超声流和激波

Ⅰ. Compressible Fluids

1. Qualitative differences between linear and nonlinear waves

　A. General Equations of Flow. Thermodynamic Notions

　　2. The medium

　　3. Ideal gases, polytropic gases, and media with separable energy

　　4. Mathematical comments on ideal gases

　　5. Solids which do not satisfy Hooke's law

　　6. Discrete media

　　7. Differential equations of motion

　　8. Conservation of energy

　　9. Enthalpy

　 10. Isentropic flow. Steady flow. Subsonic and supersonic flow

　 11. Acoustic approximation

　 12. Vector form of the flow equations

　 13. Conservation of circulation. Irrotational flow. Poten-tial

　14. Bernoulli's law

　 15. Limit speed and critical speed

　B. Differential Equations for Specific Types of Flow

　16. Steady flows

　 17. Non-steady flows

　18. Lagrange's equations of motion for one-dimensional and spherical flow

Appendix--Wave Motion in Shallow Water

　 19. Shallow water theory

Ⅱ. Mathematical Theory of Hyperbolic Flow Equations for Functions of Two Variables

20. Flow equations involving two functions of two variables..

21. Differential equations of second order type

22. Characteristic curves and characteristic equations

23. Characteristic equations for specific problems

24. The initial value problem. Domain of dependence.Range of influence

25. Propagation of discontinuities along characteristic lines..

26. Characteristic lines as separation lines between regions of different types

27. Characteristic initial values

28. Supplementary remarks about boundary data

29. Simple waves. Flow adjacent to a region of constant state

30. The hodograph transformation and its singularities.Limiting lines

31. Systems of more than two differential equations

　Appendix

　32. General remarks about differential equations for func-

tions of more than two independent variables.Char-acteristic surfaces

Ⅲ. One-Dimensional Flow

33. Problems of one-dimensional flow

A. Continuous Flow

　34. Characteristics

　 35. Domain of dependence. Range of influence

　 36. More general initial data

　 37. Riemann invariants

　 38. Integration of the differential equations of isentropic flow

　 39. Remarks on the Lagrangian representation

B. Rarefaction and Compression Waves

　40. Simple waves

　 41. Distortion of the wave form in a simple wave

　 42. Particle paths and cross-characteristics in a simple wave

　 43. Rarefaction waves

　 44. Escape speed. Complete and incomplete rarefaction waves

　45. Centered rarefaction waves

　 46. Explicit formulas for centered rarefaction waves

　 47. Remark on simple waves in Lagrangian coordinates

　 48. Compression waves

Appendix to Part B

　49. Position of the envelope and its cusp in a compression wave

C. Shacks

　 50. The shock as an irreversible process

　51. Historical remarks on non-linear flow

　 52. Discontinuity surfaces

　 53. Basic model of discontinuous motion. Shock wave in a tube

　……

Ⅳ.Isentropic Irrotational Steady Plane Flow

Ⅴ.Folw in Noxxies and Jets

Ⅵ.Folw in Three Dimensions

Bibligraphy

Index of Sybmols

Subjuct Index