Properties of the inhomogeneous viscous waves excited by a plate of finite size

We have numerically solved the set of time-dependent nonlinear equations, which describes motion of an infinitely thin plate oscillating in incompressible viscid fluid. The solution was obtained in the form of oscillation velocity field in the viscid wave. It is a function of the dimensionless length l and the dimensionless oscillation displacement a of the plate. We have plotted trajectories of the fluid particle motion in such a field. It has been shown that they differ from the straight lines normal to the direction of propagation. Such lines are peculiar to the idealized (linear) transverse viscid waves. There appeared a horizontal component of the oscillation speed of the fluid particle. The value of horizontal component depends on a. We have qualitatively analyzed characteristic features of the propagation velocity of viscid wave, excited by a finite plate.