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## Крупномасштабное течение в двумерной турбулентности при статической накачке

Письма в Журнал экспериментальной и теоретической физики. 2017. Т. 106. № 10. С. 633–636.

Two dimensional turbulence has the striking tendency to self-organize into large-scale, coherent structures due to the inverse energy cascade \cite{67Kra,68Lei,69Bat}. Here we theoretically examine the case of a static pumping where the exciting force is independent of time, the case corresponds to the experimental setup of the works . We establish dependence of the large-scale flow on the system parameters and the pumping characteristics for an unbound system and for a finite box.

Keywords: two-dimensional turbulencecoherent structuresдвумерная турбулентностькогерентные структуры inverse cascadeобратный каскад

Publication based on the results of:

I.V.Kolokolov, V.V.Lebedev, Journal of Fluid Mechanics 2016 Vol. 809 No. paper R2 P. 1–11

We analyze velocity fluctuations inside coherent vortices generated as a result of the inverse cascade in the two-dimensional ($2d$) turbulence in a finite box. As we demonstrated in \citep{16KL}, the universal velocity profile, established in \citep{14LBFKL}, corresponds to the passive regime of the flow fluctuations. The property enables one to calculate correlation functions of the ...

Added: October 23, 2016

Laurie J., Boffetta G., Falkovich G. et al., Physical Review Letters 2014 Vol. 113 No. 25 P. 254503-1–254503-5

An inverse turbulent cascade in a restricted two-dimensional periodic domain creates a condensate-a pair of coherent system-size vortices. We perform extensive numerical simulations of this system and carry out theoretical analysis based on momentum and energy exchanges between the turbulence and the vortices. We show that the vortices have a universal internal structure independent of ...

Added: October 15, 2016

Doludenko A., Fortova S., Kolokolov I. et al., Physics of Fluids 2021 Vol. 33 No. 011704 P. 1–6

We investigate the coherent vortex produced by two-dimensional turbulence excited in a finite box. We establish analytically the mean velocity
profile of the vortex for the case where the bottom friction is negligible and express its characteristics via the parameters of pumping. Our
theoretical predictions are verified and confirmed by direct numerical simulations in the framework of ...

Added: January 20, 2021

I.V.Kolokolov, V.V. Lebedev, JETP Letters 2015 Vol. 101 No. 3 P. 181–184

The inverse cascade of two-dimensional turbulence in a restricted domain leads to creating a coherent flow containing a number of system-size vortices. We examine the case of forcing turbulence with zero bottom friction where the final statistically steady state is determined by viscosity. We analytically establish structure of the coherent vortices in the state. ...

Added: October 15, 2016

Бузовкин А. Б., Kolokolov I., Lebedev V. et al., JETP Letters (английский перевод Писем в Журнал экспериментальной и теоретической физики) 2020 Vol. 111 No. 8 P. 442–446

We consider the structure of a coherent vortex formed around a solid rotating disc in two-dimensional turbulent flow. We find the average velocity profile of the coherent vortex for different rotation velocities ...

Added: July 15, 2020

I.V.Kolokolov, V.V. Lebedev, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2016 Vol. 93 No. 3 P. 033104-1–033104-7

We discuss the structure and geometrical characteristics of coherent vortices appearing as a result of the inverse cascade in two-dimensional turbulence in a finite box.We demonstrate that the universal velocity profile, established by J. Laurie et al. [Phys. Rev. Lett. 113, 254503 (2014)], corresponds to the passive regime of flow fluctuations.We find the vortex core ...

Added: October 15, 2016

Kolokolov I., Lebedev V., Chertkov M., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2010 Vol. 81 P. 015302R

Two-dimensional turbulence generated in a finite box produces large-scale coherent vortices coexisting with
small-scale fluctuations. We present a rigorous theory explaining the =1/4 scaling in the Vr− law of the
velocity spatial profile within a vortex, where r is the distance from the vortex center. This scaling, consistent
with earlier numerical and laboratory measurements, is universal in ...

