Exact Solution of Viscous Fluid Velocity and Pressure Due to Kinematic Effect of Two-Dimensional Boundary Propagating Wave

In the present study, to extend the Stokes' second problem, the bottom edge of viscous incompressible semi-space resting fluid is excited in two dimension, simultaneously. This two-dimensional excitation which is the effect of velocity of two-dimensional travelling wave, is boundary condition for the two-dimensional linear Navier-Stokes equations. The time-space exact solution for fluid velocity and pressure show that the amplitude of oscillating velocity has fast damping in space till 1.87 micron from excited surface. After this height, the amplitude of oscillating quantities has a slowly damping. In the first region (in fast damping region), phase difference between pressure and velocity is changing, but after that there is a region with constant phase difference. The space variation in velocity components of surface wave, together with the coupling of velocity components in main equations, produces pressure wave. It has been found that kinematic effect of vertical and horizontal harmonic motion cause damped rotational motion in fluid.