Geodesic
Experimental and numerical investigation of the dynamics of development of Rayleigh--Taylor instability at Atwood numbers close to unity
Matematičeskoe modelirovanie, Tome 35 (2023) no. 1, pp. 59-82

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This paper presents the experimental and numerical results of studying the growth dynamics of deterministic, given in a certain way initial perturbations. The formation, growth and further evolution of inhomogeneities of the contact boundary occurs due to the development of the Rayleigh–Taylor instability at the gas-liquid interface, in particular (in this work), air-water. A significant difference in the densities of the selected substances leads to a noticeable slowdown in the dynamics of the Kelvin–Helmholtz instability, which is responsible for the formation of mushrooms-like structures, and, as a result, to a longer growth of water jets and a later moment of their destruction and transition to mixing. In this work, a quantitative comparison of physical data recorded on the original experimental setup, which is described in this paper, with the calculated data obtained using various numerical methods is carried out. Numerical modeling is based on a complete 2D hydrodynamic model for describing the dynamics of development of the RayleighTaylor instability. Surface tension (water-air) and viscosity (water or air) are neglected in this study. The parameters of the development of instability measured in the experiment and found in the calculations indicate a satisfactory agreement between the obtained data. The quantitative results presented in this study justify the use of the classical hydrodynamics model to describe the movements of liquid and gas observed in this experiment and a fairly accurate numerical implementation of the corresponding model in the difference methods used here. An essential element of the study is the investigation of the development of turbulent mixing depending on well-defined initial conditions, and the new regularities of the laws of mixing of different-density media that arise in this case.
Keywords: Rayleigh–Taylor instability, fluid/gas contact interface, experiment, numerical modeling. 
@article{MM_2023_35_1_a4,
     author = {M. D. Bragin and S. Yu. Gus'kov and N. V. Zmitrenko and P. A. Kuchugov and I. G. Lebo and E. V. Levkina and N. V. Nevmerzhitskiy and O. G. Sin'kova and V. P. Statsenko and V. F. Tishkin and I. R. Farin and Yu. V. Yanilkin and R. A. Yakhin},
     title = {Experimental and numerical investigation of the dynamics of development of {Rayleigh--Taylor} instability at {Atwood} numbers close to unity},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {59--82},
     publisher = {mathdoc},
     volume = {35},
     number = {1},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2023_35_1_a4/}
}
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%A N. V. Nevmerzhitskiy
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%A V. P. Statsenko
%A V. F. Tishkin
%A I. R. Farin
%A Yu. V. Yanilkin
%A R. A. Yakhin
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M. D. Bragin; S. Yu. Gus'kov; N. V. Zmitrenko; P. A. Kuchugov; I. G. Lebo; E. V. Levkina; N. V. Nevmerzhitskiy; O. G. Sin'kova; V. P. Statsenko; V. F. Tishkin; I. R. Farin; Yu. V. Yanilkin; R. A. Yakhin. Experimental and numerical investigation of the dynamics of development of Rayleigh--Taylor instability at Atwood numbers close to unity. Matematičeskoe modelirovanie, Tome 35 (2023) no. 1, pp. 59-82. http://geodesic.mathdoc.fr/item/MM_2023_35_1_a4/