A strongly-nonlinear model for water waves in water of variable depth-the irrotational Green-Naghdi model

Journal of Offshore Mechanics and Arctic Engineering

Volumn 125, Issue 1, 2003, Pages 25-32

  Kim, J W ^a   Bai, K J ^b   Ertekin, R C ^c   Webster, W C ^d  

^a AMERICAN BUREAU OF SHIPPING   (United States)

^b Seoul National University   (South Korea)

^c UNIVERSITY OF HAWAII   (United States)

^d UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BEACHES; MATHEMATICAL MODELS; SOLUTIONS; WATER;

SOLITARY WAVES;

WATER WAVES;

MODELING; NON-LINEAR DYNAMICS; WAVE;

MODELING; NONLINEAR WAVE; WAVE;

EID: 0037564498     PISSN: 08927219     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.1537722     Document Type: Article

References (19)

1. Ertekin, R. C., Webster, W. C., and Wehausen, J. V., 1986. "Waves Caused by a Moving Disturbance in a Shallow Channel of Finite Width," J. Fluid Mech., 169, pp. 272-292.
2. Webster, W. C., and Kim, D. Y., 1990, "The Dispersion of Large-Amplitude Gravity Waves in Deep Water," Proc. 18th Symp. On Naval Hydrodynamics, pp. 397-415.
3. Xu, Q., Pawlowski, J. W., and Baddour, R. E., 1997, "Development of Green-Naghdi models with a wave-absorbing beach for nonlinear, irregular wave propagation," J. of Marine Sci. & Tech., pp. 21-34.
4. Kim, J. W., Bai, K. J., Ertekin. R. C., and Webster, W. C., 2001. "A derivation of the Green-Naghdi equations for irrotational flows," J. Eng. Math., 40(1), pp. 17-34.
5. Kim, J. W., and Ertekin, R. C., 2000, "A Numerical Study of Nonlinear Wave Interaction in Irregular Seas: Irrotational Green-Naghdi Model," Mar. Struct., 13(4-5), pp. 331-347.
6. Kim, J. W., and Bai, K. J., 2003, "A New Complementary Mild-Slope Equation," Submitted to J. Fluid Mech.
7. Shields, J. J., and Webster, W. C., 1988, "On Direct Methods in Water-Wave Theory," J. Fluid Mech., 197, pp. 171-199.
8. Goldstein, H., 1980. Classical Dynamics, Addison-Wesley Pub. Co., 2nd Ed.
9. Bai, K. J., and Kim, J. W., 1995, "A Finite-Element Method for Free-Surface Flow Problems," Journal of Theoretical and Applied Mechanics, 1(1), pp. 1-27.
10. Longuet-Higgins, M. S., and Fenton, J. D., 1974, "On the Mass, Momentum, Energy and Circulation of a Solitary Wave II," Proc. R. Soc. London, Ser, A, A340, 471-493.
11. Tanaka, M., 1986. "The Stability of Solitary Waves," Phys. Fluids, 29(3), pp. 650-655.
12. Longuet-Higgins, M. S., and Fox, M. J. H., 1978. "Theory of the Almost-Highest Wave Part 2. Matching and Analytic Extension," J. Fluid Mech., 85, pp. 769-786.
13. Longuet-Higgins, M. S., and Fox, M. J. H., 1996, "Asymptotic Theory for the Almost-Highest Solitary Wave," J. Fluid Mech., 317, pp. 1-19.
14. Hunter, J. K., and Vanden-Broeck, J.-M., 1983, "Accurate Computations for Steep Solitary Waves," J. Fluid Mech., 136, pp. 63-71.
15. Cokelet, E. D., 1977, "Steep Gravity Waves in Water of Arbitrary Uniform Depth," Philos. Trans. R. Soc. London, Ser. A, 286, pp. 183-230.
16. Su, C. H., and Mirie, R. M., 1980, "On Head-On Collision Between Solitary Waves," J. Fluid Mech., 98(3), pp. 509-525.
17. Ertekin, R. C., and Wehausen, J. V., 1986, "Some Soliton Calculations," Proc. 16th Symp. Naval Hydrodynamics, Berkeley, CA, pp. 167-184.
18. Chan, R. K.-C., and Street, R. L., 1970, "The Shoaling of Finite-Amplitude Water Waves on Sloping Beaches," Twelfth Conference on Coastal Engineering, ASCE, pp. 345-362.
19. Kennedy, A. B., Kirby, J. T., Chen, Q., and Dalrymple, R. A., 2001. "Boussinesq-type Equations with Improved Nonlinear Performance," Wave Motion, 33(3), pp. 225-243.