model -- 23.3 The Water Transport in the Homogeneous Lake Zurich: Results of the 8-Layer Model -- 23.3.1 West-Wind -- 23.3.2 Wind From East, South, North and South-East -- 23.3.3 Delineation of the Validity of One-Layer Models -- 23.4 Concluding Discussion -- References -- 24 Response of a Stratified Alpine Lake to External Wind Fields: Numerical Prediction and Comparison with Field Observations -- 24.1 The Problem Setting -- 24.2 Governing Equations -- 24.2.1 Field Equations for a Boussinesq Fluid -- 24.2.2 The Hydrostatic Approximation of the Boussinesq-Type Field Equations -- 24.2.3 Turbulent Closure Conditions -- 24.2.4 Boundary Conditions -- 24.3 Approximate Treatments of the Model Equations -- 24.3.1 Discretization Procedure -- 24.3.2 The Baroclinic Multi-Layer Model -- 24.4 An Almanac of Tests -- 24.4.1 Selection of the Standard Test Conditions -- 24.4.2 Inferences From Tests 1 to 4 -- 24.4.3 The Role of the Horizontal Momentum Exchange -- 24.4.4 Influence of the Horizontal Grid Size -- 24.4.5 Influence of the Vertical Momentum Exchange -- 24.4.6 Effects of Coriolis Force, Momentum Advection and Stratification -- 24.5 Comparison of Model Output with Field Observations of 1978 Lake Zurichlak]Zurich Campaign -- 24.6 Discussions and Conclusion -- References. , 25 Comparing Numerical Methods for Convectively-Dominated Problems -- 25.1 Preview and Attempt of a Judicious Evaluation -- 25.2 A Series of Numerical Methods -- 25.2.1 Central Difference Scheme -- 25.2.2 Upstream Difference Scheme -- 25.2.3 Lax-Friedrichs Scheme -- 25.2.4 Second-Order Upstream Scheme (2UDS) and Fromm's Method -- 25.2.5 QUICK Scheme -- 25.2.6 Lax-Wendroff and Beam-Warming Schemes -- 25.2.7 Flux Corrected Transport -- 25.2.8 Total Variation Diminishing -- 25.3 Comparison of Some Numerical Results -- 25.3.1 A Linear Convection Problem: Travelling Shock Wave -- 25.3.2 A Convection-Diffusion Problem -- 25.3.3 A Non-Linear Convection Problem -- 25.3.4 Deformation of Temperature Profile Caused by Vertical Convection in Stratified Lakes -- 25.4 Concluding Remarks -- References -- 26 Comparing Different Numerical Treatments of Advection Terms for Wind-Induced Circulations in Lakes -- 26.1 Computation in Environmental Fluid Mechanics -- 26.2 Basic Equations and Model Descriptions -- 26.3 Numerical Methods -- 26.3.1 Diffusion Terms: A Central Difference Treatment -- 26.3.2 Advection Terms: Three Kinds of Difference Schemes -- 26.4 Numerical Results of Wind-Induced Circulations in a Rectangular Basin -- 26.4.1 Homogeneous Water -- 26.4.2 Stratified Water -- 26.5 Numerical Results of Wind-Induced Circulations in Lake Constance -- 26.5.1 Homogeneous Water -- 26.5.2 Stratified Water -- 26.6 Concluding Remarks -- References -- 27 Subgrid-Scale Parameterization in Numerical Simulations of Lake Circulation -- 27.1 Turbulent Parameterization: A Journey Past Scylla and Charybdis -- 27.2 A Subgrid-Scale Parameterization -- 27.2.1 Horizontal Turbulence Closure Mixing -- 27.2.2 Vertical Turbulence Closure for Mixing -- 27.3 Numerical Results and Discussions -- 27.3.1 Results for a Rectangular Basin -- 27.3.2 Results for Lake Constance. , 27.4 Internal Seiches: An Eigenvalue Problem of the Two-Layer Model -- 27.5 Review and Outlook -- References -- Part II Observation, Measurements and Laboratory Experiments -- Part2 -- 28 Instruments and Sensors -- 28.1 Measurement of Water Currents -- 28.1.1 Current Meters -- 28.1.2 Buoys, Floats, Tracers, Profilers -- 28.2 Measurement of Water Temperature, Electrical Conductivity and Density -- 28.2.1 Main Principles of Operation of Temperature Sensors -- 28.2.2 Salinity Measurements -- 28.2.3 Density Measurements and Calculations -- 28.3 Water Level and Water Depth Measurement -- 28.3.1 Water Level Elevation -- 28.3.2 Measurement of the Water Depth -- 28.4 Optical Measurements -- 28.4.1 The Optical