Free-surface motion of a thin sheet of inviscid fluid

The impact of a water wave against a seawall or cliff can cause a mass of water to be projected upward as a thin nearly flat high‐speed sheet of water, moving between two free surfaces. The flow is described as a quasi‐two‐dimensional velocity field in the mid‐plane of the sheet. The third velocity component, normal to the mid‐plane, is relegated to ensuring the velocity field satisfies the incompressibility condition and the free‐surface kinematic conditions. Gravity is included but surface tension is neglected. The components of the gradient of the internal pressure are shown to be negligible, so that Euler's equations may be integrated. This is done for arbitrary initial velocity and initial sheet‐boundary position. Example calculations are presented: a one‐parameter family of converging–diverging flows in a circular sheet and two descriptions of plumes due to sea‐wave impacts against a plane vertical wall.