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## Correlations of Vorticity inside a Coherent Vortex

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 cas-

cade in two-dimensional turbulence. Temporal and spatial correlations can be characterized by the pair cor-

relation 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 which the pumping is short-correlated in

time and derive explicit expressions for the Gaussian spatial correlation function for the pumping force.

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

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

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

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

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

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

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., 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

Kolokolov I., Lebedev V., 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 ...

Added: November 12, 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

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

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

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

Blyakhman L. G., Gromov E., Malomed B. A. et al., Chaos, Solitons and Fractals 2018 No. 117 P. 264-268

The dynamics of two-component solitons with a small spatial displacement of the high-frequency (HF) component relative to the low-frequency (LF) one is investigated in the framework of the Zakharov-type system. In this system, the evolution of the HF field is governed by a linear Schrödinger equation with the potential generated by the LF field, while ...

Added: November 12, 2018

Blyakhman L. G., Morozov V. P., Tyutin V. V., Труды НГТУ им. Р.Е. Алексеева 2016 № 3 (114) С. 9-15

Цель работы: Исследована динамика двухкомпонентных (векторных) солитонов Давыдова-Скотта(ДС) при пространственно-скоростном рассогласовании высокочастотных (ВЧ) и низкочастотных (НЧ) компонент. Рассмотрение проведено в рамках Захаровского типа системы двух связанных уравнений для ВЧ и НЧ поля. В этой системе ВЧ поле описывается линейным уравнением Шредингера с переменным во времени и пространстве потенциалом, вызванным НЧ компонентой. НЧ компонента в этой ...

Added: October 5, 2016

Kolokolov I., Lebedev V., Журнал экспериментальной и теоретической физики 2024 Т. 165 № 1 С. 128-140

We examine fluctuations of vorticity excited by an external random force in two-dimensional fluid in the presence of a strong external shear flow. The problem is motivated by the analysis of big coherent vortices appearing as a consequence of the inverse energy cascade in a finite box at large Reynolds numbers. We develop the perturbation ...

Added: January 29, 2024

Leuven : KU Leuven Methusalem Group, 2015

Added: March 22, 2016

O.N. Savina, E.M. Gromov, V.V. Tyutin, Geomagnetism and Aeronomy 2015 Vol. 55 No. 5 P. 658-662

The possibility of the existence of a solitary internal gravity wave at heights of the Earth’s thermosphere is considered. Analytical results were obtained in local approximation with weak nonisothermality of the atmosphere. For internal gravity waves, the Korteweg–de Vries equation was derived and studied with allowance for inhomogeneity, nonlinearity, and dissipation. The theoretical results were ...

Added: October 23, 2015

Konstantin Yu. Arutyunov, Hongisto T. T., Lehtinen J. S. et al., Scientific Reports 2012 Vol. 2 No. 293 P. 1-7

The smaller the system, typically - the higher is the impact of fluctuations. In narrow superconducting wires
sufficiently close to the critical temperature Tc thermal fluctuations are responsible for the experimentally
observable finite resistance. Quite recently it became possible to fabricate sub-10 nm superconducting
structures, where the finite resistivity was reported within the whole range of experimentally obtainable
temperatures. ...

Added: March 24, 2014

Karminsky A. M., Kostrov A., Murzenkov T., Финансовая аналитика: проблемы и решения 2012 № 41(131) С. 2-13

В соответствии с Базельскими соглашениями одной из перспективных задач риск-менеджмента является совершенствование моделей вероятности дефолта. Авторы исследуют влияние на вероятность дефолта российских банков финансовых факторов, уделяя особое внимание расширению горизонта исследования и нелинейностям по объясняющим переменным. Проведен анализ адекватности модели. Отмечено, что учет нелинейностей по относительным финансовым переменным существенно улучшает качество модели. Выделены объясняющие переменные, ...

Added: December 7, 2012

Arutyunov K., Sajavaara T., Lehtinen J. S. et al., Physical Review B: Condensed Matter and Materials Physics 2012 Vol. 85 No. 9 P. 0945081-0945087

Electron transport properties of titanium nanowires were experimentally studied. Below the effective diameter
50nm all samples demonstrated a pronounced broadening of the R(T ) dependencies, which cannot be accounted
for by thermal fluctuations. Extensive microscopic and elemental analyses indicate the absence of structural or/and
geometrical imperfections capable of broadening the R(T ) transition to such an extent. We ...

Added: March 24, 2014

Munyaev V., Smirnov L., Kostin V. et al., New Journal of Physics 2020 Vol. 22 Article 023036

We study populations of globally coupled noisy rotators(oscillators with inertia) allowing a nonequilibrium transition from a desynchronized state to a synchronous one (with the nonvanishing order parameter). The newly developed analytical approaches resulted in solutions describing the synchronous state with constant order parameter for weakly inertial rotators, including the case of zero inertia, when the ...

Added: October 31, 2020

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

Knyazeva H., Foresight and STI Governance 2020 Vol. 14 No. 4 P. 34-45

The modern theory of complex systems changes our view of historical processes, accompanied by uncertainties,
instabilities and ambiguities. The knowledge of this theory allows us to master a system or holistic thinking, and to
understand the laws of functioning and growth of not just structural, but dynamic complexity. Uncertainties and chaotic elements that indicate any state of ...

Added: December 25, 2020