River Flow

  • Andrew Fowler
Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 36)


Chapter 4, the shortest in the book, deals with river flow modelling, and centres round the St. Venant equations and their variants: in particular, short wave and long wave approximations, which give rise to the shallow water equations and slowly-varying flow, respectively. Waves are discussed, including the monoclinal flood wave, and there are substantial discussions of roll waves and tidal bores.


Friction Factor Reynolds Stress Froude Number Overland Flow Shallow Water Equation 
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  1. Abbott MR, Lighthill MJ (1956) A theory of the propagation of bores in channels and rivers. Math Proc Camb Philos Soc 52:344–362 MATHCrossRefGoogle Scholar
  2. Balmforth NJ, Mandre S (2004) Dynamics of roll waves. J Fluid Mech 514:1–33 MATHCrossRefMathSciNetGoogle Scholar
  3. Benjamin TB, Bona JL, Mahony JJ (1972) Model equations for long waves in nonlinear dispersive systems. Philos Trans R Soc Lond A 272:47–78 MATHCrossRefMathSciNetGoogle Scholar
  4. Chanson H (2005) Physical modelling of the flow field in an undular tidal bore. J Hydraul Res 43:234–244 CrossRefGoogle Scholar
  5. Chanson H (2009) Current knowledge in hydraulic jumps and related phenomena A survey of experimental results. Eur J Mech B, Fluids 28:191–210 MATHCrossRefMathSciNetGoogle Scholar
  6. Chorley RJ (ed) (1969) Introduction to physical hydrology. Methuen, London Google Scholar
  7. Chow VT (1959) Open-channel hydraulics. McGraw-Hill, New York Google Scholar
  8. Dressler RF (1949) Mathematical solution of the problem of roll waves in inclined open channels. Commun Pure Appl Math 2:149–194 MATHCrossRefMathSciNetGoogle Scholar
  9. Fowler AC (1997) Mathematical models in the applied sciences. Cambridge University Press, Cambridge Google Scholar
  10. French RH (1994) Open-channel hydraulics. McGraw-Hill, New York Google Scholar
  11. Jeffreys H (1925) The flow of water in an inclined channel of rectangular section. Philos Mag 49:793–807 Google Scholar
  12. Lynch DK (1982) Tidal bores. Sci Am 247:131–143 CrossRefGoogle Scholar
  13. Needham DJ, Merkin JH (1984) On roll waves down an open inclined channel. Proc R Soc Lond A 394:259–278 MATHCrossRefGoogle Scholar
  14. Ockendon H, Ockendon JR (2004) Waves and compressible flow. Springer, New York MATHGoogle Scholar
  15. Peregrine DH (1966) Calculations of the development of an undular bore. J Fluid Mech 25:321–330 CrossRefGoogle Scholar
  16. Pugh DT (1987) Tides, surges and mean sea-level. Wiley, Chichester Google Scholar
  17. Rayleigh, Lord (1908) Note on tidal bores. Proc R Soc Lond A 81:448–449 MATHCrossRefGoogle Scholar
  18. Richards K (1982) Rivers: form and process in alluvial channels. Methuen, London Google Scholar
  19. Rowbotham F (1970) The Severn bore, 2nd edn. David and Charles, Newton Abbot Google Scholar
  20. Stoker JJ (1957) Water waves: the mathematical theory with applications. Interscience, New York MATHGoogle Scholar
  21. Su MD, Xu X, Zhu JL, Hon YC (2001) Numerical simulation of tidal bore in Hangzhou Gulf and Qiantangjiang. Int J Numer Methods Fluids 36:205–247 MATHCrossRefGoogle Scholar
  22. Tricker RAR (1965) Bores, breakers, waves and wakes. Elsevier, New York Google Scholar
  23. Ward RC, Robinson M (2000) Principles of hydrology, 4th edn. McGraw-Hill, New York Google Scholar
  24. Whitham GB (1974) Linear and nonlinear waves. Wiley, New York MATHGoogle Scholar
  25. Wolanski E, Williams D, Spagnol S, Chanson H (2004) Undular tidal bore dynamics in the Daly Estuary, Northern Australia. Estuar Coast Shelf Sci 60:629–636 CrossRefGoogle Scholar
  26. Yu J, Kevorkian J (1992) Nonlinear evolution of small disturbances into roll waves in an inclined open channel. J Fluid Mech 243:575–594 MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.MACSI, Department of Mathematics & StatisticsUniversity of LimerickLimerickIreland

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