Related papers: Anomalous Regularization in Kraichnan's Passive Sc…
We establish exact inequalities for the structure-function scaling exponents of a passively advected scalar in both the inertial-convective and viscous-convective ranges. These inequalities involve the scaling exponents of the velocity…
The field-theoretic renormalization group (RG) and the operator product expansion are applied to the model of a divergence-free vector quantity, passively advected by the ``synthetic'' turbulent flow with a finite correlation time. The…
The problem of the effects of compressibility and large-scale anisotropy on anomalous scaling behavior is considered for two models describing passive advection of scalar density and tracer fields. The advecting velocity field is Gaussian,…
We show that the statistics of a turbulent passive scalar at scales larger than the pumping may exhibit multiscaling due to a weaker mechanism than the presence of statistical conservation laws. We develop a general formalism to give…
We show that the Kolmogorov-1941 picture of fully developed hydrodynamic turbulence (with the scaling of the structure functions $S_n(R) \propto R^{n/3}$) necessarily leads to an anomalous scaling for correlation functions which include the…
We study a model of fully developed turbulence of a compressible fluid, based on the stochastic Navier-Stokes equation, by means of the field theoretic renormalization group. In this approach, scaling properties are related to the fixed…
The third order correlation function of the scalar field advected by a Gaussian random velocity, with a spatial scaling exponent $2 - \epsilon$, and in the presence of a mean gradient, is calculated perturbatively in $\epsilon << 1$. This…
The problem of the interplay between normal and anomalous scaling in turbulent systems stirred by a random forcing with a power law spectrum is addressed. We consider both linear and nonlinear systems. As for the linear case, we study…
The renormalization group and operator product expansion are applied to the model of a passive scalar quantity advected by the Gaussian self-similar velocity field with finite, and not small, correlation time. The inertial-range energy…
The field theoretic renormalization group and operator product expansion are applied to the model of a passive scalar advected by the Gaussian velocity field with zero mean and correlation function $\propto\delta(t-t')/k^{d+\eps}$.…
Recent experiments demonstrate the importance of substrate curvature for actively forced fluid dynamics. Yet, the covariant formulation and analysis of continuum models for non-equilibrium flows on curved surfaces still poses theoretical…
We investigate a generic non-phase invariant Hamiltonian model that governs the dynamics of nonlinear dispersive waves. We give evidence that initial data characterized by random phases naturally evolve into phase correlations between…
Infrared asymptotic behaviour of a scalar field, passively advected by a random shear flow, is studied by means of the field theoretic renormalization group and the operator product expansion. The advecting velocity is Gaussian, white in…
This work investigates the influence of a generic anomalous diffusion model on mass convection in a fluid-saturated porous medium, focusing on superdiffusive regimes. A mathematical model is developed, and tability analyses - both linear…
The study of passive scalar transport in a turbulent velocity field leads naturally to the notion of generalized flows which are families of probability distributions on the space of solutions to the associated ODEs, which no longer satisfy…
The problem of anomalous scaling in the model of a transverse vector field $\theta_{i}(t,x)$ passively advected by the non-Gaussian, correlated in time turbulent velocity field governed by the Navier--Stokes equation, is studied by means of…
We consider the compressible Kraichnan model of turbulent advection with small molecular diffusivity and velocity field regularized at short scales to mimic the effects of viscosity. As noted in ref.[5], removing those two regularizations…
We study anomalous dissipation in the context of passive scalars and we construct a two-dimensional autonomous divergence-free velocity field in $C^\alpha$ (with $\alpha \in (0,1)$ arbitrary but fixed) which exhibits anomalous dissipation.…
Introductory lectures on the Kraichnan model of passive advection
A recent analysis of the 4-point correlation function of the passive scalar advected by a time-decorrelated random flow is extended to the N-point case. It is shown that all stationary-state inertial-range correlations are dominated by…