Rank Analysis of Quasi-Two-Dimensional Vortex Flows in a Closed Cubic Volume

Intense atmospheric vortices—tropical cyclones (hurricanes) and tornadoes—are among the most destructive natural disasters. A necessary element in these processes is rapid differential rotation, in which different parts of an object rotate around a common axis with different angular velocities, maintaining the structure not only in azimuth, but also vertically. One approach to studying these phenomena is numerical experiment, which has exceptional information content and the ability to obtain predictive results that cannot be achieved by any other methods. In this paper, based on direct numerical modeling of the Navier–Stokes system of equations, the formation of coherent column structures in a cubic closed volume in the presence of rotation (Coriolis force) and a constantly acting external force (forcing) is investigated. In these experiments, depending on the values of the rotation and forcing parameters, several types of motion of the fluid were obtained: a turbulent regime, a regime with the occurrence of several cyclonic vortices, and a regime with the occurrence of one large anticyclone. This paper establishes a mutual correspondence between the single-point statistics of vorticity, energy, and pressure values and the indicated types of flows. We show that using a rank-based approach and the occurrence frequencies of these quantities is productive in this way. The correspondence of the rank curves for a numerical and physical experiment conducted in a similar formulation is obtained. Without claiming to describe real atmospheric phenomena, the authors propose an original method for identifying different types of vortex flows based on the rank distribution of the occurrence frequencies of flow parameters.