Properties of Natural Water and the Distribution of the Field of Light -- 28.4.2 Instruments for Optical Measurements -- 28.5 Measurement of Turbulence -- 28.5.1 Turbulence in Lakes -- 28.5.2 Instruments -- References -- 29 Measuring Methods and Techniques -- 29.1 Stationary Instruments -- 29.1.1 Anchored Buoy Stations: Moorings -- 29.1.2 Lake Diagnostic Systems -- 29.1.3 Bottom Gradient Stations -- 29.2 On-Board Methods: Towing, Profiling, Sounding -- 29.3 Drifter-Based Measurements -- 29.4 Sampling Method -- 29.4.1 Concluding Remarks -- References -- 30 Dimensional Analysis, Similitude and Model Experiments -- 30.1 Introductory Motivation -- 30.1.1 Dimensional Analysis -- 30.1.2 Similitude and Model Experiments -- 30.1.3 Systems of Physical Entities -- 30.2 Theory of Dimensional Equations -- 30.2.1 Dimensional Homogeneity -- 30.2.2 Buckingham's Theoremaut]Buckingham@Buckingham -- 30.2.3 Two Hydraulic Examples -- 30.3 Application to Hydrodynamic Problems -- 30.3.1 Instability of Stratified Shear Flows -- 30.3.2 Wave Theory in Stratified Shear Flows -- 30.3.3 Self-Similar Structures in Turbulent Boundary Layers at Large Reynolds Numbers. , 30.3.4 Dispersion of an Oil Spill on a `Still' Water Surface -- 30.4 Theory of Physical Models -- 30.4.1 Analysis of the Downscaling of Physical Processes -- 30.4.2 Applications -- 30.5 Model Theory and Differential Equations -- 30.5.1 Navier--Stokes--Fourier--Fick Equations -- 30.5.2 Non-Dimensionalization of the NSFF Equations -- 30.6 Physical Hydrodynamic Models -- 30.6.1 Background -- 30.6.2 Physical Conditions for Tidal Models -- 30.6.3 Rotating Laboratory Study of Lake Constance -- 30.7 Discussion and Conclusion -- References -- Part III Detritus and Particle Laden Transport in Lakes -- Part3 -- 31 Prograding and Retrograding Hypo- and Hyper-Pycnal Deltaic Formations into Quiescent Ambients -- 31.1 Introduction: Estuarine Development Due to Riverine Sediment Inflow -- 31.1.1 Fluvio-Deltaic Sedimentation in Lakes From Rivers -- 31.1.2 Morpho-Dynamics of Hypo-, Homo- and Hyper-Pycnal Flows -- 31.2 Sediment Transport in the River -- 31.3 Similarity Solution for the Homogeneous Diffusion Equation -- 31.3.1 Bedrock-Alluvial Transition -- 31.3.2 Overtopping Failure of a Dam -- 31.4 Hypopycnal (Gilbert-Type) Deltas -- 31.4.1 The Classical Stefan Problem -- 31.4.2 Prograding Deltas -- 31.4.3 Fluvial `Grade' in River-Lake Systems -- 31.4.4 Experimental Verification -- 31.5 Hyper-Pycnal Deltas -- 31.5.1 Foreset Diffusion Model -- 31.5.2 Combined Topset-Foreset Diffusion Process for Hyper-Pycnal Deltas -- 31.6 Laboratory Experiments -- 31.6.1 Progradation of Hyper-Pycnal Deltas -- 31.6.2 Reservoir Infill by Hypo- and Hyperpycnal Deltas Over Bedrock -- 31.7 Formation and Evolution of Tributary Dammed Lakes -- 31.7.1 Introduction -- 31.7.2 Theory -- 31.7.3 Experiments -- 31.8 Discussion and Conclusions -- References -- 32 Sediment Transport in Alluvial Systems -- 32.1 Description of the Sediment Transport Model. , 32.2 Governing Equations in Lake Domain I -- 32.2.1 Laminar Flow -- 32.2.2 Turbulent Motion -- 32.2.3 Boussinesq and Shallow Water Approximations in Model 2 -- 32.2.4 Boussinesq and Hydrostatic Pressure Assumption in Model 2 -- 32.3 A Primer on Boundary and Transition Conditions -- 32.3.1 Kinematic Surface Condition -- 32.3.2 Dynamic Surface Jump Conditions -- 32.3.3 Surface Balance Laws -- 32.4 Boundary Conditions: A Simple Model of Detritus Layer -- 32.4.1 Boundary Conditions at the Free Surface -- 32.4.2 Boundary Conditions at the Rigid Bed -- 32.5 Transformation of the Surface Mass Distribution into a Detritus Layer Thickness -- 32.6 Discussion and Conclusion -- References -- Acronyms -- Name Index -- Lake Index -- Subject Index.

