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.
1. Vanden-Broeck, J.-M. Gravity-Capillary Free-Surface Flows. Cambridge University Press, 2010.
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.
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.
5. Grimshaw, R. H. J. and Smith, N. Resonant flow of a stratified fluid over topography. J. Fluid Mech., 1986, 169, 429–464.
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.
8. Akylas, T. R. On the excitation of long nonlinear waves by a moving pressure distribution. J. Fluid Mech., 1984, 141, 455–466.
9. Wu, T. Y. Generation of upstream advancing solitons by moving disturbances. J. Fluid Mech., 1987, 184, 75–99.
10. Milewski, D. and Vanden-Broeck, J.-M. Time dependent gravity-capillary flows past an obstacle. Wave Motion, 1998, 29, 63–79.