Topics in Fluid Mechanics
The book offers a novel but unified treatment of an established subject. It presents each topic as part of a wider class of problems so that a unity of concepts is emphasized over a unity of material. The authors aim for simplicity in presentation, stressing physical understanding over mathematical development. Specialized subjects such as chaotic advection, chaos and the onset of turbulence—problems that are being tackled in research and industry now—are given particular attention.
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This book offers a novel but unified treatment of an established subject. Rather than describe the standard topics in fluid mechanics in traditional form, the book presents each topic as part of a wider class of problems so that a unity of concepts is emphasized over a unity of material.
PrefaceNotation1Basic Concepts11.1Continuum11.2Description of fluid motion11.3Pathlines, streaklines, and streamlines31.4Example of flow lines41.5Visualization of streamlines, pathlines, and streaklines61.6Basic equations for an inviscid fluid72Toward a Constitutive Law for Fluid Materials132.2Volume forces and surface forces acting on a fluid132.3Representation of surface forces by the stress tensor142.4The equations of motion192.5Preliminary remarks on the internal properties of continuous media212.6The Navier-Stokes equations252.7Generalized Newtonian fluids312.8Memory effects342.9Influence of scaling on the description of a physical phenomenon403Vorticity Laws453.2Crocco's theorem463.3Basic equations473.4The vorticity flux across a closed surface is null513.5Three theorems on the development of vortex lines543.6The velocity field deduced from the vorticity field613.7Implications of the vortex theory in complex computations664Fundamental Concepts of Turbulence774.2A statistical approach to turbulent flow814.3The scaling of turbulence904.4Global behavior of turbulent boundary layers1014.5The concept of boundary layer in turbulent flows: Case of the free jet1125Dynamical Systems and Chaotic Advection1215.2Dynamical systems1225.3Quantifying chaos1265.4Strange attractors and the Lorenz system1315.5Chaos in fluids1336Chaos and the Onset of Turbulence1416.1Hamiltorian systems and dissipative systems1416.2Routes to turbulence1426.3Routes to chaos1446.4Chaos quantification1496.5Application to fluid mechanics1557Boundary Layer Theory1637.2Introduction to development of flow with vorticity1647.3Boundary layer approximation1677.4The mathematical structure of the equations1707.5An introduction to singular perturbation1757.6The boundary layer equations1807.7Coupled phenomena1927.8Combustion problems in fluid mechanics1987.9Three-dimensional boundary layers2078Wave Propagation2118.2Sound waves2128.3Surface disturbances and wave speed2158.4Internal waves2188.5Pressure wave in an elastic duct2248.6Alfven waves2268.7Wave scattering due to turbulence2338.8Waves of finite amplitude2389Fundamentals of Classical Thermodynamics2419.2The first law of thermodynamics2469.3The second law of thermodynamics2539.4The energy equation at a point263App. A: The concept of "objective time derivatives"275App. B: Partial differential equations of mathematical physics281App. C: Perturbation theory301Index319
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