Note: Intro -- Preface -- References -- Contents -- List of Symbols -- Roman Symbols -- Greek Symbols -- Special Symbols -- Chapter 1: Introduction -- 1.1 Aims and Scopes of This Book -- 1.2 A Brief Tour d´Horizon Through Today´s Turbulence Field and Modeling -- References -- Chapter 2: Reynold´s Averaging of the Navier-Stokes Equations (RANS) -- References -- Chapter 3: The Closure Problem -- References -- Chapter 4: Boussinesq´s ``Constitutive Law´´ -- References -- Chapter 5: First Turbulence Models for Shear Flows -- 5.1 Shear Flows and the Works of Prandtl, Taylor, and Contemporaries -- 5.2 Momentum and Vorticity Transfer Models -- 5.2.1 Prandtl´s Mixing Length Model -- 5.2.2 von Krmn´s Local Model -- 5.2.3 Reichardt´s Inductive Model -- 5.2.4 Prandtl´s Mean Gradient Model -- 5.2.5 Prandtl´s Shear Layer Model -- 5.2.6 Taylor´s Vorticity Transfer Model -- 5.3 Overview of Deficiencies of Local Models -- 5.4 More General Deficiencies and Fallacies -- 5.5 Questioning the Logarithmic Law -- 5.6 Logarithmic Versus (Deficit) Power Law -- References -- Chapter 6: Review of Nonlinear and Nonlocal Models -- 6.1 Nonlocality in Phase Space -- 6.2 Atomic and Continuum Theories -- 6.3 Stress as an Objective Polynomial Function of the Mean Rate of Strain Tensor -- 6.4 Modified Diffusivity Models -- 6.5 Truly History Dependent and Nonlocal Models -- References -- Chapter 7: The Difference-Quotient Turbulence Model (DQTM) -- 7.1 The Discovery and Prandtl´s Models -- 7.2 Momentum Transfer Approach -- 7.2.1 Molecular Transport -- 7.2.2 Transport by Eddies -- 7.2.3 Comparison of Laminar and Turbulent Flows -- 7.2.4 Lévy Flight Turbulence Model and K41 -- 7.2.4.1 Introduction -- 7.2.4.2 Lévy Walks on a One-Dimensional Lattice -- 7.2.4.3 Lévy Walks, Lévy Flights, Lévy Pairs, and Eddies in Turbulence -- 7.2.4.4 Eddy Class Statistics -- 7.2.4.5 The Lifetime of Eddies. , 7.2.4.6 The Eddy Diameters -- 7.2.4.7 A Fractal Eddy Cascade Model -- 7.2.4.8 The Occupation Number -- 7.2.4.9 The Occupation Probability -- 7.2.4.10 The Momenta of Eddies -- 7.2.4.11 The Number of Eddy Classes -- 7.2.4.12 Lévy Flight Statistics, β-Fractal Model, and the DQTM -- 7.3 New Nonlocal Turbulence Models -- 7.3.1 Introduction -- 7.3.2 Liouville Fractional Derivative -- 7.3.3 Overview of the Derivation of Important Nonlocal Turbulence Models -- 7.3.4 Liouville-Prandtl Mixing Length Model -- 7.3.5 The Heaviside-Liouville-Prandtl Shear Layer Model -- 7.3.6 The Liouville-Heaviside Turbulence Model -- 7.3.7 The Difference-Quotient Turbulence Model -- 7.3.8 Summary -- References -- Chapter 8: Self-Similar RANS -- Reference -- Chapter 9: Elementary Turbulent Shear Flow Solutions -- 9.1 Plane Wake Flows -- 9.2 Axi-Symmetric Jets -- 9.2.1 Jets in Quiescent Surroundings -- 9.2.2 Jets in Parallel Co-flows -- 9.3 Plane Couette Flows -- 9.4 Plane Poiseuille Flows -- 9.5 ``Wall Turbulent´´ Flows -- References -- Chapter 10: Thermodynamics of Turbulence -- 10.1 Introduction -- 10.1.1 Microscopic and Macroscopic Theories -- 10.1.2 Langevin and Fokker-Planck Equations -- 10.1.3 Reduction of the Degrees of Freedom by Scaling -- 10.1.4 Different Thermodynamic Concepts -- 10.2 A Brief Review of Some Essentials of Boltzmann-Gibbs Thermodynamics -- 10.3 Kraichnan´s BG Equilibrium Thermodynamics of 2-d and 3-d Turbulent Fields -- 10.4 An Introduction to the Nonextensive Thermodynamics of Tsallis -- 10.5 Relation Between Lévy Statistics and Tsallis Nonextensive Thermodynamics -- 10.6 Escort Probability Distribution and Expectation Values -- 10.7 Generalized Thermodynamic Potentials -- 10.8 Fractional Calculus: A Promising Future-Oriented Method to Describe Turbulence -- 10.9 Jackson´s Fractional Derivative and the DQTM. , 10.10 Beck-Tsallis Thermodynamics of Turbulence -- 10.11 Fractional Generalization of Kraichnan´s Energy-Enstrophy Spectrum and its Validation by Numerical Experiments -- 10.12 Velocity Structure Functions -- 10.13 Justification of the Quadratic Form of the Energy