scholarly journals Normal and anomalous scaling of the fourth-order correlation function of a randomly advected passive scalar

1995 ◽  
Vol 52 (5) ◽  
pp. 4924-4941 ◽  
Author(s):  
M. Chertkov ◽  
G. Falkovich ◽  
I. Kolokolov ◽  
V. Lebedev
Keyword(s):  
Correlation Function ◽  
Fourth Order ◽  
Passive Scalar ◽  
Anomalous Scaling

scholarly journals Inverse cascade anomalies in fourth-order Leith models

2021 ◽  
Author(s):  
Simon Thalabard ◽  
Sergey Medvedev ◽  
Vladimir Grebenev ◽  
Sergey Nazarenko
Keyword(s):  
Fourth Order ◽  
Field Model ◽  
Kinetic Equations ◽  
Vacuum Field ◽  
Wave Turbulence ◽  
Anomalous Scaling ◽  
Time Singularity ◽  
Linear Diffusion ◽  
Local Approximations ◽  
Finite Time Singularity

Abstract We analyze a family of fourth-order non-linear diffusion models corresponding to local approximations of 4-wave kinetic equations of weak wave turbulence. We focus on a class of parameters for which a dual cascade behaviour is expected with an infrared finite-time singularity associated to inverse transfer of waveaction. This case is relevant for wave turbulence arising in the Nonlinear Schrödinger model and for the gravitational waves in the Einstein’s vacuum field model. We show that inverse transfer is not described by a scaling of the constant-flux solution but has an anomalous scaling. We compute the anomalous exponents and analyze their origin using the theory of dynamical systems.

scholarly journals COMBINED EFFECTS OF SMALL SCALE ANISOTROPY AND COMPRESSIBILITY ON ANOMALOUS SCALING OF A PASSIVE SCALAR

2008 ◽  
Vol 22 (21) ◽  
pp. 3589-3617 ◽  
Author(s):  
E. JURČIŠINOVÁ ◽  
M. JURČIŠIN ◽  
R. REMECKY ◽  
M. SCHOLTZ
Keyword(s):  
Operator Product Expansion ◽  
Passive Scalar ◽  
Inertial Range ◽  
Isotropic Case ◽  
Operator Product ◽  
Small Scale ◽  
Anomalous Scaling ◽  
Critical Dimensions ◽  
First Order ◽  
Anisotropy Parameters

The model of a passive scalar field advected by the compressible Gaussian strongly anisotropic velocity field with the covariance ∝ δ(t - t′)|x - x′|2ε is studied using the field theoretic renormalization group and the operator product expansion. The inertial-range stability of the corresponding scaling regime is established. The anomalous scaling of the single-time structure functions is studied and the corresponding anomalous exponents are calculated. Their dependence on the compressibility parameter and anisotropy parameters is analyzed. It is shown that, as in the isotropic case, the presence of compressibility leads to the decrease of the critical dimensions of the important composite operators, i.e., the anomalous scaling is more pronounced in the compressible systems. All calculations are done to the first order in ε.

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