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Numerical experiment in turbulence (on the 100th anniversary of Academician O.M. Belotserkovsky)

Fortova S.V.

2025, issue 2, P. 148–193 DOI: https://doi.org/10.47910/FEMJ202512

Abstract

The paper presents the main results on numerical modeling of turbulent flows, carried out under the guidance of academician O.M. Belotserkovsky and continued by his students. For the problem of the shear layer of a liquid, the process of formation of spatial turbulence and a developed large-scale turbulent flow is analyzed. It is shown that large vortices play a leading role in the formation of the direct Kolmogorov energy cascade (Belotserkovsky's hypothesis). When studying the modes of two-dimensional flow of a viscous, slightly compressible liquid under the action of an external periodic force in both coordinates, the modified Kolmogorov flow, various methods for analyzing hydrodynamic characteristics were used and tested. The implemented approaches make it possible to specify which of the flow modes: laminar, chaotic, and vortex – can be observed when selecting the bottom friction coefficient, amplitude, and pumping force. For the modified Kolmogorov flow, the development of the reverse energy cascade characteristic of vortex flows in two-dimensional turbulence is numerically demonstrated. The problem of the flow of an incompressible rotating fluid in a cube shows the formation of column vortices and the occurrence of both a direct cascade of energy, characteristic of three-dimensional turbulence, and the reverse, characteristic of flat flows. A model is proposed and numerical simulation of the elastic turbulence effect that occurs for small Reynolds numbers in the presence of a polymer impurity in the flow is performed.

Keywords: numerical modeling, turbulent flows, forward and reverse energy cascades, Kolmogorov problem, quasi-two-dimensional flows, shear flows, elastic turbulence.

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References

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