as a Function of Space and Velocity Coordinates -- 10.14 A Generalized Temperature of Turbulence -- 10.15 Final Discussion on Nonextensive Thermodynamics of Turbulence -- References -- Chapter 11: Turbulence: A Cooperative Phenomenon -- 11.1 Introduction -- 11.2 Cooperative Phenomena -- 11.2.1 What is a Critical or a Cooperative Phenomenon? -- 11.2.2 Stress and Order Parameter -- 11.2.3 Symmetry Breaking -- 11.2.4 Response Functions and Critical Exponents -- 11.2.5 Pair Correlation Function and Correlation Length -- 11.2.6 Universality: Yes or No ? -- 11.2.7 Turbulent Phase Transition with its Two Phases -- 11.3 Mean Field Theory of a Paramagnetic to Ferromagnetic Phase Transition -- 11.4 Mean Field Theory of Turbulence -- 11.5 First Experiments for a Qualitative Comparison -- 11.6 Discussion of Results -- References -- Chapter 12: Conclusions and Outlook -- References -- Correction to: Turbulence: A Cooperative Phenomenon -- Correction to: Chapter 11 in: P. W. Egolf, K. Hutter, Nonlinear, Nonlocal and Fractional Turbulence, https://doi.org/10.1007/9... -- Correction to: Nonlinear, Nonlocal and Fractional Turbulence -- Correction to: P. W. Egolf, K. Hutter, Nonlinear, Nonlocal and Fractional Turbulence, https://doi.org/10.1007/978-3-030-26033-0 -- Appendices -- Appendix A: Normalization of Probability Distribution -- Appendix B: The Variance of Lévy Flight Processes -- Appendix C: The Structure Function -- Appendix D: Circular Mean Velocity Profile of Plane Turbulent Poiseuille Flows -- Appendix E: Fourier Transform for q-Generalized Energy Spectrum of Turbulent Flows -- References. , Author Index -- Subject Index.

Note: Intro -- Preface -- Fluid and Thermodynamics-Volume 1: Basic Fluid Mechanics -- Fluid and Thermodynamics-Volume 2: Advanced Fluid Mechanics and Thermodynamic Fundamentals -- Fluid and Thermodynamics-Volume 3: Structured and Multiphase Fluids -- Contents -- 21 Balance Laws of Continuous System -- 21.1 Classification of Continuous Systems -- 21.1.1 Balance Laws -- 21.1.2 Single Constituent Systems -- 21.1.3 Multiphase Continua and Mixtures -- 21.1.4 Boltzmann and Polar Continua -- 21.2 General Balance Laws for the Constituents -- 21.3 Balance Laws for the Mixture as a Whole -- 21.4 Summary -- 21.5 Discussion -- References -- 22 Kinematics of Classical and Cosserat Continua -- 22.1 Preamble -- 22.2 Classical Motion -- 22.3 Classical Deformation Measures -- 22.4 Micromotion -- 22.5 Extended Deformation Measures -- 22.6 Curvature Tensors -- 22.7 Velocity Gradient and Gyration Tensor -- 22.8 Natural Basis System -- 22.9 Deformation Measures Referred to the Natural Basis -- 22.10 Cosserat Deformation Tensors and Natural Bases -- 22.11 Balance of Micro-Inertia -- 22.12 Cosserats Book of 1909, Its Reception and Influence on the 20th Century and Beyond -- References -- 23 Thermodynamics of Class I and Class II Classical Mixtures -- 23.1 General Introduction -- 23.2 Diffusion of Tracers in a Classical Fluid -- 23.2.1 Basic Assumptions -- 23.2.2 Material Theory for Diffusion Processes -- 23.3 Saturated Mixture of Nonpolar Solid and Fluid Constituents -- 23.3.1 Motivation -- 23.3.2 Choice of the Material Class and Material Theory -- 23.3.3 Some Properties of Differential (Pfaffian) Forms -- 23.3.4 The Differential of the Entropy -- 23.3.5 Thermodynamic Equilibrium -- 23.3.6 Extension to Nonequilibrium States -- 23.4 Discussion -- References -- 24 Thermodynamics of Binary Solid-Fluid Cosserat Mixtures -- 24.1 Introductory Remarks. , 24.2 Thermodynamics of an Elastic Solid Plus a Viscoelastic Fluid -- 24.3 Evolution Equations for the Volume Fractions -- 24.4 Process Variables and Constitutive Functions -- 24.5 Handling of the Entropy Inequality -- 24.6 Detailed Exploitation of (24.23)-(24.43) -- 24.7 Behavior at and Near Thermodynamic Equilibrium -- 24.7.1 Equilibrium Helmholtz Free