Barenblatt G.I. Flow, deformation and fracture: lectures on fluid mechanics and the mechanics of deformable solids for mathematicians and physicists (Cambridge, 2014). - ОГЛАВЛЕНИЕ / CONTENTS

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ОбложкаBarenblatt G.I. Flow, deformation and fracture: lectures on fluid mechanics and the mechanics of deformable solids for mathematicians and physicists. - Cambridge: Cambridge university press, 2014. - xix, 55 p.: ill. - (Cambridge texts in applied mathematics). - Bibliogr.: p.243-252. - Ind.: p.253-255. - ISBN 978-0-521-88752-6
 

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Оглавление / Contents
 
Foreword ....................................................... xi
Preface ...................................................... xiii
Introduction .................................................... 1
1  Idealized continuous media: the basic concepts .............. 10
   1.1  The idealized model of a continuous medium ............. 10
   1.2  Properties of a continuum and its motion. Density,
        flux and velocity. Law of mass balance ................. 18
   1.3  Law of momentum balance. Stress tensor ................. 24
2  Dimensional analysis and physical similitude ................ 29
   2.1  Examples ............................................... 29
   2.2  Dimensional analysis ................................... 37
   2.3  Physical similitude .................................... 40
   2.4  Examples. Classical parameters of similitude ........... 43
3  The ideal incompressible fluid approximation: general
   concepts and relations ...................................... 48
   3.1  The fundamental idealization (model). Euler equations .. 48
   3.2  Decomposition of the velocity field in the vicinity
        of an arbitrary point. The vorticity. The strain-rate
        tensor ................................................. 51
   3.3  Irrotational motions. Lagrange's theorem. Potential
        flows .................................................. 53
   3.4  Lagrange-Cauchy integral. Bernoulli integral ........... 56
   3.5  Plane potential motions of an ideal incompressible
        fluid .................................................. 58
4  The ideal incompressible fluid approximation: analysis
   and applications ............................................ 63
   4.1  Physical meaning of the velocity potential. The
        Lavrentiev problem of a directed explosion ............. 63
   4.2  Lift force on a wing ................................... 66
5  The linear elastic solid approximation. Basic equations
   and boundary value problems in the linear theory of
   elasticity .................................................. 79
   5.1  The fundamental idealization ........................... 79
   5.2  Basic equations and boundary conditions of the linear
        theory of elasticity ................................... 86
   5.3  Plane problem in the theory of elasticity .............. 89
   5.4  Analytical solutions of some special problems in
        plane elasticity ....................................... 95
6  The linear elastic solid approximation. Applications:
   brittle and quasi-brittle fracture; strength of
   structures ................................................. 101
   6.1  The problem of structural integrity ................... 101
   6.2  Defects and cracks .................................... 102
   6.3  Cohesion crack model .................................. 109
   6.4  What is fracture from the mathematical viewpoint? ..... 113
   6.5  Time effects; lifetime of a structure; fatigue ........ 119
7  The Newtonian viscous fluid approximation. General
   comments and basic relations ............................... 124
   7.1  The fundamental idealization. The Navier-Stokes
        equations ............................................. 124
   7.2  Angular momentum conservation law ..................... 128
   7.3  Boundary value and initial value problems for the
        Newtonian viscous incompressible fluid approximation.
        Smoothness of the solutions ........................... 129
   7.4  The viscous dissipation of mechanical energy into
        heat .................................................. 135
8  The Newtonian viscous fluid approximation. Applications:
   the boundary layer ......................................... 137
   8.1  The drag on a moving wing. Friedrichs'example ......... 137
   8.2  Model of the boundary layer at a thin weakly
        inclined wing of infinite span ........................ 140
   8.3  The boundary layer on a flat plate .................... 143
9  Advanced similarity methods: complete and incomplete
   similarity ................................................. 150
   9.1  Examples .............................................. 150
   9.2  Complete and incomplete similarity .................... 153
   9.3  Self-similar solutions of the first and second kind ... 157
   9.4  Incomplete similarity in fatigue experiments (Paris'
        law) .................................................. 158
   9.5  A note concerning scaling laws in nanomechanics ....... 161
10 The ideal gas approximation. Sound waves; shoclc waves ..... 164
   10.1 Sound waves ........................................... 164
   10.2 Energy equation. The basic equations of the ideal
        gas model ............................................. 167
   10.3 Simple waves. The formation of shock waves ............ 168
   10.4 An intense explosion at a plane interface: the
        external intermediate asymptotics ..................... 171
   10.5 An intense explosion at a plane interface: the
        internal intermediate asymptotics ..................... 173
11 Tbrbulence: generalities; scaling laws for shear flows ..... 182
   11.1 Kolmogorov's example .................................. 185
   11.2 The Reynolds equation. Reynolds stress ................ 187
   11.3 Turbulent shear flow .................................. 189
   11.4 Scaling laws for turbulent flows at very large
        Reynolds numbers. Flow in pipes ....................... 190
   11.5 Turbulent flow in pipes at very large Reynolds
        numbers: advanced similarity analysis ................. 195
   11.6 Reynolds-number dependence of the drag in pipes
        following from the power law .......................... 201
   11.7 Further comparison of the Reynolds-number-dependent
        scaling law and the universal logarithmic law ......... 204
   11.8 Modification of the Izakson-Millikan-von Mises
        analysis of the flow in the intermediate region ....... 208
   11.9 Further comparison of scaling laws with experimental
        data .................................................. 211
   11.10 Scaling laws for turbulent boundary layers ........... 219
12 Turbulence: mathematical models of turbulent shear flows
   and of the local structure of turbulent flows at very
   large Reynolds numbers ..................................... 225
   12.1 Basic equations for wall-bounded turbulent shear
        flows. Wall region .................................... 225
   12.2 Kolmogorov-Prandtl semi-empirical model for the wall
        region of a shear flow ................................ 227
   12.3 A model for drag reduction by polymeric additives ..... 230
   12.4 The local structure of turbulent flows at very large
        Reynolds numbers ...................................... 234
Bibliography and References ................................... 243
Index ......................................................... 253


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