Nonlinear hydrodynamic pressure on an accelerating plate

Nonlinear theory is developed to determine accurately the hydrodynamic pressure on an accelerating vertical plate. The plate is assumed to move horizontally towards the fluid with an acceleration which may be expressed in a power series in time. The fluid is initially at rest and the plate motion is impulsive. When the horizontal plate displacement is small in comparison with the undisturbed fluid depth, the method of small time expansions is adopted to obtain analytical solutions up to and including the third order velocity potential. The free surface profile of the fluid is also determined. An example for the constant acceleration case is presented to illustrate the method.