Introduction to Mathematical Fluid Dynamics

Preface Acknowlegments 1 Kinematics 1 Introduction 2 Lagrangian description 3 Eulerian description 4 Conservation of mass 5 Circulation 6 Some potential flows 7 Vorticity 8 Line vortex 9 Vortex sheet 2 Momentum Principle and Ideal Fluid 10 Conservation of linear momentum 11 Mixing and lift 12 Equations of motion 13 D'Alembert's theorem 14 Kelvin's theorem 15 Conservation of angular momentum 3 Newtonian Fluid 16 The Couette experiment 17 Constitutive equation 18 Kinetic theory 19 Some viscous fluid motions 4 Fluids of Small Viscosity 20 Reynolds number 21 A singular perturbation example 22 Limit equations for the flat plate 23 Discussion of Blasius' solution 24 Limit equations with pressure gradient and wall curvature 25 Similarity solutions 26 Momentum integral 27 Separation 28 Wake 5 Some Aspects of Rotating Fluids 29 Bjerknes' theorem 30 Rossby number 31 Ekman layer 32 Taylor-Proudman theorem 6 Some Effects of Compressibility 33 Thermodynamic state 34 Flow initiation 35 Conservation of energy 36 Shock relations 37 Shock structure 38 Navier-Stokes equations Bibliography Index