Theory and applications of viscous fluid flows /

Theory and applications of viscous fluid flows /

Saved in:
Bibliographic Details
Author / Creator:Zeytounian, R. Kh. (Radyadour Kh.), 1928-
Imprint:Berlin ; New York : Springer, c2004.
Description:xv, 488 p. : ill. ; 24 cm.
Language:English
Subject:
Viscous flow.
Fluid dynamics.
Fluid dynamics.
Viscous flow.
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/4999965
Hidden Bibliographic Details
ISBN:3540440135 (alk. paper)
Notes:Includes bibliographical references (p. [449]-483) and index.
Table of Contents:
  • Introduction
  • 1. Navier-Stokes-Fourier Exact Model
  • 1.1. The Transport Theorem
  • 1.2. The Equation of Continuity
  • 1.3. The Cauchy Equation of Motion
  • 1.4. The Constitutive Equations of a Viscous Fluid
  • 1.4.1. Stokes's Four Postulates: Stokesian Fluid
  • 1.4.2. Classical Linear Viscosity Theory: Newtonian Fluid
  • 1.5. The Energy Equation and Fourier's Law
  • 1.5.1. The Total Energy Equation
  • 1.5.2. Heat Conduction and Fourier's Law
  • 1.6. The Navier-Stokes-Fourier Equations
  • 1.6.1. The NSF Equation for an Ideal Gas when C v and C p are Constants
  • 1.6.2. Dimensionless NSF Equations
  • 1.6.3. Reduced Dimensionless Parameters
  • 1.7. Conditions for Unsteady-State NSF Equations
  • 1.7.1. The Problem of Initial Conditions
  • 1.7.2. Boundary Conditions
  • 2. Some Features and Various Forms of NSF Equations
  • 2.1. Isentropicity, Polytropic Gas, Barotropic Motion, and Incompressibility
  • 2.1.1. NS Equations
  • 2.1.2. Navier System
  • 2.1.3. Navier System with Time-Dependent Density
  • 2.1.4. Fourier Equation
  • 2.2. Some Interesting Issues in Navier Incompressible Fluid Flow
  • 2.2.1. The Pressure Poisson Equation
  • 2.2.2. ¿ N − ¿ N and u N − ¿ N Formulations
  • 2.2.3. The Omnipotence of the Incompressibility Constraint
  • 2.2.4. A First Statement of a Well-Posed Initial Boundary-Value Problem (IBVP) for Navier Equations
  • 2.2.5. Cauchy Formula for Vorticity
  • 2.2.6. The Navier Equations as an Evolutionary Equation for Perturbations
  • 2.3. From NSF to Hyposonic and Oberbeck-Boussinesq (OB) Equations
  • 2.3.1. Model Equations for Hyposonic Fluid Flows
  • 2.3.2. The Oberbeck-Boussinesq Model Equations
  • 3. Some Simple Examples of Navier, NS and NSF Viscous Fluid Flows
  • 3.1. Plane Poiseuille Flow and the Orr-Sommerfeld Equation
  • 3.1.1. The Orr-Sommerfeld Equation
  • 3.1.2. A Double-Scale Technique for Resolving the Orr-Sommerfeld Equation
  • 3.2. Steady Flow Through an Arbitrary Cylinder under Pressure
  • 3.2.1. The Case of a Circular Cylinder
  • 3.2.2. The Case of an Annular Region Between Concentric Cylinders
  • 3.2.3. The Case of a Cylinder of Arbitrary Section
  • 3.3. Steady-State Couette Flow Between Cylinders in Relative Motion
  • 3.3.1. The Classic Taylor Problem
  • 3.3.2. The Taylor Number
  • 3.4. The Bénard Linear Problem and Thermal Instability
  • 3.5. The Bénard Linear Problem with a Free Surface and the Marangoni Effect
  • 3.5.1. The Case when the Neutral State is Stationary
  • 3.5.2. Free-Surface Deformation
  • 3.6. Flow due to a Rotating Disc
  • 3.6.1. Small Values of ¿
  • 3.6.2. Large Values of ¿
  • 3.6.3. Joining (Matching)
  • 3.7. One-Dimensional Unsteady-State NSF Equations and the Rayleigh Problem
  • 3.7.1. Small M 2 Solution - Close to the Flat Plate but far from the Initial Time
  • 3.7.2. Small M 2 Solution - Far from a Flat Plate
  • 3.7.3. Small M 2 Solution - Close to the Initial Time
  • 3.8. Complementary Remarks
  • 4. The Limit of Very Large Reynolds Numbers
  • 4.1. Introduction
  • 4.2. Classical Hierarchical Boundary-Layer Concept and Regular Coupling
  • 4.2.1. A 2-D Steady-State Navier Equation for the Stream Function
  • 4.2.2. A Local Form of the 2-D Steady-State Navier Equation for the Stream Function
  • 4.2.3. A Large Reynolds Number and "Principal" and "Local" Approximations
