Flow of a viscous incompressible fluid after a sudden point impulse near a wall

The flow of a viscous incompressible fluid generated by a sudden impulse near a wall with no-slip boundary condition is studied on the basis of the linearized Navier-Stokes equations. It turns out that the flow differs significantly from that for the perfect slip boundary condition, except far from the wall and at short times. At short time the flow is irrotational and can be described by a potential which varies with the square root of time. Correspondingly the pressure disturbance is quite large at short times. It shows an oscillation at later times if the impulse is directed parallel to the wall and decays monotonically for impulse perpendicular to the wall.