Numerical Study of Transient Regimes of Kolmogorov Flow in a Square Cell

The problem of two-dimensional flow of a viscous weakly compressible fluid in a square cell under excitation by a spatially periodic static external force (Kolmogorov flow) is considered. A new method for determining the flow structure is presented. It is based on the analysis of the vorticity field at different times. This method is used to classify types of flows the characteristics of which were obtained by numerical simulation. The main flow regimes are identified depending on the values of the friction coefficient against the bottom and the pumping force: laminar, chaotic and vortex regimes. Transitional types of flow are studied separately: the quasi-periodic regime, which arises through a sequence of bifurcations when the laminar and chaotic flow regimes change, and the alternation regime, which occurs during the transition from the chaotic to vortex flow. Phase diagrams are constructed in the space the amplitude of the external force–the friction coefficient against the bottom, which made it possible to classify the type of flow on the basis of the values of the friction coefficient against the bottom and the pumping force.