Energies -- 24.7.2 Equilibrium Implications -- 24.7.3 Exploitation of the Entropy Inequality in the Neighborhood of the Equilibrium -- 24.8 On Classes of Alternative Models -- 24.8.1 The Hybrid Model I (HMI) -- 24.8.2 The Hybrid Model II (HMII) -- 24.8.3 The Incompressible Model (IM) -- 24.9 Specification of the Material Behavior -- 24.9.1 Rules of Aequipresence and Phase Separation and Their Approximate use for a Binary Mixture -- 24.9.2 A Linear Model of Thermoelasticity of a Cosserat Single-Constituent Body -- 24.9.3 Elastic Energies for Isotropic Solid Boltzmann Bodies -- References -- 25 A Continuum Approach to Liquid Crystals-The Ericksen-Leslie-Parody Formulation -- 25.1 A Phenomenological View of Liquid Crystals -- 25.2 A Continuum Formulation of Nematic Liquid Crystals -- 25.2.1 General Physical Conservation Laws -- 25.2.2 Hydrostatics of Nematic Liquid Crystals -- 25.2.3 Hydrodynamics of Nematic Liquid Crystals -- 25.3 A Thermodynamic Theory for Nematic Liquid Crystals -- 25.3.1 Kinematics -- 25.3.2 Conservation Laws and Entropy Inequality -- 25.3.3 Constitutive Relations and Exploitation of the Entropy Principle -- 25.4 Thermodynamics of an Incompressible Liquid … -- 25.5 Explicit Constitutive Parameterizations -- 25.5.1 Frank's Parameterization of the Free Energy -- 25.5.2 Parameterization of the Nonequilibrium Stress, Intrinsic Director Body Force, and Heat Flux Vector -- 25.5.3 Parodi Relation for a Nematic Liquid Crystal -- 25.6 Solutions for Simple Flow Problems -- 25.6.1 Shear Flows. , 25.7 Discussion -- References -- 26 Nematic Liquid Crystals with Tensorial Order Parameters -- 26.1 Nematic Liquid Crystals with Tensorial Order Variables -- 26.1.1 Motivation and Literature Review -- 26.1.2 Variational Principle -- 26.1.3 Liquid Crystals with Tensorial Order Parameters and Dissipative Microstructure -- 26.2 Uniaxial Nematic Crystals -- 26.2.1 Introductory Note -- 26.2.2 Uniaxial Nematics with Constant Order Parameter -- 26.2.3 Leslie's Alternative Formulation for Uniaxial Nematics -- 26.2.4 Uniaxial Nematics with Variable Scalar Order Parameter -- 26.3 Nematic Liquid Crystals Based on a Rank-2 Alignment Tensor -- 26.3.1 Motivation -- 26.3.2 Lagrange-Rayleigh Theory of the Alignment Tensor -- 26.4 Discussion and Conclusions -- 26.4.1 Pereira Borgmeyer-Hess Theory -- 26.4.2 Elastic and Viscous Contributions -- 26.4.3 The Role of the Inertia of the Microrotation -- 26.A.1 Constraints of Coordinates -- 26.A.2 Generalized Coordinates -- 26.A.3 d'Alembert's Principle, Principle of Virtual Work -- 26.A.4 Derivation of the Lagrange Equations -- References -- 27 Multiphase Flows with Moving Interfaces and Contact Line-Balance Laws -- 27.1 Introduction -- 27.2 General Balance Equations for Physical Bulk, Surface, and Line Quantities -- 27.2.1 Integral Form of the General Balance Statement -- 27.2.2 Transport Theorems, Divergence Theorems, and Kinematics -- 27.2.3 Local Forms of the General Balance Statement -- 27.3 Specified Balance Equations -- 27.3.1 Conservations of Mass -- 27.3.2 Solute Transport -- 27.3.3 Balance of Linear Momentum -- 27.3.4 Balance of Angular Momentum -- 27.3.5 Conservation of Energy -- 27.3.6 Entropy Inequality -- 27.4 Implicit Representation of Phase Interfaces and Contact Line -- 27.5 One-Fluid Conservation Equations -- 27.6 Concluding Remarks -- References. , 28 Multiphase Flows with Moving Interfaces and Contact Line-Constitutive Modeling -- 28.1 Introduction -- 28.2 Thermodynamic Processes in a Boltzmann-Type Mixture -- 28.2.1 Balance Relations -- 28.2.2 Entropy Principle -- 28.3 Constitutive Relations for the Phase Interface -- 28.3.1 Constitutive Assumptions and Restrictions -- 28.3.2 Thermodynamic Equilibrium -- 28.3.3 Linear Theory for the Nonequilibrium Parts -- 28.4 Constitutive Relations for the Three-Phase Contact Line -- 28.4.1 Constitutive Assumptions