On the enclosed crest angle of the limiting profile of standing waves. (English) Zbl 1074.76521
Summary: We derive local solutions of standing waves analytically. They show that the enclosed crest angle of the limiting standing wave is 90\(^\circ\) and the limiting wave has a sharp corner only at a certain instant when the velocity in the whole region is zero. We have found that the crest of the limiting wave is not a singular point but a saddle point for pressure distribution.
MSC:
| 76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |
References:
| [1] | Penney, W. G.; Price, A. T., Finite periodic stationary gravity waves in a perfect liquid, Phil. Trans. Roy. Soc. London, A 244, 254-284 (1952), Part II |
| [2] | Taylor, G. I., An experimental study of standing waves, (Proc. Roy. Soc., A 218 (1953)), 44-59 |
| [3] | Grant, M. A., Standing Stokes waves of maximum height, J. Fluid Mech., 60, 593-604 (1973) · Zbl 0281.76011 |
| [4] | Schwartz, L. W.; Whitney, A. K., A semi-analytic solution for nonlinear standing waves in deep water, J. Fluid Mech., 107, 147-171 (1981) · Zbl 0462.76024 |
| [5] | Mercer, G. N.; Roberts, A. J., Standing waves in deep water: Their stability and extreme form, Phys. Fluids, A 4, 259-269 (1992) · Zbl 0745.76009 |
| [6] | Longuet-Higgins, M. S., A technique for time-dependent free-surface flows, (Proc. Roy. Soc. London, A 371 (1980)), 441-451 · Zbl 0444.76007 |
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