  • 4.2.4. Matching
  • 4.2.5. The Prandtl-Blasius and Blasius BL Problems
  • 4.3. Asymptotic Structure of Unsteady-State NSF Equations at Re ≫ 1
  • 4.3.1. Four Significant Degeneracies of NSF Equations
  • 4.3.2. Formulation of a Simplified Initial Boundary-Value Problem for the NSF Full Unsteady-State Equations
  • 4.3.3. Various Facets of Large Reynolds Number Unsteady-State Flow
  • 4.3.4. The Two Adjustment Problems
  • 4.4. The Triple-Deck Concept and Singular Interactive Coupling
  • 4.4.1. The Triple-Deck Theory in 2-D Steady-State Navier Flow
  • 4.5. Complementary Remarks
  • 4.5.1. Three-Dimensional Boundary-Layer Equations
  • 4.5.2. Unsteady-State Incompressible Boundary-Layer Formulation
  • 4.5.3. The Inviscid Limit: Some Mathematical Results
  • 4.5.4. Rigorous Results for the Boundary-Layer Theory
  • 5. The Limit of Very Low Reynolds Numbers
  • 5.1. Large Viscosity Limits and Stokes and Oseen Equations
  • 5.1.1. Steady-State Stokes Equation
  • 5.1.2. Unsteady-State Oseen Equation
  • 5.1.3. Unsteady-State Stokes and Steady-State Oseen Equations
  • 5.1.4. Unsteady-State Matched Stokes-Oseen Solution at Re ≪ 1 for the Flow Past a Sphere
  • 5.2. Low Reynolds Number Flow due to an Impulsively Started Circular Cylinder
  • 5.2.1. Formulation of the Steady-State Problem
  • 5.2.2. The Unsteady-State Problem
  • 5.3. Compressible Flow
  • 5.3.1. The Stokes Limiting Case and Steady-State Compressible Stokes Equations
  • 5.3.2. The Oseen Limiting Case and Steady-State Compressible Oseen Equations
  • 5.4. Film Flow on a Rotating Disc: Asymptotic Analysis for Small Re
  • 5.4.1. Solution for Small Re ≪ 1: Long-Time Scale Analysis
  • 5.4.2. Solution for Small Re ≪ 1: Short-Time Scale Analysis
  • 5.5. Some Rigorous Mathematical Results
  • 6. Incompressible Limit: Low Mach Number Asymptotics
  • 6.1. Introduction
  • 6.2. Navier-Fourier Asymptotic Model
  • 6.2.1. The Initialization Problem and Equations of Acoustics
  • 6.2.2. The Fourier Model
  • 6.2.3. Influence of Weak Compressibility: Second-Order Equations for u′ and ¿′
  • 6.2.4. Concluding Remarks
  • 6.3. Compressible Low Mach Number Models
  • 6.3.1. Hyposonic Model for Flow in a Bounded Cavity
  • 6.3.2. Large Channel Aspect Ratio, Low Mach Number, Compressible Flow
  • 6.4. Viscous Nonadiabatic Boussinesq Equations
  • 6.4.1. The Basic State
  • 6.4.2. Asymptotic Derivation of Viscous, Nonadiabatic Boussinesq Equations
  • 6.5. Some Comments
  • 7. Some Viscous Fluid Motions and Problems
  • 7.1. Oscillatory Viscous Incompressible Flow
  • 7.1.1. Acoustic Streaming Effect
  • 7.1.2. Study of the Steady-State Streaming Phenomenon
  • 7.1.3. The Role of Parameters ¿ Re = Re S and Re/¿ = ß 2
  • 7.1.4. Other Examples of Viscous Oscillatory Flow
  • 7.2. Unsteady-State Viscous, Incompressible Flow past a Rotating and Translating Cylinder
  • 7.2.1. Formulation of the Governing Problem
  • 7.2.2. Method of Solution
  • 7.2.3. Determination of the Initial Flow
  • 7.2.4. Results of Calculations and Comparison with the Visualization of Coutanceau and Ménard (1985)
  • 7.2.5. A Short Comment
  • 7.3. Ekman and Stewartson Layers
  • 7.3.1. General Equations and Boundary Conditions
  • 7.3.2. The Ekman Layer
  • 7.3.3. The Stewartson Layer
  • 7.3.4. The Inner, Outer, and Upper Regions
  • 7.3.5. Comments
  • 7.4. Low Reynolds Number Flows: Further Investigations
  • 7.4.1. Unsteady-State Adjustment to the Stokes Model in a Bounded Deformable Cavity ¿(t)
  • 7.4.2. On the Wake in Low Reynolds Number Flow
  • 7.4.3. Oscillatory Disturbances as Admissible Solutions and their Possible Relationship to the Von Karman Sheet Phenomenon
  • 7.4.4. Some References
  • 7.5. The Bénard-Marangoni Problem: An Alternative
  • 7.5.1. Dimensionless Dominant Equations
  • 7.5.2. Dimensionless Dominant Boundary Conditions