and Restrictions -- 28.4.2 Thermodynamic Equilibrium -- 28.4.3 Linear Theory for the Nonequilibrium Parts -- 28.5 Constitutive Relations for Phase Interfaces with Memory -- 28.5.1 Evaluation of the Entropy Inequality -- 28.5.2 Thermodynamic Equilibrium -- 28.5.3 Isotropic Theory for the Dynamic Part -- 28.6 Closing Summary -- 28.7 Concluding Remarks -- References -- 29 A Granular Fluid as a Limit of a Binary Mixture Theory-Treated as a One-Constituent Goodman-Cowin-Type Material -- 29.1 Introduction -- 29.2 Thermodynamic Processes -- 29.2.1 Balance Relations -- 29.2.2 Entropy Inequality -- 29.3 Constitutive Relations -- 29.3.1 Constitutive Assumptions and Restrictions -- 29.3.2 Thermodynamic Equilibrium -- 29.3.3 Linear Theory for the Nonequilibrium Parts -- 29.4 Constitutive Equations for Special Granular Materials -- 29.5 Horizontal Shearing Flow Problem -- 29.5.1 Basis Equations and Boundary Conditions for Horizontal Shearing Flow -- 29.5.2 Numerical Method -- 29.5.3 Numerical Results -- 29.6 Inclined Gravity-Flow Problem -- 29.7 Vertical Channel-Flow Problems -- 29.8 Alternative Formulations -- 29.8.1 Fluid Models for Cohesionless Granular Materials with Internal Length Parameter -- 29.8.2 Application to Simple Shear, Plane Poiseuille, and Gravity-Driven Flows -- 29.9 Concluding Remarks -- References. , 30 A Granular Mixture Model with Goodman-Cowin-Type Microstructure and its Application to Shearing Flows in Binary Solid-Fluid Bodies -- 30.1 Introduction -- 30.2 Thermodynamic Considerations -- 30.2.1 Balance Relations -- 30.2.2 Entropy Principle -- 30.3 Constitutive Modeling -- 30.3.1 Constitutive Equations -- 30.3.2 Thermodynamic Equilibrium -- 30.4 Saturated Solid-Fluid Mixture with Incompressible Constituents -- 30.5 Horizontal Shearing Flow Problem -- 30.5.1 Basic Equations and Boundary Conditions for Horizontal Shearing Flows -- 30.5.2 Numerical Method -- 30.5.3 Numerical Results -- 30.6 Concluding Remarks -- References -- 31 Modeling of Turbulence in Rapid Granular Flows -- 31.1 Introduction -- 31.2 Laminar Motions -- 31.3 Turbulent Motions -- 31.4 Entropy Principle -- 31.5 Exploitation of the Entropy Inequality -- 31.6 Restriction to the Laminar Case -- 31.7 Thermodynamic Equilibrium -- 31.8 Linear Deviations from Thermodynamic Equilibrium in Dynamic Processes -- 31.9 Discussion and Conclusions -- References -- List of Biographies -- Name Index -- Subject Index.

Note: Intro -- Preface -- Fluid and Thermodynamics -- Fluid and Thermodynamics -- Contents -- 11 Creeping Motion Around Spheres at Rest in a Newtonian Fluid -- 11.1 Motivation -- 11.2 Mathematical Preliminaries -- 11.3 Stokes Flow Around a Stagnant Sphere -- 11.3.1 Rigid Sphere and No-Slip Condition on the Surface of the Sphere -- 11.3.2 Cunningham's Correction -- 11.3.3 Rigid Infinitely Thin Spherical Shell Filled with a Fluid of Different Viscosity -- 11.4 Oseen's TheoryFor a brief biography of Carl Wilhelm Oseen, see Fig. 11.8. -- 11.4.1 Governing Equations of the Oseen Theory -- 11.4.2 Construction of a Particular Integral of (11.58) -- 11.4.3 `Stokes-Lets' and `Oseen-Lets' -- 11.5 Theory of Lagerstöm and Kaplun -- 11.5.1 Motivation -- 11.5.2 Stokes Expansion -- 11.5.3 Oseen Expansion -- 11.5.4 Matching Procedure -- 11.6 Homotopy Analysis Method---The Viscous Drag Coefficient Computed for Arbitrary Reynolds Numbers -- 11.6.1 The Mathematical Concept -- 11.6.2 Selection of ψ0, mathcalH, hbar and Approximate Solution -- 11.7 Conclusions and Discussion -- References -- 12 Three-Dimensional Creeping Flow--- Systematic Derivation of the Shallow Flow Approximations -- 12.1 Introductory Motivation -- 12.2 Model Equations -- 12.2.1 Field Equations -- 12.2.2 Boundary Conditions -- 12.3 Scaling Procedure -- 12.4 Lowest Order Model Equations for Flow Down Steep Slopes (Strong Steep Slope Shallow Flow Approximation) -- 12.5 A