Nonlinear effects in a viscous wave field excited by a finite-size plate

We have numerically investigated nonlinear nonstationary velocity and pressure fields in a viscous incompressible fluid near an oscillating absolutely rigid plate of an infinitely small thickness and a limited length in the direction of oscillations. It is shown that the limitation imposed on the plate size along the direction of its oscillations leads to nonlinearity of the problem even for a small amplitude of surface oscillations of the plate. We have analyzed the velocity and pressure fields for large amplitudes of plate oscillations. The emergence of displacement flows during oscillations of an infinitely thin plate of a finite length is explained. The mechanism of formation of instantaneous vortex motions in the viscous fluid is investigated.