EAP - Proceedings of the Estonian Academy of Sciences

PUBLISHED
SINCE 1952

proceedings
of the estonian academy of sciences

ISSN 1736-7530 (Electronic)
ISSN 1736-6046 (Print)

Open Access Journal

CiteScore: 2.4

Impact Factor (2022): 0.9

Numerical simulation of capillary gravity waves excited by an obstacle in shallow water; pp. 278–284

PDF | doi: 10.3176/proc.2015.3.11

Authors

Motonori Hirata, Shinya Okino, Hideshi Hanazaki

Abstract

Capillary gravity waves excited by an obstacle are investigated by numerical simulations. Under the resonant condition for which large-amplitude solitary waves are generated, solutions of the Euler equations show that the capillary effects induce the generation of short waves both upstream of the solitary waves and downstream of the obstacle. Overall characteristics of these waves agree with the weakly nonlinear theory, although the theory overestimates the wavelength of the upstream short waves.

References

1. Vanden-Broeck, J.-M. Gravity-Capillary Free-Surface Flows. Cambridge University Press, 2010.
http://dx.doi.org/10.1017/CBO9780511730276

2. Lee, S.-J., Yates, G. T., and Wu, T. Y. Experiments and analyses of upstream-advancing solitary waves generated by moving disturbances. J. Fluid. Mech., 1989, 199, 569–593.
http://dx.doi.org/10.1017/S0022112089000492

3. Choi, J., Sun, S.-M., Oh, S., Lee, D., and Whang, S.-I. Numerical and experimental study of Scott Russell’s solitary waves. B. Am. Phys. Soc., 2010, 55, 66.

4. Zhang, D. and Chwang, A. T. Numerical study of nonlinear shallow waves produced by a submerged moving disturbance in viscous flow. Phys. Fluids, 1995, 8, 147–155.
http://dx.doi.org/10.1063/1.868822

5. Grimshaw, R. H. J. and Smith, N. Resonant flow of a stratified fluid over topography. J. Fluid Mech., 1986, 169, 429–464.
http://dx.doi.org/10.1017/S002211208600071X

6. Zhang, D. and Chwang, A. T. Generation of solitary waves by forward- and backward-step bottom forcing. J. Fluid Mech., 2001, 432, 341–350.

7. Zhu, Y. Resonant generation of nonlinear capillary-gravity waves. Phys. Fluids, 1995, 7, 2294–2296.
http://dx.doi.org/10.1063/1.868479

8. Akylas, T. R. On the excitation of long nonlinear waves by a moving pressure distribution. J. Fluid Mech., 1984, 141, 455–466.
http://dx.doi.org/10.1017/S0022112084000926

9. Wu, T. Y. Generation of upstream advancing solitons by moving disturbances. J. Fluid Mech., 1987, 184, 75–99.
http://dx.doi.org/10.1017/S0022112087002817

10. Milewski, D. and Vanden-Broeck, J.-M. Time dependent gravity-capillary flows past an obstacle. Wave Motion, 1998, 29, 63–79.
http://dx.doi.org/10.1016/S0165-2125(98)00021-3

11. Karpman, V. I. Radiation by solitons due to higher-oder dispersion. Phys. Rev. E, 1993, 47, 2073–2082.
http://dx.doi.org/10.1103/PhysRevE.47.2073

Back to Issue