Mathematical Modelling of Short Waves in Surf Zone

  • Th. Karambas
  • Chr. Koutitas
Part of the NATO ASI Series book series (NSSE, volume 178)

Abstract

A numerical model for the propagation of breaking waves is developed. Using an apropriate F.D. scheme in the solution of BOUSSINESQ type of equations, a third-order accuracy is obtained, without the need of including the additional SERRE terms.

By providing the above equations with a suitable dissipative mechanism by introducing a dispersion term (using the Boussinesq eddy viscosity concept), we are able to simulate breaking waves. In this way it is possible to compute both the dissipation of the wave height and set-up, and in the 2-D case, the longshore currents. In the above cases the radiation stresses are genarated automatically.

Keywords

Wave Height Eddy Viscosity Breaking Wave Hydraulic Jump Surf Zone 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Basco, D.R. (1985). ‘A qualitative description of wave breaking’ J.Waterw.Fort Coastal Eng. ASCE 111: 171–188.CrossRefGoogle Scholar
  2. Battjes,J.A. (1975) ‘Modeling of turbulence in the surf zone’, Proc. Symp. Modeling Techniques, ASCE pp 1050–1061.Google Scholar
  3. Battjes, J.A. and Janssen, J.P.F.M. (1978). ‘Energy loss and set-up due to breaking of random waves’ Proc. 16th Int. Conf. Coastal Eng., ASCE pp 569–587.Google Scholar
  4. Battjes, J.A. and Sakai T. (1980) ‘Velocity field in a steady breaker’, Proc. 17th Int. Conf. Coastal Eng., ASCE pp 498–511.Google Scholar
  5. Battjes, J.A. (1986) Energy dissipation in breaking solitary and periodic waves, Communications on hydraulic and geotechnical engineering, TU Delft Report nr 86–6.Google Scholar
  6. Battjes, J.A. (1988) ‘Surf-zone dynamics’, Ann. Rev. Fluid Mech. 20: 257–293.CrossRefGoogle Scholar
  7. Dally, W.R., Dean R.G. and Dalrymple R.A. (1984) ‘A model for breaker decay on beaches’ Proc. 19th Int. Conf. Coastal Eng., ASCE pp 82–98.Google Scholar
  8. Goda, U. (1970), A synthesis of breaker indices, Trans. Jap. Soc. Civil Eng., vol 180, pp 39–49 (in Japanesse)Google Scholar
  9. Horikawa, K. and Kuo C.T. (1966), ‘A study on wave transformation inside surf zone’, Proc. 10th Int. Conf. Coastal Eng., ASCE pp 69–81.Google Scholar
  10. Johns, B (1980) ‘tThe modelling of the approach of bores to a shoreline’, Coastal Engineering, 3: 207–219.CrossRefGoogle Scholar
  11. Koutitas C., (1988), Mathematical Models in Coastal Engineering Pentech Press.Google Scholar
  12. Madsen, P.A, and Svendsen, I.A. (1983) ‘Turbulent bores and hydraulic jumps’, J. Fluid Mech. vol. 129, pp 1–25.CrossRefMATHGoogle Scholar
  13. Mizugushi, M. (1980) ‘An heuristic model of wave height distribution in surf zone’. Proc. 17th Int. Conf. Coastal Eng., ASCE pp 278–289.Google Scholar
  14. Mizugushi, M. (1986) ‘Experimental study on kinematics and dynamics of wave-breaking’ Proc. 20th Int. conf. Coastal Eng., ASCE pp 589–603.Google Scholar
  15. Peregrine, E.H. (1972) ‘Equations for waters waves and approximations behind them’ Waves on Beaches and Resulting Sediment Transport’ (ed R.E. Meyer) Academic PressGoogle Scholar
  16. Peregrine, D.H. and Svendsen, I.A. (1978) ‘Spilling breakers, bores and hydraulic jumps’, Proc. 16th Int. conf. Coastal Eng., ASCE pp 540–550.Google Scholar
  17. Rodi W., (1980) Turbulence models and their application in hydraulics, IAHR.Google Scholar
  18. Rosenberg, D.U. (1969) Methods for the Solution of Differential Equations, Elsevier N.Y.MATHGoogle Scholar
  19. Sakai, S., Hiyamizu, K., Saeki, H. (1986), ‘wave height decay model within a surf zone’, Proc. 20th Int. Conf. Coastal Eng., ASCE pp 686–696Google Scholar
  20. Stive, M.J.F. (1980) ‘Velocity and pressure field of spilling breakers’, Proc. 17th Int. conf. Coastal Eng., ASCE pp 547–566.Google Scholar
  21. Stive, M.J.F. and Wind, H.G. (1982) ‘A study of radiation stress and set-up in the nearshore region’, Coastal Engineering, 6: 1–25.CrossRefGoogle Scholar
  22. Stive, M.J.F. (1984) ‘Energy dissipation in waves breaking on gentle slopes’, Coastal Engineering, 8: 99–127.CrossRefGoogle Scholar
  23. Svendsen, I.A., Madsen, P.A. and Hansen J.B. (1978) ‘Wave characteristics in the surf zone’, Proc. 16th Int. Conf. Coastal Eng., ASCE pp 520–539.Google Scholar
  24. Svendsen, I.A., Madsen, P.A (1984) ‘A turbulent bore on a beach’ J. Fluid Mech. vol. 148, pp 73–96CrossRefMATHGoogle Scholar
  25. Svendsen, I.A. (1984) ‘Wave heights and set-up in a surf zone’ Coastal Engineering, 8: 303–329.CrossRefGoogle Scholar
  26. Svendsen, I.A. (1987) ‘Analysis of surf zone turbulence’, J. of Geophysical Research, vol. 92, no C5, pp 5115–5124.CrossRefGoogle Scholar
  27. Tennekes, H. and Lumley, J.L. (1972), A First Course in Turbulence, The MIT Press, pp 104–145.Google Scholar
  28. Uasuda, T., Goto, Sh. and Tsuchiya, I. (1982), ‘0n the relation between changes in intergral quantities of shoaling waves and breaking inception’, Proc. 18th Int. Conf. Coastal Eng., ASCE pp 23–37.Google Scholar
  29. Yasuda, T., Yamashita, T., Goto, Sh. and Tsuchiya, Y. (1982), ‘Numerical calculations for wave shoaling on a sloping bottom by K-dV equation’, Coastal Eng. in Japan, JSCE, Vol. 25.Google Scholar

Copyright information

© Kluwer Academic Publisher 1990

Authors and Affiliations

  • Th. Karambas
    • 1
  • Chr. Koutitas
    • 1
  1. 1.Division of Hydraulics and Environmental Engineering, Department of Civil EngineeringAristotle University of ThessalonikiGreece

Personalised recommendations