Direct Numerical Simulation and Rank Analysis of Two-Dimensional Kolmogorov-type Vortex Flows

The article is devoted to direct numerical modeling of viscous weakly compressible Kolmogorov-type flows in a square calculation cell. Several different conditions are observed. One of them is dominated by a large vortex with a well-defined average profile. In another state, strong chaotic large-scale fluctuations prevail. In the third state, laminar flow is observed. The nature of the realized state depends on the coefficient of kinematic viscosity of the liquid, the amplitude of the external pumping force, and the bottom friction coefficient. At constant values of the kinematic viscosity and the wave vector, a small value of the friction coefficient leads to the appearance of the first state. As the bottom friction coefficient increases, there is a transition from a flow with one large vortex to a laminar flow through a series of states with several unstable vortices, which we call chaotic flow. A rank analysis of the values of vorticity, energy, and pressure, as well as the frequency of their occurrence, is proposed. It is shown that for chaotic, vortex, laminar and transitional regimes of fluid motion, the inflection point in the rank frequency distributions of the above fields is a universal characteristic for classifying various types of flow.