流体力学建模

本书是一部讲述近代流体力学成果的英文专著，本书认为数学方法和模型是应用数学和理论物理学的分支。本书致力于阐释流体力学建模的相关内容，由四章组成，其中包含大量有用的练习和解决方案。我们在每章末尾的参考书目中提供了相关主题的相对完整的参考资料。

Foreword Preface 1 Mathematical Background 1.1 Dynamical systems 1.1.1 Vector felds and dynamical systems 1.1.2 Critical points in phase space 1.1.3 Higher-order autonomous systems 1.1.4 Dirac delta function 1.1.5 Special functions 1.1.6 Green's function 1.1.7 Boundary and initial value problems 1.2 Asymptotic behavior and stability 1.2.1 Asymptotic expansions 1.2.2 Asymptotic behavior of autonomous systems 1.2.3 Stability of autonomous systems 1.2.4 More on stability 1.3 Bifurcations 1.3.1 Instability and bifurcations 1.3.2 Saddle-node bifurcation 1.3.3 Transcritical and pitchfork bifurcations 1.3.4 Hopf bifurcation 1.3.5 Saddle-node bifurcation of a periodic orbit 1.3.6 Global bifurcation 1.4 Attractors 1.4.1 Chaotic motion and symbolic dynamics 1.4.2 Homoclinic tangles and Smale's horseshoe map 1.4.3 Poincaré return map 1.4.4 Lyapunov's exponents and entropy 1.4.5 Attracting sets and attractors 1.5 Fractals 1.5.1 Local structure of fractals 1.5.2 Operations with fractals 1.5.3 Fractal attractors in dynamical systems 1.6 Perturbations 1.6.1 Regular perturbation theory 1.6.2 Singular perturbation theory 1.7 Elements of tensor analysis 1.7.1 Transformations of coordinate systems 1.7.2 Covariant and contravariant derivatives 1.7.3 Christoffel symbols and curvature tensor 1.7.4 Integral formulas 1.8 Navier-Stokes equations for nonequilibrium gas mixture 1.8.1 Continuity,momentum and energy equations 1.8.2 Closing relations and transport coefficients 1.8.3 Boundary conditions 1.8.4 Deducing Navier-Stokes equation 1.8.5 Estence and uniqueness of solutions of the Navier—Stokes equation 1.8.6 Relativistic Navier—Stokes equation 1.9 Exercises bliography 2 Models for Hydrodynamic Instabilities 2.1 Stability concepts 2.1.1 Boundary conditions 2.1.2 Inviscid and high-Reynolds—number flow 2.1.3 Basic definitions 2.2 Rayleigh—Taylor instability 2.2.1 Potential flow 2.2.2 Plane boundaries 2.2.3 Spherical boundaries 2.2.4 Nonlinear perturbation theory 2.2.5 Inhomogeneous fluids 2.2.6 Ⅵscous fluids 2.3 Kelvin-Helmholtz instability 2.3.1 Instability of annular inpressible jet 2.3.2 Rotating jets 2.3.3 Supersonic viscous jet 2.3.4 Supersonic viscous jet with Gaussian sound velocity distribution 2.3.5 Relativistic jet 2.4 Exercises bliography 3 Models for Turbulence 3.1 Symmetries and conservation laws 3.1.1 Euler and Navier—Stokes equations 3.1.2 Symmetries 3.1.3 Conservation laws 3.2 Anomalous scaling exponents 3.2.1 Multifractal models 3.2.2 Random variables and correlation functions 3.2.3 Richardson-Kolmogorov concept of turbulence 3.2.4 Scaling of the structure hmctions 3.2.5 Dissipative and dynamical scaling 3.2.6 Fusion rules in turbulence systems 3.3 Calculation of scaling exponents 3.3.1 Basic formulas 3.4 Bifurcations for the Kuramoto-Sivashinsky equation 3.4.1 Symmetry：translations, reflections, and O(2)-equivariance 3.4.2 Kuramoto-Sivashinsky equation 3.5 Strange attractors and turbulence 3.5.1 The Taylor—Couette experiment 3.5.2 Dynamical systems with one observable 3.5.3 Limit capacity and dimension 3.5.4 Dimension and entropy 3.6 Global attractor for Navier-Stokes equation 3.6.1 The ladder inequality 3.6.2 Estimates 3.6.3 Length scales in the two-dimensional case 3.6.4 Three-dimensional regularity 3.6.5 The attractor dimension 3.7 Hierarchical sheU models 3.7.1 Gledzer-Ohkitani-Yamada shell model 3.7.2 (N，￡)-sabra shell models 3.7.3 Navier-Stokes equations in the mon wavelets representation 3.8 Entropy principle maximum 3.8.1 Entropy and probability 3.8.2 Derivation of the motion equations 3.8.3 The hierarchical dynamical system 3.8.4 Fokker-Planck equation 3.9 Appendix: inequalities 3.10 Exercises Bibliography 4 Modeling of Flow over Blunted Bodies 4.1 Onsager's theory 4.1.1 General concept of a multi-component gas mixture 4.1.2 Thermodynamic potentials, forces and flows 4.1.3 Closing relations 4.2 Governing equations for hypersonic viscous gas flow 4.2.1 Conditons on the surface of discontinuity 4.2.2 Governing parameters 4.2.3 Transformation of initial equations 4.3 Flow regimes for hypersonic viscous gas flow 4.3.1 Viscous shock layer 4.3.2 Vortex intersection, nonstrong and strong injection 4.3.3 Boundary layer, nonstrong and strong injection 4.3.4 Boundary layer and strong struction 4.4 Shock wave structure 4.4.1 Outer sublayer 4.4.2 Middle sublayer 4.4.3 Inner sublayer 4.5 Viscous shock layer 4.5.1 Main equations 4.5.2 Generalized Rankine-Hugoniot conditions at the shock wave 4.6 Models for shock sublayers 4.6.1 Inviscid shock and boundary layers 4.6.2 Injection gas layer 4.6.3 Viscous boundary and mixing gas layers 4.6.4 Viscous boundary layer with strong suction 4.6.5 Flow at viscous boundary layer 4.7 Flow at injection gas layer 4.7.1 General stagnation point 4.7.2 Wings at incidence at slipping angles 4.7.3 Flow over swirling axisymmetric bodies 4.8 Nonuniform flow at inviscid shock layer 4.8.1 Nonuniform flow of the far-wake type 4.8.2 Upstream swirling flow over axisymmetric bodies 4.9 Exercises Bibliography Index 编辑手记

伊戈尔·盖辛斯基（Igor Gaissinski），以色列数学家，以色列理工大学航空工程学院高级研究员；弗拉基米尔·罗文斯基（Vladimir Rovenski），以色列数学家，以色列理工大学数学系教授。

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