Added: February 7, 2017

Kolokolov I., Lebedev V., Chertkov M. et al., Physical Review Letters 2007 Vol. 99 P. 084501-1–084501-4

We report a numerical study, supplemented by phenomenological explanations, of ‘‘energy condensation’’
in forced 2D turbulence in a biperiodic box. Condensation is a finite size effect which occurs after
the standard inverse cascade reaches the size of the system. It leads to the emergence of a coherent vortex
dipole. We show that the time growth of the dipole ...

Added: February 10, 2017

Kolokolov I., Kostenko M., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2020 Vol. 101 No. 033108 P. 1–3

We consider two-dimensional turbulence in the presence of a condensate. The nondiagonal correlation
functions of the Lagrangian accelerations are calculated, and it is shown that they have the same universality
properties as the nondiagonal correlation functions of the velocity fluctuations. ...

Added: March 25, 2020

А.В. Орлов, М.Ю. Бражников, А.А. Левченко, Письма в Журнал экспериментальной и теоретической физики 2018 Т. 107 № 3-4 С. 166–171

Экспериментально исследована эволюция вихревого течения, возбуждаемого электромагнитным методом в тонком слое проводящей жидкости. Мелкомасштабные вихри, возбуждаемые на масштабе накачки, вследствие нелинейности взаимодействия со временем сливаются и образуют крупномасштабные структуры - формируется обратный каскад энергии. Зависимость энергетического спектра в развитом обратном каскаде хорошо описывается законом Крайчнана k^{-5/3}. На крупных масштабах обратный каскад ограничивается размерами ячейки, и ...

Added: December 17, 2018

Slunyaev A., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2020 Vol. 101 Article 062214

A method of windowed spatiotemporal spectral filtering is proposed to segregate different nonlinear wave components and to calculate the surface of free waves. The dynamic kurtosis (i.e., produced by the free wave component) is shown able to contribute essentially to the abnormally large values of the surface displacement kurtosis, according to the direct numerical simulations of realistic sea ...

Added: June 28, 2020

Kolokolov I., Chertkov M., Vergassola M., Physical Review Letters 1998 Vol. 80 P. 512

A model of scalar turbulent advection in compressible flow is analytically investigated. It is shown that, depending on the dimensionality d of space and the degree of compressibility of the smooth advecting velocity field, the cascade of the scalar is direct or inverse. If d>4 the cascade is always direct. For a small enough degree of compressibility, the cascade ...

Added: March 5, 2017

I. V. Kolokolov, V. V. Lebedev, M. M. Tumakova, JETP Letters 2023 Vol. 117 No. 2 P. 122–125

We study the correlations of vorticity fluctuations inside a coherent vortex resulting from the inverse energy
cascade in two-dimensional turbulence. The presence of a coherent flow, which is a differential rotation, suppresses small-scale fluctuations of the flow, which are created by an external force, and lead to the fact that
these fluctuations can be considered as non-interacting ...

Added: February 19, 2023

I. V. Kolokolov, V. V. Lebedev, Tumakova M. M., Journal of Experimental and Theoretical Physics 2023 Vol. 136 No. 6 P. 785–794

We investigate fluctuations of vorticity inside a coherent vortex generated by the inverse energy cascade in two-dimensional turbulence. Temporal and spatial correlations can be characterized by the pair correlation function. The interaction of fluctuations leads to a nonzero third moment of vorticity. We analyze the
pair correlation function and the third moment using a model in ...

Added: June 8, 2023

Nikolay A. Ivchenko, Vergeles S. S., Physics of Fluids 2021 Vol. 33 No. 10 Article 105102

A condensate in two-dimensional turbulence confined to a finite domain was predicted by Kraichnan. The most common spatial form of the condensate is a coherent vortex of radius comparable with the domain size, which is statistically steady over times much longer than its turnover time. The vortices were successively studied during the last four decades, ...

Added: October 14, 2021

Kolokolov I., Lebedev V., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2020 Vol. 102 No. 2 P. 1–5

We examine coherent vortices appearing as a result of the inverse cascade of two-dimensional turbulence in a
finite box in the case of pumping with arbitrary correlation time in the quasilinear regime. We demonstrate that
the existence of the vortices depends on the ratio between the values of the bottom friction coefficient α and the
viscous damping of ...

