Note on a Solitary Wave in a Slowly Varying Channel.

摘要

A description of a solitary wave in water of slowly varying depth is extended to a channel of slowly varying breadth and depth b and d on the assumption that the scale for the variation of b and d is large compared with d to the 5/2th power/a to the 3/2th power. It is inferred from conservation of energy that the amplitude of the wave is proportional to (1/b to the 2/3rds power)/d (ef. Green's law a approximately square root (1/b) quarter root (1/d) for long waves of small amplitude). Comparison with experiment yields fairly satisfactory agreement for a linearly converging channel of constant depth. The agreement for a linearly diverging channel is not satisfactory, but the experimental data are inadequate to support any firm conclusion.