Slightly More General Steep Slope Shallow Flow Approximation (Weak Steep Slope Shallow Flow Approximation) -- 12.6 Phenomenological Expressions for Creeping Glacier Ice -- 12.7 Applications to Downhill Creeping Flows -- 12.7.1 Computational Procedure -- 12.7.2 Profiles and Flows for Isothermal Conditions -- 12.7.3 Remarks for Use of the Shallow Flow Approximation for Alpine Glaciers. , 12.8 Free-Surface Gravity-Driven Creep Flow of a Very Viscous Body with Strong Thermomechanical Coupling---A Rigorous Derivation of the Shallow Ice Approximation -- 12.8.1 The Classical Shallow Flow Approximation -- 12.8.2 Applications -- 12.9 Discussion and Conclusions -- References -- 13 Shallow Rapid Granular Avalanches -- 13.1 Introduction -- 13.2 Distinctive Properties of Granular Materials -- 13.2.1 Dilatancy -- 13.2.2 Cohesion -- 13.2.3 Lubrication -- 13.2.4 Liquefaction -- 13.2.5 Segregation, Inverse Grading, Brazil Nut Effect -- 13.3 Shallow Flow Avalanche Modeling -- 13.3.1 Voellmy's Avalanche Model -- 13.3.2 The SH Model, Reduced to Its Essentials -- 13.4 A Three-Dimensional Granular Avalanche Model -- 13.4.1 Field Equations -- 13.4.2 Curvilinear CoordinatesIn this section and henceforth knowledge of the basic elements of tensor calculus are supposed known. There is a great number of books on this e.g. R. Bowenaut]Bowen and C.C. Wangaut]Wang [7], I.S. Sokolnikoffaut]Sokolnikoff [76], E. Klingbeilaut]Klingbeil [48], L. Brillouinaut]Brillouin [8]. -- 13.4.3 Equations in Dimensionless Form -- 13.4.4 Kinematic Boundary Conditions -- 13.4.5 Traction Free Condition at the Free Surface -- 13.4.6 Coulomb Sliding Law at the Base -- 13.4.7 Depth Integration -- 13.4.8 Ordering Relations -- 13.4.9 Closure Property -- 13.4.10 Nearly Uniform Flow Profile -- 13.4.11 Summary of the Two-Dimensional SH Equations -- 13.4.12 Standard Form of the Differential Equations -- 13.5 Avalanche Simulation and Verification with Experimental Laboratory Data -- 13.5.1 Introduction -- 13.5.2 Classical and High Resolution Shock Capturing Numerical Methods -- 13.6 Attempts of Model Validation and Verification of Earthquake and Typhoon Induced Landslides -- References -- 14 Uniqueness and Stability -- 14.1 Introduction -- 14.2 Kinetic Energy of the Difference Motion. , 14.3 Uniqueness -- 14.4 Stability -- 14.5 Energy Stability of the Laminar Channel Flow -- 14.6 Linear Stability Analysis of Laminar Channel Flow -- 14.6.1 Basic Concepts -- 14.6.2 The Orr--Sommerfeld and the Rayleigh Equations -- 14.6.3 The Eigenvalue Problem -- References -- 15 Turbulent Modeling -- 15.1 A Primer on Turbulent Motions -- 15.1.1 Averages and Fluctuations -- 15.1.2 Filters -- 15.1.3 Reynolds Versus Favre Averages -- 15.2 Balance Equations for the Averaged Fields -- 15.3 Turbulent Closure Relations -- 15.3.1 Reynolds Stress Hypothesis and Turbulent Dissipation Rate -- 15.3.2 Averaged Density Field ρ -- 15.3.3 Turbulent Heat Flux qt and Turbulent Species Mass Flux jt -- 15.3.4 One- and Two-Equation Models -- 15.4 k-ε Model for Density Preserving and Boussinesq Fluids -- 15.4.1 The Balance Equations -- 15.4.2 Boussinesq Fluid Referred to a Non-inertial Frame -- 15.4.3 Summary of the k - ε Equations -- 15.4.4 Boundary Conditions -- 15.4.5 Closing Remarks -- References -- 16 Turbulent Mixing Length Models and Their Applications to Elementary Flow Configurations -- 16.1 Motivation/Introduction -- 16.2 The Turbulent Plane Wake -- 16.3 The Axisymmetric Isothermal Steady Jet -- 16.4 Turbulent Round Jet in a Parallel Co-flow -- 16.5 A Study of Turbulent Plane Poiseuille Flow -- 16.6 Discussion -- References -- 17 Thermodynamics---Fundamentals -- 17.1 Concepts and Some Historical Remarks -- 17.2 General Notions and Definitions -- 17.2.1 Thermodynamic System -- 17.2.2 Thermodynamic States, Thermodynamic Processes -- 17.2.3 Extensive, Intensive, Specific and Molar State