An approximation for the highest gravity waves on water of finite depth

Planar steady gravity waves of finite amplitude at the surface of an ideal incompressible fluid above a flat bottom are studied theoretically. A new approach to the construction of some steady flows of heavy fluid with a partially free surface is proposed. The hypothesis is suggested and justified that these flows are close to gravity waves. For the case of the highest waves a one-parameter family of exact solutions describing free boundary flows above a flat bottom and under two uneven symmetrically located caps is derived. This family of solutions gives an approximation to the highest water waves in moderate to shallow water depths, enabling relatively simple calculation of their properties.