HANDBUCH DER PHYSIK

HERAUSGEGEBEN VON

S. FLÜGGE

BAND IX

STRÖMUNGSMECHANIK III

MITHERAUSGEBER

C.TRUESDELL

MIT 248 FIGUREN

SPRINGER-VERLAG BERLIN . GÖTTINGEN • HEIDELBERG

1960

Contents. Page

Analytical Theory of Subsonic and Supersonic Flows. By Professor Dr. MENAHEM SCHIFFER, Dept. of Mathematics, Stanford University, California (USA.). (With 24 Figures) 1

Introduction 1

I. Physical and mathematical foundations 2

I I . Linearized theory 26

II I . The hodograph method 56

IV. The analytical theory of two-dimensional subsonic flows 92

V. The analytical theory of two-dimensional transonic flows 130

G e n e r a l r e f e r e n c e s a n d t e x t b o o k s 154

Theorie des ondes de choc. Par H E N R I CABANNES, Professeur de Mecanique Generale ä la Faculte des Sciences de Marseille (France). (Avec 59 Figures) 162

A. Les equations des phenomenes de choc 162 a) Introduction 162 b) Demonstration des equations des phenomenes de choc 165 c) Chocs stationnaires dans les ecoulements uniformes 168

B. Les ondes de choc dans les ecoulements stationnaires 170

I. La formation des ondes de choc 171

II . Les ondes de choc detachees 174

II I . Les ondes de choc attachees dans les ecoulements plans 180 a) Etude des chocs uniformes 180 b) Ecoulement autour d'un obstacle termine par un diedre 182 c) Ecoulement autour d'une ogive 185

IV. Les ondes de choc attachees dans les ecoulements к trois dimensions . . . . 188 a) Ecoulements coniques de revolution 188 b) Ecoulements de revolution 189 c) Ecoulements coniques 192

C. Les ondes de choc dans les ecoulements non stationnaires 195 I. Formation et propagation des ondes de choc planes 196

a) Etude des chocs uniformes 196 b) Exemples de chocs non uniformes 200 c) La formation des chocs dans les tuyeres 203

II . Rencontre d'une onde de choc plane et d'un diedre 204 a) Cas de la reflexion reguliere 204 b) Cas de la reflexion de MACH 206 c) Etude de Г ecoulement apres le choc . 209

I I I . Etude des ondes de choc spheriques 211 IV. Etude des translations rectilignes de vitesse variable 214

Annexe. Propagation des chocs dans les gaz ionises 220 B i b l i o g r a p h i e 221

V I Contents

Page

Theory of Characteristics of Inviscid Gas Dynamics. By RICHARD E. MEYER, Pro­fessor of Applied Mathematics, Brown University, Providence, R.I. (U.S.A.). (With 44 Figures) 225

A. Introduction 225

B. One-dimensional unsteady motion 228

I. Homentropic motion 228 a) Characteristic equations and simple waves 228 b) Structure of the motion 231 c) Solution of the general wave-interaction problem 237

II . Motion with entropy variation 240

C. Steady two-dimensional supersonic flow 249

I. Homentropic irrotational flow 249 a) Characteristic equations and simple waves 249 b) Structure of the flow 255 c) Analytical solution methods 268

II . Flow with entropy variation 272

D. Steady axially symmetrical supersonic flow . 274

Appendix 282

R e f e r e n c e s 282

Linearized Theory of Unsteady Flow of a Compressible Fluid. By Professor Dr. R. TIMMAN, Technische Hogeschool, Insti tuut voor Toegepaste Wiskunde, Afdeling der Algemene Wetenschappen, Delft (Netherlands). (With 5 Figures) 283

I. Formulation of the problem 283

II . Explicit solutions 291 a) Subsonic case 291 b) Applications 294

II I . The method of integral equations 299

IV. Reciprocity relations 307

R e f e r e n c e s 309

Jets and Cavities. By DAVID GILBARG, Professor of Mathematics, Stanford University,

Stanford, California (USA.). (With 60 Figures) 311

I. Physical and mathematical foundations 311

II . Particular flows 326 a) The hodograph method 326 b) The method of reflection 347 c) Inverse and semi-inverse solutions 350 d) Approximate theories 363

II I . Qualitative theory 368 a) Geometric properties of free streamlines 371 b) Comparison methods 380 c) Variational principles 387

IV. Existence and uniqueness theory 391 a) Existence theory 391 b) Uniqueness theory 406

V. Numerical methods 415 a) Plane flows past curved obstacles 416 b) Axially symmetric flows 421

General references 438

B i b l i o g r a p h y 438

Contents VII Page

Surface Waves. By JOHN VROOMAN WEHAUSEN, Ph. D., Professor of Engineering Science and EDMUND V. LAITONE, Professor of Aeronautical Science, University of California, Berkeley, California (USA). (With 56 Figures) 446

A. Introduction 446

B. Mathematical formulation 447 1. Coordinate systems and conventions 447 2. Equations of motion 448 3. Boundary conditions at an interface 451 4. Boundary conditions on rigid surfaces 454 5. Other types of boundary surfaces 455

C. Preliminary remarks and developments 455 6. Classification of problems 455 7. Progressive waves and wave velocity —standing waves 456 8. Energy 458 9. Momentum 461

10. Expansion of solutions in powers of a parameter 461

D. Theory of infinitesimal waves 469 11. The fundamental equations 469 12. Other boundary conditions 471 13. Some mathematical solutions 472 14. Some simple physical solutions 495 15. Group velocity and the propagation of disturbances and of energy 506 16. The solution of special boundary problems 522 17. Two-dimensional progressive and standing waves in unbounded regions with

fixed boundaries 525 18. Three-dimensional progressive and standing waves in unbounded regions with

fixed boundaries 542 19. Problems with steadily oscillating boundaries 553 20. Motions which may be treated as steady flows 568 21. Waves resulting from pressure distributions 592 22. Initial-value problems 603 23. Waves in basins of bounded extent 620 24. Gravity waves in the presence of surface tension 631 25. Waves in a viscous fluid 638 26. Stability of free surfaces and interfaces 646 27. Higher-order theory of infinitesimal waves 653

E. Shallow-water waves 667

28. The fundamental equations for the first approximation 667 29. The linearized shallow-water theory 668 30. Nonlinear shallow-water theory 676 31. Higher-order theories and the solitary and cnoidal waves 701

F. Exact solutions 714 32. Some general theorems 715 33. Waves of maximum amplitude 731 34. Explicit solutions 736 35. Existence theorems 749

G. B i b l i o g r a p h y 758

Sachverzeichnis (Deutsch-Englisch) 779

Subject Index (English-German) 797

Table des matieres (Francais) 815