Variables -- 17.2.4 Adiabatic and Diathermic Walls -- 17.2.5 Empirical Temperature, Gas Temperature and Temperature Scales -- 17.3 Thermal Equations of State -- 17.3.1 Ideal Gas -- 17.3.2 Real Gases -- 17.3.3 The Phenomenological Model of van der Waals. , 17.4 Reversible and Irreversible Thermodynamic Processes -- 17.4.1 Diffusion -- 17.4.2 Reversible Expansion and Compaction of a Gas -- 17.5 First Law of Thermodynamics -- 17.5.1 Mechanical Energies -- 17.5.2 Definitions, Important for the First Law -- 17.5.3 Caloric Equations of State for Fluids and Gases -- 17.5.4 Simple Applications of the First Law -- 17.5.5 Specific Heats of Real Gases -- 17.6 The Second Law of Thermodynamics---Principle of Irreversibility -- 17.6.1 Preamble -- 17.6.2 The Second Law for Simple Adiabatic Systems -- 17.6.3 Generalizations for Non-adiabatic Systems -- 17.7 First Applications of the Second Law of Thermodynamics -- References -- 18 Thermodynamics---Field Formulation -- 18.1 The Second Law of Thermodynamics for Continuous Systems -- 18.2 Two Popular Forms of the Entropy Principle -- 18.2.1 Entropy Principle 1: Clausius--Duhem Inequality -- 18.2.2 Entropy Principle of Ingo MüllerIngo Müller ( ast1936), a physicist- engineer with doctorate (1966) and habilitation (1971) from the Technische Hochschule Aachen, is among the rational thermodynamicists, who was chiefly involved in research to generalize the entropy principle, to make it more flexible and better apt for thermodynamic processes than the Clausius--Duhem inequality with its absolute temperature and the a priori estimate of the entropy flux asq/T. This is seen already in his -- 18.3 Thermal and Caloric Equations of State -- 18.3.1 Canonical Equations of State -- 18.3.2 Specific Heats and Other Thermodynamic Quantities -- 18.3.3 Application to Ideal Gases -- 18.3.4 Isentropic Processes in Caloric Ideal Gases -- 18.4 Thermodynamics of an Inviscid, Heat Conducting -- 18.4.1 The Coleman-Noll Approach -- 18.4.2 The Rational Thermodynamics of Ingo Müller -- References -- 19 Gas Dynamics -- 19.1 Introductory Remarks. , 19.2 Propagation of Small Perturbations in a Gas -- 19.2.1 Fundamental Equations -- 19.2.2 Plane and Spherical Waves -- 19.2.3 Eigen Oscillations Determined with Bernoulli's Method -- 19.3 Steady, Isentropic Stream Filament Theory -- 19.4 Theory of Shocks -- 19.4.1 General Concepts -- 19.4.2 Jump Conditions -- 19.4.3 Stationary Shocks in Simple Fluids Under Adiabatic Conditions -- 19.5 Final Remarks -- References -- 20 Dimensional Analysis, Similitude and Physical Experiments at Laboratory Scale -- 20.1 Introductory MotivationThe topic presented here in this chapter is a popular theme in fluid mechanics and is the subject of several books, e.g., G.I. Barenblattaut]Barenblatt [1], Henry Görtleraut]Gortler@Görtler [17], H.L. Langhaaraut]Langhaar [26], Joseph Spurkaut]Spurk [40], K. Hutteraut]Hutter and K. Jöhnkaut]Johnk@Jöhnk [20] and others. A mathematical theory, based on a system of axioms with an extensive list of related references is given by D.E. Carlsonaut]Carlson [13, 14]. -- 20.1.1 Dimensional Analysis -- 20.1.2 Similitude and Model ExperimentsFrom K. Hutteraut]Hutter et al.: Physics of Lakes, Vol. 3 [21], pp. 313--314. -- 20.1.3 Systems of Physical Entities -- 20.2 Theory of Dimensional Equations -- 20.2.1 Dimensional Homogeneity -- 20.2.2 Buckingham's Theorem -- 20.2.3 A Set of Examples from Fluid Mechanics -- 20.3 Theory of Physical Models -- 20.3.1 Analysis of the Downscaling of Physical Processes -- 20.3.2 Applications -- 20.4 Model Theory and Differential Equations -- 20.4.1 Avalanching Motions down Curved and Inclined Surfaces -- 20.4.2 Navier--Stokes--Fourier--Fick Equations -- 20.4.3 Non-dimensionalization of the NSFF Equations -- 20.5 Discussion and Conclusions -- References -- List of Biographies -- Name Index -- Subject Index.