Gravity waves of finite amplitude. III. Steady, symmetrical, periodic waves in a channel of finite depth

Introduction.Part I of this series** is concerned with the theory of finite amplitude gravity waves in a channel of infinite depth, Part II deals with the problem of the solitary wave.In the present paper, the finite amplitude wave problem is considered for a channel of finite depth and it will be shown that Parts I and II are special cases of this problem.The basic approach will not be explained in detail here since it is given in Part I, but the problem will be solved independently of the earlier parts.1. Statement of problem.We deal with an incompressible fluid in a channel with a horizontal base, the fluid having been set in motion in such a way that the flow is two-dimensional and irrotational.The fluid motion is periodic with wave length X in where (u, v) are the velocity components relative to 0{x, y).