An example of numerical simulation of a self-oscillating regime of viscous incompressible flow

The two-dimensional flow of a viscous uniform incompressible fluid generated by a spatially periodic force is studied theoretically. Consideration is given to both the subcritical and supercritical regimes in the presence of mean flow, and an exact analytical solution is found for the general case of the subcritical regime. In a series of numerical experiments the patterns of secondary flow are determined, and the period of motion for the self-oscillating regime is found to be dependent on values for the initial flow superimposed on the secondary flow. It is shown that the results agree well with the analytical results of Iudovich (1965).