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E. Balkovsky

Publications and source records attributed to E. Balkovsky.

12 recordsLinked to original sources
arXiv2001

On Turbulence of Polymer Solutions

We investigate high-Reynolds number turbulence in dilute polymer solutions. We show the existence of a critical value of the Reynolds number which separates two different regimes. In the first regime, below the transition, the influence of the polymer molecules on the flow is negligible and they can be regarded as passively embedded in the flow. This case admits a detailed investigation of the statistics of the polymer elongations. The second state is realized when the Reynolds number is larger than the critical value. This regime is characterized by the strong back reaction of polymers on the flow. We establish some properties of the statistics of the stress and velocity in this regime and discuss its relation to the drag reduction phenomenon.

nlin.CD↗
arXiv2000

Clustering of inertial particles in turbulent flows

We consider inertial particles suspended in an incompressible turbulent flow. Due to inertia of particles, their velocity field acquires small compressible component. Its presence leads to a new qualitative effect --- possibility of clustering. We show that this effect is significant for heavy particles, leading to strong fluctuations of the concentration.

chao-dyn↗
arXiv2000

On the Turbulent Dynamics of Polymer Solutions

We study properties of dilute polymer solutions which are known to depend strongly on polymer elongation. The probability density function (PDF) of polymer end-to-end extensions $R$ in turbulent flows is examined. We demonstrate that if the value of the Lyapunov exponent $λ$ is smaller than the inverse molecular relaxation time $1/τ$ then the PDF has a strong peak at the equilibrium size $R_0$ and a power tail at $R\gg R_0$. This confirms and extends the results of \cite{Lumley72}. There is no essential influence of polymers on the flow in the regime $λτ<1$. At $λ>1/τ$ the majority of molecules is stretched to the linear size $R_{\rm op}\gg R_0$. The value of $R_{\rm op}$ can be much smaller than the maximal length of the molecules because of back reaction of the polymers on the flow, which suppresses velocity gradients thus preventing the polymers from maximal possible stretching.

chao-dyn↗
arXiv1999

Universal long-time properties of Lagrangian statistics in the Batchelor regime and their application to the passive scalar problem

We consider transport of dynamically passive quantities in the Batchelor regime of smooth in space velocity field. For the case of arbitrary temporal correlations of the velocity we formulate the statistics of relevant characteristics of Lagrangian motion. This allows to generalize many results obtained previously for the delta-correlated in time strain, thus answering the question of universality of these results.

chao-dyn↗
arXiv1999

Large-scale properties of passive scalar advection

We consider statistics of the passive scalar on distances much larger than the pumping scale. Such statistics is determined by statistics of Lagrangian contraction that is by probabilities of initially distant fluid particles to come close. At the Batchelor limit of spatially smooth velocity, the breakdown of scale invariance is established for scalar statistics.

chao-dyn↗
arXiv1998

Instanton for the Kraichnan Passive Scalar Problem

We consider high-order correlation functions of the passive scalar in the Kraichnan model. Using the instanton formalism we find the scaling exponents $ζ_n$ of the structure functions $S_n$ for $n\gg1$ under the additional condition $dζ_2\gg1$ (where $d$ is the dimensionality of space). At $n n_c$ they are $n$-independent: $ζ_n=ζ_2 n_c/4$. We also estimate $n$-dependent factors in $S_n$, particularly their behavior at $n$ close to $n_c$.

chao-dyn↗
arXiv1997

Two complementary descriptions of intermittency

We describe two complementary formalisms designed for the description of probability density function (PDF) of the gradients of turbulent fields. The first approach, we call it adiabatic, describes PDF at the values much less than dispersion. The second, instanton, approach gives the tails of PDF at the values of the gradient much larger than dispersion. Together, both approaches give satisfactory description of gradient PDFs, as illustrated here by an example of a passive scalar advected by a one-dimensional compressible random flow.

chao-dyn↗
arXiv1996

Viscous Instanton for Burgers' Turbulence

We consider the tails of probability density functions (PDF) for different characteristics of velocity that satisfies Burgers equation driven by a large-scale force. The saddle-point approximation is employed in the path integral so that the calculation of the PDF tails boils down to finding the special field-force configuration (instanton) that realizes the extremum of probability. We calculate high moments of the velocity gradient $\partial_xu$ and find out that they correspond to the PDF with $\ln[{\cal P}(\partial_xu)]\propto-(-\partial_xu/{\rm Re})^{3/2}$ where ${\rm Re}$ is the Reynolds number. That stretched exponential form is valid for negative $\partial_xu$ with the modulus much larger than its root-mean-square (rms) value. The respective tail of PDF for negative velocity differences $w$ is steeper than Gaussian, $\ln{\cal P}(w)\sim-(w/u_{\rm rms})^3$, as well as single-point velocity PDF $\ln{\cal P}(u)\sim-(|u|/u_{\rm rms})^3$. For high velocity derivatives $u^{(k)}=\partial_x^ku$, the general formula is found: $\ln{\cal P}(|u^{(k)}|)\propto -(|u^{(k)}|/{\rm Re}^k)^{3/(k+1)}$.

chao-dyn↗
arXiv1995

The Fourth-Order Correlation Function of a Randomly Advected Passive Scalar

Advection of a passive scalar $θ$ in $d=2$ by a large-scale velocity field rapidly changing in time is considered. The Gaussian feature of the passive scalar statistics in the convective interval was discovered in \cite{95CFKLa}. Here we examine deviations from the Gaussianity: we obtain analytically the simultaneous fourth-order correlation function of $θ$. Explicit expressions for fourth-order objects, like $\langle(θ_1-θ_2)^4\rangle$ are derived.

chao-dyn↗