http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
UPSO (University Press Scholarship Online)
Cover; Fluid Mechanics: A Geometrical Point of View; Copyright; Dedication; Preface; Acknowledgments; Contents; List of figures; 1. Vector Fields; 1.1 The velocity field; 1.2 Space-time approach; 1.3 Eulerian vs Lagrangian picture; 1.4 Integral curves; 1.5 The method of characteristics; 1.6 Conservation law; 1.7 Densities vs scalars; 1.8 Steady flows; 1.9 Incompressible flow; 1.10 Irrotational flow; 1.11 Irrotational and incompressible flow; 1.12 Jacobi matrix; 1.13 Flow near a fixed point; 2. Euler's Equations; 2.1 Conservation of momentum; 2.2 The stress tensor; 2.3 Incompressible flow
2.4 Conservation of energy2.5 Helmholtz equation; 2.6 Steady flows; 2.7 Equations of state; 2.7.1 Constant temperature; 2.7.2 Constant entropy; 2.8 Transport form of Euler's equation; 2.9 Linearization of Euler's equations: sound; 2.10 Inviscid Burgers equation; 2.11 Scale invariance; 2.11.1 The role of boundary conditions; 2.12 d'Alembert's paradox: limitations the ideal fluid model; 3. The Navier-Stokes Equations; 3.1 Viscosity; 3.2 Viscous incompressible flow; 3.3 Dissipation of energy at constant density; 3.4 Dissipation of energy for compressible flows
3.5 Scale invariance: Reynolds number3.6 Navier-Stokes in curvilinear coordinates; 3.7 Diffusion and advection; 3.8 The diffusion kernel; 3.9 Growth of entropy in diffusion; 3.10 The advection-diffusion kernel; 4. Ideal Fluid Flows; 4.1 Statics; 4.2 Solutions of Laplace's equation; 4.2.1 A sphere moving through a fluid; 4.2.2 Flow past a wedge; 4.3 Complex analytic methods; 4.4 Fluid with a stirrer; 4.4.1 Fluid in the upper half-plane with a stirrer; 4.4.2 Stirrer inside a circle; 4.5 Flow past a cylinder; 4.6 The d'Alembert paradox; 4.7 Joukowski airfoil; 4.8 Surface waves; 5. Viscous Flows
5.1 Pipe Poiseuille flow5.2 Circular Couette flow; 5.3 Stokes flow; 5.4 Stokes flow past a sphere; 5.5 Vortex with dissipating core; 6. Shocks; 6.1 The Burgers equations; 6.2 The Cole-Hopf transformation; 6.3 The limit of small viscosity; 6.4 Maxwell-Lax-Oleneik minimum principle; 6.4.1 The Cheshire cat; 6.5 The Riemann problem; 7. Boundary Layers; 7.1 Prandtl's theory; 7.2 The Blasius reduction; 7.3 Weyl's method; 7.4 Drag on a flat plate; 7.5 Limitations of boundary layer theory; 8. Instabilities; 8.1 The Rayleigh-Taylor instability; 8.2 Linearization of Navier-Stokes equations
8.2.1 Poiseuille and plane Couette flows8.3 Orr-Sommerfeld equation; 8.3.1 Linear stability of pipe Poiseuile flow; 8.4 Transient solutions of linear equations; 8.5 Normal operators; 8.6 A non-normal operator; 8.7 A nonlinear model with transients; 8.8 Stability regained; 8.9 Rapidly changing external force; 8.10 The Kapitza pendulum; 9. Integrable Models; 9.1 KdV; 9.2 The soliton solution; 9.3 Multi-soliton solutions; 9.4 Lax pair; 9.5 Hamiltonian formalism of Fadeev and Zakharov; 9.6 The hamiltonian formalism of Magri; 9.7 The vortex filament; 9.8 Geometry of curves
Includes bibliographical references and index.