  • 7.5.3. The Rayleigh-Bénard (RB) Thermal Shallow Convection Problem
  • 7.5.4. The Bénard-Marangoni (BM) Problem
  • 7.6. Some Aspects of Nonadiabatic Viscous Atmospheric Flow
  • 7.6.1. The L-SSHV Equations
  • 7.6.2. The Tangent HV (THV) Equations
  • 7.6.3. The Quasi-Geostrophic Model
  • 7.7. Miscellaneous Topics
  • 7.7.1. The Entrainment of a Viscous Fluid in a Two-Dimensional Cavity
  • 7.7.2. Unsteady-State Boundary Layers
  • 7.7.3. Various Topics Related to Boundary-Layer Equations
  • 7.7.4. More on the Triple-Deck Theory
  • 7.7.5. Some Problems Related to Navier Equations for an Incompressible Viscous Fluid
  • 7.7.6. Low and Large Prandtl Number Flow
  • 7.7.7. A final comment
  • 8. Some Aspects of a Mathematically Rigorous Theory
  • 8.1. Classical, Weak, and Strong Solutions of the Navier Equations
  • 8.2. Galerkin Approximations and Weak Solutions of the Navier Equations
  • 8.2.1. Some Comments and Bibliographical Notes
  • 8.3. Rigorous Mathematical Results for Navier Incompressible and Viscous Fluid Flows
  • 8.3.1. Navier Equations in an Unbounded Domain
  • 8.3.2. Some Recent Rigorous Results
  • 8.4. Rigorous Mathematical Results for Compressible and Viscous Fluid Flows
  • 8.4.1. The Incompressible Limit
  • 8.5. Some Concluding Remarks
  • 9. Linear and Nonlinear Stability of Fluid Motion
  • 9.1. Some Aspects of the Theory of the Stability of Fluid Motion
  • 9.1.1. Linear, Weakly Nonlinear, Nonlinear, and Hydrodynamic Stability
  • 9.1.2. Reynolds-Orr, Energy, Sufficient Stability Criterion
  • 9.1.3. An Evolution Equation for Studying the Stability of a Basic Solution of Fluid Flow
  • 9.2. Fundamental Ideas on the Theory of the Stability of Fluid Motion
  • 9.2.1. Linear Case
  • 9.2.2. Nonlinear Case
  • 9.3. The Guiraud-Zeytounian Asymptotic Approach to Nonlinear Hydrodynamic Stability
  • 9.3.1. Linear Theory
  • 9.3.2. Nonlinear Theory - Confined Perturbations. Landau and Stuart Equations
  • 9.3.3. Nonlinear Theory - Unconfined Perturbations. General Setting
  • 9.3.4. Nonlinear Theory - Unconfined Perturbations. Tollmien-Schlichting Waves
  • 9.3.5. Nonlinear Theory - Unconfined Perturbations. Rayleigh-Bénard Convection
  • 9.4. Some Facets of the RB and BM Problem
  • 9.4.1. Rayleigh-Bénard Convective Instability
  • 9.4.2. Bénard-Marangoni (BM) Thermocapillary Instability Problem for a Thin Layer (Film) with a Deformable Free Surface
  • 9.5. Couette-Taylor Viscous Flow Between Two Rotating Cylinders
  • 9.5.1. A Short Survey
  • 9.5.2. Bifurcations
  • 9.6. Concluding Comments and Remarks
  • 10. A Finite-Dimensional Dynamical System Approach to Turbulence
  • 10.1. A Phenomenological Approach to Turbulence
  • 10.2. Bifurcations in Dissipative Dynamical Systems
  • 10.2.1. Normal Form of the Pitchfork Bifurcation
  • 10.2.2. Normal Form of the Hopf Bifurcation
  • 10.2.3. Bifurcation from a Periodic Orbit to an Invariant Torus
  • 10.3. Transition to Turbulence: Scenarios, Routes to Chaos
  • 10.3.1. The Landau-Hopf "Inadequate" Scenario
  • 10.3.2. The Ruelle-Takens-Newhouse Scenario
  • 10.3.3. The Feigenbaum Scenario
  • 10.3.4. The Pomeau-Manneville Scenario
  • 10.3.5. Complementary Remarks
  • 10.4. Strange Attractors for Various Fluid Flows
  • 10.4.1. Viscous Isochoric Wave Motions
  • 10.4.2. The Bénard-Marangoni Problem for a Free-Falling Vertical Film: The Case of Re = O(1) and the KS Equation
  • 10.4.3. The Bénard-Marangoni Problem for a Free-Falling Vertical Film: The Case of Re/¿ = O(1) and the KS-KdV Equation
  • 10.4.4. Viscous and Thermal Effects in a Simple Stratified Fluid Model
  • 10.4.5. Obukhov Discrete Cascade Systems for Developed Turbulence
  • 10.4.6. Unpredictability in Viscous Fluid Flow Between a Stationary and a Rotating Disk
  • 10.5. Some Comments and References
  • References
  • Index
The Ann and John Wilson Library Fund bookplate

Similar Items