RIVER WAVES 



M. J. Lighthill 

 Manchester University 



CONTENTS 



Page 



1 . Introduction 17 



2. Frequency dispersion and amplitude dispersion 18 



3. Gravity waves of small amplitude 18 



4. Capillary waves 19 



5. Viscous attenuation 20 



6. Wave-making resistance to two-dimensional obstacles 20 



7. Stationary waves on non-uniform streams 20 



8. Three-dimensional wave pattern due to an obstacle 21 



9. Waves of greatest height 23 



1 0. Amplitude dispersion 24 



1 1 . Cnoidal waves and the solitary wave 24 



12. Occurrence of hydraulic jumps in steady flow 25 



13. Mechanics of energy loss in bores 26 



14. Cnoidal wave trains behind bores 27 



15. Energy-momentum diagram for steady flows 28 



16. Attenuation of long waves by turbulent friction 29 



17. Conditions for the formation of tidal bores 30 



18. Effect of friction on the downstream propagation of flood waves 31 



19. Kinematic waves 32 



20. Other fields of application of kinematic wave theory 33 



21 . Kinematic shock waves 34 



22. A new method for calculating flows with kinematic shock waves 34 



23. Mechanisms governing the flow-concentration relation 36 



24. Reversed-flow regions in steady river flow 36 



25. Improvements of kinematic wave theory 37 



26. Roll waves 38 



27. Conclusion 39 



7. Introduction 



There are few pastimes more pleasant than water-watching, and fortunately 

 most people live near enough to some river or stream to be able to enjoy it. Like 

 other aesthetic pleasures, this is one that is greatly enhanced if one makes an effort 

 to learn something of the underlying causes and effects. My aim in this lecture is to 

 describe the results of reading and thinking undertaken in this spirit, and combined 



17 



