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## Coherent vortex in two-dimensional turbulence: Interplay of viscosity and bottom friction.

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 the flow fluctuations at the pumping scale.

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, 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

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

Kolokolov I., Gamba A., Journal of Statistical Physics 1999 Vol. 94 No. 5/6 P. 759-777

We compute analytically the probability distribution function PP(ε) of the dissipation field ε=(∇θ)2 of a passive scalar θ advected by a d-dimensional random flow, in the limit of large Peclet and Prandtl numbers (Batchelor–Kraichnan regime). The tail of the distribution is a stretched exponential: for ε→∞, ln PP(ε)∼−(d2ε)1/3. ...

Added: March 5, 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

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

Zybin K., Sirota V. A., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2012 Vol. 85 No. 5

We develop a theory of turbulence based on the inviscid Navier-Stokes equation. We get a simple but exact stochastic solution (vortex filament model) which allows us to obtain a power law for velocity structure functions in the inertial range. Combining the model with the multifractal conjecture, we calculate the scaling exponents without using the extended ...

Added: October 20, 2014

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

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

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

Zybin K., Il'yn A. S., Physics-Uspekhi 2016 Vol. 59 No. 12 P. 1241-1244

This paper reviews the statistical properties and calculates the velocity structure functions of flows produced by a large-scale random scaling force in the Burgers model. ...

Added: September 22, 2017

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., Falkovich G. et al., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 1996 Vol. 54 No. 5 P. 4896

We describe the method for finding the non-Gaussian tails of the probability distribution function (PDF) for solutions of a stochastic differential equation, such as the convection equation for a passive scalar, the random driven Navier-Stokes equation, etc. The existence of such tails is generally regarded as a manifestation of the intermittency phenomenon. Our formalism is ...

Added: March 8, 2017

I.V.Kolokolov, L.L.Ogorodnikov, S.S.Vergeles, Physical Review Fluids 2020 Vol. 5 No. 3 Article 034604

It is known that the turbulence in a fast-rotating volume becomes effectively twodimensional. The latter is characterized by an inverse energy cascade leading to the
formation of coherent flow in finite systems. In a rotating three-dimensional vessel this
flow has the form of columnar vortices. Here we develop an analytical theory describing
interaction of the vortex with turbulent ...

Added: April 1, 2020

Zybin K., Sirota V. A., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2013 Vol. 88 No. 4

The appearance of vortex filaments, the power-law dependence of velocity and vorticity correlations and their multiscaling behavior are derived from the Navier-Stokes equation. This is possible due to interpretation of the Navier-Stokes equation as an equation with multiplicative noise and remarkable properties of random matrix products. ...

Added: October 20, 2014

Kolokolov I., JETP Letters 2000 Vol. 71 No. 1 P. 12-14

Leading terms of the asymptotic behavior of the pair and higher order correlation functions for finite times and large distances have been calculated for the Burgers equation involving thermal noise. It is shown that an intermittence phenomenon occurs, whereby certain correlation functions are much greater than their reducible parts. ...

Added: March 5, 2017

Pelinovsky E., E.G. Shurgalina, Sergeeva A. et al., Physical Letters A 2013 Vol. 377 No. 1 P. 272-275

Two-soliton interactions play a definitive role in the formation of the structure of soliton turbulence in integrable systems. To quantify the contribution of these interactions to the dynamical and statistical characteristics of the nonlinear wave field of soliton turbulence we study properties of the spatial moments of the two-soliton solution of the Korteweg–de Vries (KdV) ...

Added: January 18, 2013

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, 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

49606783, Mathematical notes 2017 Vol. 102 No. 2 P. 234-251

It is shown in the paper that the number pN(M) of partitions of a positive integer M
into N positive integer summands coincides with the Bose and Fermi distributions with logarithmic
accuracy if one identifies M with energy and N with the number of particles. We use the Gentile
statistics (a.k.a. parastatistics) to derive self-consistent algebraic equations that ...

Added: October 29, 2018

П.А. Беспалов, О.Н. Савина, Письма в Астрономический журнал 2015 Т. 41 № 10 С. 651-656

The connection of between the formation and properties of areas characterized by the sharp gradient of electron temperature, with electrostatic turbulence, providing high a high effective electrons collision frequency and a low thermal conductivity of medium, is discussed. Simple dependences for the thermal conductivity, effective collision frequency and noise electric fields are obtained. For ...

Added: June 4, 2015

Kolokolov I., Turitsyn K., Journal of Experimental and Theoretical Physics 2002 Vol. 94 No. 6 P. 1193-1200

For the field u(x, t) governed by the Burgers equation with a thermal noise, short-time asymptotics
of multipoint correlators are obtained. Their exponential parts are independent of the correlator number. This
means that they are determined by a single rare fluctuation and exhibit the intermittency phenomenon ...

Added: February 25, 2017

Bespalov P. A., O.N. Savina, Astronomy Letters 2015 Vol. 41 No. 10 P. 601-605

We discuss the connection of the formation and properties of solar atmosphere transition region
characterized by a steep electron temperature gradient with electrostatic turbulence, which provides a high
effective electron collision frequency and a low thermal conductivity of the medium. A simple dependence
of the noise electric field in the transition region on the effective collision frequency has ...

Added: September 30, 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