Added: October 6, 2020

Orlov A., В кн. : Труды 60-й Всероссийской научной конференции МФТИ. Фундаментальная и прикладная физика. Т. Фундаментальная и прикладная физика.: М.: МФТИ, 2017. С. 120–122.

В эксперименте исследована эволюция квазидвумерного вихревого течения, возбуждаемого электромагнитным методом в тонком слое проводящей жидкости. Мелкомасштабные вихри, возбуждаемые на масштабе накачки, вследствие нелинейности взаимодействия со временем сливаются и образуют крупномасштабные структуры – формируется обратный каскад энергии. На крупных масштабах обратный каскад ограничивается размерами ячейки, и наблюдается формирование крупномасштабного когерентного вихревого течения, занимающего почти всю площадь ...

Added: December 16, 2018

Doludenko A. N., Fortova S. V., Kolokolov I. et al., Annals of Physics 2022 Vol. 447 No. Pt. 2 Article 169072

We examine analytically and numerically the state of a two-dimensional fluid in a finite box appearing as a result of the inverse cascade supported by a permanent pumping. We argue that there are two different states. One of the states is dominated by big coherent vortices with a well-defined mean profile. The other state is ...

Added: December 10, 2022

Parfenyev V., Physics of Fluids 2024 Vol. 36 No. 1 Article 015148

An inverse turbulent cascade in a periodic square box produces a coherent system-sized vortex dipole. We study the statistics of its motion by carrying out direct numerical simulations performed for various bottom friction $\alpha$, pumping intensity $\varepsilon$, and fluid hyperviscosity $\nu$. In the main approximation, coherent vortices can be considered as point vortices, and within ...

Added: January 24, 2024

Kolokolov I., Lebedev V., Parfenyev V., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2024 Vol. 109 No. 3 Article 035103

We analytically examine fluctuations of vorticity excited by an external random force in two-dimensional fluid. We develop the perturbation theory enabling one to calculate nonlinear corrections to correlation functions of the flow fluctuations found in the linear approximation. We calculate the correction to the pair correlation function and the triple correlation function. It enables us ...

Added: March 25, 2024

Parfenyev V., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2022 Vol. 106 No. 2 Article 025102

It is well known that an inverse turbulent cascade in a finite ($2 \pi \times 2 \pi$) two-dimensional periodic domain leads to the emergence of a system-sized coherent vortex dipole. We report a numerical hyperviscous study of the spatial vorticity profile inside one of the vortices. The exciting force was shortly correlated in time, random ...

Added: August 10, 2022

Andrew G. Semenov, Zaikin A., Physical Review B: Condensed Matter and Materials Physics 2013 Vol. 88 No. 5 P. 054505-1–054505-10

We investigate the effect of interacting quantum phase slips on persistent current and its fluctuations in ultrathin superconducting nanowires and nanorings pierced by the external magnetic flux. We derive the effective action for these systems and map the original problem onto an effective sine-Gordon theory on torus. We evaluate both the flux dependent persistent current ...

Added: February 9, 2015

Pelinovsky E., Didenkulova I., Rybkin A., Journal of Fluid Mechanics 2014 Vol. 748 P. 416–432

We present an exact analytical solution of the nonlinear shallow water theory for wave run-up in inclined channels of arbitrary cross-section, which generalizes previous studies on wave run-up for a plane beach and channels of parabolic cross-section. The solution is found using a hodograph-type transform, which extends the well-known Carrier–Greenspan transform for wave run-up on ...

Added: November 19, 2014

Окубо Ю. undefined., Journal of Physics: Conference Series 2017 Vol. 804 No. 012036 P. 1–8

We investigate the existence and the orthogonality of the generalized Jack symmetric functions which play an important role in the AGT relations. We show their orthogonality by deforming them to the generalized Macdonald symmetric functions. ...

Added: October 26, 2017