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Compressible vortex structures and their role in the onset of hydrodynamic turbulence

 a, b,  c, d, b,  e,  b, f
a P.P. Shirshov Institute of Oceanology, Russian Academy of Sciences, ul. Krasikova 23, Moscow, 117218, Russian Federation
b Skolkovo Institute of Science and Technology, Bolshoy Boulevard 30, bld. 1, Moscow, 121205, Russian Federation
c Lebedev Physical Institute, Russian Academy of Sciences, Leninsky prosp. 53, Moscow, 119991, Russian Federation
d Landau Institute for Theoretical Physics, Russian Academy of Sciences, ul. Kosygina 2, Moscow, 119334, Russian Federation
e Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Rio de Janeiro, CEP 22460-320, Brasil
f Khristianovich Institute of Theoretical and Applied Mechanics SB RAS, Institutskaya str., 4/1, Novosibirsk, 630090, Russian Federation

We study the formation of quasi-two-dimensional (thin pancake) vortex structures in three-dimensional flows, and of quasi-one-dimensional structures in two-dimensional hydrodynamics. These structures are formed at large Reynolds numbers, when their evolution is described in the leading order by the Euler equations for an ideal incompressible fluid. We show numerically and analytically that the compression of these structures and, as a consequence, the increase in their amplitudes is due to the compressibility of the frozen-in-fluid fields: the field of continuously distributed vortex lines in the three-dimensional case and the field of vorticity rotor lines (divorticity) for two-dimensional flows. We find that the growth of vorticity and divorticity can be considered as a process of overturning of the corresponding fields. At high intensities, this process demonstrates a Kolmogorov-type scaling relating the maximum amplitude with the corresponding thicknesses-to-width ratio of the structures. The possible role of these coherent structures in the formation of the Kolmogorov turbulent spectrum, as well as in the Kraichnan spectrum corresponding to a constant flow of enstrophy in the case of two-dimensional turbulence is analyzed.

Keywords: vortex lines, divorticity, overturning, turbulence, frozen-in-fluid fields
DOI: 10.3367/UFNe.2020.11.038875
Citation: Agafontsev D S, Kuznetsov E A, Mailybaev A A, Sereshchenko E V "Compressible vortex structures and their role in the onset of hydrodynamic turbulence" Phys. Usp., accepted

Received: 31st, August 2020, 18th, November 2020

Оригинал: Агафонцев Д С, Кузнецов Е А, Майлыбаев А А, Серещенко Е В «Сжимаемые вихревые структуры и их роль в зарождении гидродинамической турбулентности» УФН, принята к публикации; DOI: 10.3367/UFNr.2020.11.038875

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