An analytical solution is constructed using Laplace transform for the development of the linear flow field due to the instantaneous application of a constant point force in an infinite porous medium assuming the validity of the Brinkman model. In the initial stages of flow development, the flow field exhibits a dipolar structure with its centre at the origin O and the axis along the direction of the impressed force. This induced fluid motion occurs in the form of weak toroidal vortices on either side of the axis of symmetry. The circulating flow field encloses the stagnation points whose distance from the origin increases with time.

porous medium, Brinkman model, point force, toroidal vortex.