Keywords:
Thermodynamics.
;
Electronic books.
Type of Medium:
Online Resource
Pages:
1 online resource (647 pages)
Edition:
1st ed.
ISBN:
9783319336367
Series Statement:
Advances in Geophysical and Environmental Mechanics and Mathematics Series
URL:
https://ebookcentral.proquest.com/lib/geomar/detail.action?docID=4602515
DDC:
620.106
Language:
English
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.
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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.
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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.
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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.
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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.
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