Inverse versus direct cascades in turbulent advection

  title={Inverse versus direct cascades in turbulent advection},
  author={Michael Chertkov and Igor V. Kolokolov and M. Vegrassola},
  journal={Physical Review Letters},
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 is direct again. Otherwise it is inverse; i.e., very large scales are excited. The dynamical hint for the direction of the cascade… 
Phase transition in the passive scalar advection
Abstract The paper studies the behavior of the trajectories of fluid particles in a compressible generalization of the Kraichnan ensemble of turbulent velocities. We show that, depending on the
Inverse cascades in turbulence and the case of rotating flows
We first summarize briefly several properties concerning the dynamics of two-dimensional (2D) turbulence, with an emphasis on the inverse cascade of energy to the largest accessible scale of the
Inverse cascade and intermittency of passive scalar in one-dimensional smooth flow
Random advection of a Lagrangian tracer scalar field $\ensuremath{\theta}(t,x)$ by a one-dimensional, spatially smooth and short-correlated in time velocity field is considered. Scalar fluctuations
Scaling of turbulence and turbulent mixing using Terascale numerical simulations
We report basic results from newnumerical simulations of passive scalar mixing at Schmidt numbers (Sc) of the order of 1000 in isotropic turbulence. The required high gridresolution is made possible
Turbulent mixing of a critical fluid: The non-perturbative renormalization
Non-perturbative Renormalization Group (NPRG) technique is applied to a stochastical model of a non-conserved scalar order parameter near its critical point, subject to turbulent advection. The
Split energy cascade in turbulent thin fluid layers
We discuss the phenomenology of the split energy cascade in a three-dimensional thin fluid layer by means of high resolution numerical simulations of the Navier-Stokes equations. We observe the
Dual constant-flux energy cascades to both large scales and small scales
In this paper, we present an overview of concepts and data concerning inverse cascades of excitation towards scales larger than the forcing scale in a variety of contexts, from two-dimensional fluids
Turbulent compressible fluid: Renormalization group analysis, scaling regimes, and anomalous scaling of advected scalar fields.
The existence of additional regimes, which could not be found using the direct perturbative approach of the previous work, are explored, and the crossover between different regimes is analyzed to determine them near the special value of space dimension 4 in the framework of double y and ɛ expansion.
A turbulent constitutive law for the two-dimensional inverse energy cascade
  • G. Eyink
  • Physics
    Journal of Fluid Mechanics
  • 2006
The inverse energy cascade of two-dimensional turbulence is often represented phenomenologically by a Newtonian stress–strain relation with a ‘negative eddy viscosity’. Here we develop a fundamental
Inverse Cascade and Intermittency of Passive Scalar in 1D Smooth Flow; Inverse Cascade in Multidimensional Compressible Flows
We considere random advection of Lagrangian tracer scalar field θ(t, y) by a compressible, spatially smooth and short-correlated in time velocity field [1, 2], see also [3]. Scalar fluctuations are


Inverse cascade and intermittency of passive scalar in one-dimensional smooth flow
Random advection of a Lagrangian tracer scalar field $\ensuremath{\theta}(t,x)$ by a one-dimensional, spatially smooth and short-correlated in time velocity field is considered. Scalar fluctuations
Perturbative expansions for intermittency scaling exponents in the Kraichnan passive scalar model [Phys. Rev. Lett. 72, 1016 (1994)] are investigated. A one-dimensional compressible model is
Statistics of a passive scalar advected by a large-scale two-dimensional velocity field: Analytic solution.
The change of variables that allows one to map the matrix problem onto a scalar one is found and to prove the central limit theorem for the stretching rate statistics, valid for any finite correlation time of the velocity field.
Small‐Scale Structure of a Scalar Field Convected by Turbulence
Batchelor's theory of the turbulent straining of small‐spatial‐scale amplitude variations of a convected scalar field is re‐examined to see the effects of fluctuation of the rates of strain in space
Anomalous scaling of the passive scalar.
Anomalous inertial range scaling of structure functions is established for a model of advection of a passive scalar by a random velocity field and for all but the second structure functions the anomalous exponents are nonvanishing.
Small-scale variation of convected quantities like temperature in turbulent fluid Part 1. General discussion and the case of small conductivity
When some external agency imposes on a fluid large-scale variations of some dynamically passive, conserved, scalar quantity θ like temperature or concentration of solute, turbulent motion of the
Inertial Ranges in Two‐Dimensional Turbulence
Two‐dimensional turbulence has both kinetic energy and mean‐square vorticity as inviscid constants of motion. Consequently it admits two formal inertial ranges, E(k)∼e2/3k−5/3 and E(k)∼η2/3k−3, where
Normal and anomalous scaling of 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 and analytically the simultaneous fourth-order correlation function of θ is obtained.
Turbulence without pressure.
  • Polyakov
  • Mathematics, Medicine
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1995
It is demonstrated that the breakdown of Galilean invariance is responsible for intermittency and the operator product expansion is established, and the effects of pressure can be turned on perturbatively.
) 5
The growing importance of knowledge and innovations for modern organisations (Davenport, DeLong, & Breers, 1998; Drucker, 1998; Nonaka, 1998; Stewart, 1997), and increasing demands for new skills and