TRANSFORMATION OF NONLINEAR LONG WAVES

Nobuo Shuto

Abstract


Kakutani's equation is extended to include the effects of variable width of the channel and the bottom friction. Based on the equation, several solutions are derived and compared with experimental results. For example, Green's law is obtained if the nonlinearity, dispersion and bottom friction are neglected. With the nonlinearity included, it is shown that the wave amplitude follows Green's law and at the same time the wave profile deforms due to the nonlinear effect. Discussion of the present paper is mainly focused on the effect of the bottom friction. From the experimental results of cnoidal waves in a channel of constant depth and width, on the bottom of which artificial roughnesses are planted, it is shown that the friction coefficient estimated from Kajiura's theories gives good agreements, thus confirming the validity of the method of conversion, proposed in the present paper, between sinusoidal and cnoidal wave motions. Change in height of cnoidal waves on a slope is also solved. The friction coefficient determined from wave characteristics and bottom conditions, by means of Kajiura's theories and the method of conversion stated above, is used in the comparison with experimental results. Theoretical prediction agrees very well with experimental results.

Keywords


wave transformation; long waves; nonlinear waves

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