RADIAL STRUCTURIZATION OF VORTICAL ELEMENTS IN QUASI-TWO-DIMENSIONAL TURBULENCE

Abstract

The objective of this study is to examine the equations that describe the structural elements of turbulence in a quasi-two-dimensional vortex packet in an immersed medium. Investigating individual vortices is essential for understanding the role of turbulent structures in mixing and other related processes. An analytical approach based on the vorticity equation and the stream function allows for the modeling of elementary vortex formations as structural elements of quasi-two-dimensional turbulence. The expressions obtained from this approach are used to analyze the characteristics of homogeneous turbulence and to assess the contribution of individual vortices to mixing processes. Analytical solutions describing localized vortex structures have been derived using the vorticity form of the Navier-Stokes equations with the application of the stream function. It has been shown that by selecting logarithmically oscillating functions, one can obtain solutions with ring-like symmetry and scale invariance. The resulting graphical analysis enabled the interpretation of the single vortex structure as a model vortex in a turbulent flow, which is confirmed by the isoline patterns and the surface topology of the stream function. A relationship between the parameter l, the flow function f(y), and flow regimes has been established and summarized in the parameter table.

The obtained results confirm the effectiveness of describing turbulent flows through the dynamics of their structural elements. This approach allows for the analysis of not only spectral, but also spatially localized properties of turbulent fields.