| 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 |
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