Capillary Waves Generated by a Rock in a Stream
Abstract
Takeo R.M. Nakagawa and Ai Nakagawa
This paper is concerned with capillary waves generated by a rock, or fishing line in a stream. It is found mathematicaly that the angle between the capillary wave envelope and the direction of a point source is dependent of the velocity, surface tension, and density of the fluid:
This angle increases with increasing the surface tension, but decreases with increasing the square of velocity and the density of fluid. These theoretical outcomes are consistent with the detailed behaviors of capillary waves observed in the natural running streams. To enhance the mathematical analyses on capillary waves generated by a fishing line with constant speed, the relevant non-dimensional parameters 1=Ut/r and
2=r3 /(t2 ) have derived based on the Buckingham -Theorem, where U the relative stream velocity, t the time, r the distance from the point source of wave generation, the surface tension, and the density of the fluid.
It has been confirmed by the present proposed approach that the angle between the gravity wave envelope and the direction of a duck or ship moving on the calm water surface is constant of 19.28 which agrees with the result obtained by “Thomson, W., 1887 On ship waves, Institution of Mechanical Engineers, Minutes of Proceedings, 409-434” and “Adam, J.A., 2003 Mathematics in nature: modelling patterns in the natural world, Princeton University Press, Princeton, 161-172”.
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