Rank Analysis of Flows at Low Reynolds Numbers for a Polymer Solution

The flow of a viscous polymer solution is numerically investigated in a square computational domain with solid boundaries under the action of an external periodic force (Kolmogorov flow). The external force intensity is such that the flow dynamics is characterized by a small value of the Reynolds number, which makes it possible to observe the elastic turbulence phenomenon. A model of the flow of a weakly compressible viscous polymer solution is constructed, and a numerical technique is developed to approximate the model. A methodology of rank distributions is applied to analyze different types of flow. It is shown that, for chaotic and laminar regimes, the inflection point in the rank frequency distributions of the vorticity is a universal characteristic for classifying various types of flow.