A unified model for periodic non-linear dispersive waves in intermediate and shallow water

Journal of Coastal Research

Volumn 15, Issue 1, 1999, Pages 128-139

  Karambas, Theofanis V ^a  

^a ARISTOTLE UNIVERSITY OF THESSALONIKI   (Greece)

Author keywords

Boussinesq equations; Numerical model; Wave theory

Indexed keywords

NONLINEAR WAVE; WAVE PROPAGATION;

EID: 0032948470     PISSN: 07490208     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (39)

1. ABBOTT, M.B.; PETERSEN, H.M., and SKOVGAARD, O., 1978. On the numerical modelling of short waves in shallow waters. Journal Hydraulic Research, 16(3), 173-204.
2. ABBOTT, M.B.; MCCOWAN, A.D., and WARREN, I.R., 1984. Accuracy of short-wave numerical models. Journal Hydraulic Engineering, V 110 (10) 1287-1301.
3. BERKHOFF, J.C.W.; BOOY N., and RADDER A.C., 1982. Verification of numerical wave propagation models for simple harmonic linear water waves. Coastal Engineering, 6, 255-279.
4. BUHR, H.J. and SVENDSEN I.A., 1979. Regular Waves in Shoaling Water Experimental Data. Series Paper 21, Institute of Hydrodynamics and Hydraulic Engineering, Technical University of Denmark.
5. CHAPALAIN, G.; COINTE, R., and TEMPERVILLE, A., 1992. Observed and modeled resonantly interacting progressine water-waves. Coastal Engineering, 16, 267-300.
6. CHAPLIN, J.R., 1980. Development of stream-function wave theory. Coastal Engineering, 3, 179-205.
7. COPELAND, G.J.M., 1985. A Practical alternative to the mild-slope equation. Coastal Engineering, 9, 125-149.
8. DINGEMANS, M.W., 1993. Comparison of computations with Boussinesq-like models and laboratory measurements. MAST-G8 Coastal Morphodynamics, Overall Workshop, pp 1.7.
9. DINGEMANS, M.W., 1997. Water Wave Propagation Over Uneven Bottoms. World Scientific.
10. EAGLESON, P.S. and DEAN R.G., 1966. Small amplitude wave theory. In: A. T. Ippen (ed.), Estuary and Coastline Hydrodynamics. New York: McGraw-Hill.
11. HAUGEL, A., 1980. A Numerical model of storm waves in shallow water. Proceedings 17th Conference of Coastal Engineering (ASCE).
12. HUANG M-C, 1990. Kinematics prediction by Stokes and Fourier wave theories. Journal of Waterway, Port, Coastal and Ocean Eng., 116 (1), 137-148.
13. ITO, Y. and TANIMOTO, K., 1972. A Method of Numerical Analysis of Wave Propagation - Application to Wave Diffraction and Refraction. Proceedings 13th Conference of Coastal Engineering (ASCE), pp. 503-522.
14. KARAMBAS, TH. V.; KRESTENITIS, Y., and KOUTITAS, C., 1990. A numerical solution of Boussinesq equations in the inshore zone. Hydrosoft, Vol 3(1), pp 34-37.
15. KARAMBAS, TH. V., 1991. Mathematical Model of Non-linear Dispersive Wave Propagation in the Inshore Zone, Ph. D. Thesis, Aristotle University of Thessaloniki, Department Civil Engineering (in Greek).
16. KARAMBAS, TH. V. and KOUTITAS, C., 1992. A breaking wave propagation model based on the Boussinesq equations. Coastal Engineering, 18, 1-19.
17. KINSMAN, B., 1984. Wind Waves. Englewood Cliffs, New Jersey: Prentice-Hall.
18. LE MEAUTE, B.; DIVOKY, D. and LIN, A., 1968. Shallow water waves: a comparison of theories and experiments. Proceedings 11th Conference of Coastal Engineering (ASCE), pp 86-107.
19. MADSEN, P.A. and WARREN, I.R., 1983. Performance of a numerical short-wave model. Coastal Engineering, 8, 73-93.
20. MADSEN, P.A.; MURRAY, R., and SORENSEN, O.R., 1991. A new form of the Boussinesq equations with improved linear dispersion characteristics. Coastal Engineering, 15, 371-388.
21. MADSEN, P.A. and SORENSEN, O.R., 1992. A new form of the Boussinesq equations with improved linear dispersion characteristics. Part 2. A slowly-varying bathymetry. Coastal Engineering, 18, 183-204.
22. MADSEN, P.A. and SORENSEN, O.R., 1993. Bound waves and trial interactions in shallow water. Ocean Engineering, 20, (4), 359-388.
23. MATSOUKIS, P.F., 1986. The Development of a Finite Difference Model for the Propagation of Storm Waves in Shallow Waters. Hydraulics Research Wallingford, Report No SR 80.
24. MCDONALD, B.E. and WITTING, J.M., 1984. A conservation law related to Kelvin's circulation theorem. Journal Computational Physics, 56, 237-243.
25. MEI, C.C., 1983. The Applied Dynamics of Ocean Surface Waves. New York: Wiley.
26. NEVES, R.J.J. and SILVA A.J.R., 1988. A non-linear model for surface waves. In: Schrefler and Zienkiewicz, (eds.) Computer Modelling in Ocean Engineering. Balkema, pp. 107-113.
27. NWOGU, O., 1993. Alternative form of Boussinesq equations for nearshore wave propagation. Journal of Waterway, Port, Coastal and Ocean Eng., 119, (6), 618-638.
28. PEREGRINE, D.H., 1967. Long waves on a beach. Journal Fluid Mechanics 29, 815-827.
29. PEREGRINE, D.H., 1972. Equations for water waves and the approximation behind them. Waves on Beaches and Resulting Sediment Transport, New York: Academic.
30. SCHAFFER, H.A. and MADSEN, P.A., 1995. Further enhancements of Boussinesq-type equations. Coastal Engineering, 26, 1-14.
31. SERRE, F., 1953. Contribution a l'etude des ecoulements permanents et variables dans les canaux. La Houille Blanche, 8, 830-872.
32. SHIELDS, J.J. and WEBSTER, W.C., 1988. On direct methods in water-wave theory. Journal Fluid Mechanics 197, 171-199.
33. STEFFLER, P.M. and JIN, Y-C, 1993. Depth averaged and moment equations for moderately shallow free surface flow. Journal Hydraulic Research, 31(1), 5-17.
34. STIVE, M.J.F., 1983. Two-dimensional breaking of waves on a beach. Report M 1585, Delft Hydraulics Laboratory.
35. WATANABE, A. and MARUYAMA, K., 1986. Numerical modeling of nearshore wave field under combined refraction, diffraction and breaking. Coastal Engineering in Japan, 29, 19-39.
36. WEI, G. and KIRBY, J.T., 1995. Time-dependent numerical code for extended Boussinesq equations. Journal of Waterway, Port, Coastal and Ocean Engineering, 121(5), 251-261.
37. WEI, G.; KIRBY, J.T.; GRILLI S.T., and SUBRAMANYA R., 1995. A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves. Journal of Fluid Mechanics, 294, 71-92.
38. WITTING, J.M., 1984. A unified model for the evolution of nonlinear water waves. Journal Computational Physics, 56, 203-236.
39. YASUDA, T.; YAMASHITA, T.; GOTO, S., and TSUCHIYA, Y., 1982. Numerical calculation for wave shoaling on a sloping bottom by K-dV equation. Coastal Engineering in Japan, 25, 1-23.