ANOMALOUS SCALING OF THE PASSIVE SCALAR

Abstract

We establish anomalous inertial range scaling of structure functions for a model of advection of a passive scalar by a random velocity field. The velocity statistics is taken gaussian with decorrelation in time and velocity differences scaling as $|x{|}^{\kappa /2}$ in space, with $0\le \kappa <2$. The scalar is driven by a gaussian forcing acting on spatial scale $L$ and decorrelated in time. The structure functions for the scalar are well defined as the diffusivity is taken to zero and acquire anomalous scaling behavior for large pumping scales $L$. The anomalous exponent is calculated explicitly for the $4^{\m\rm th}$ structure function and for small $\kappa$ and it differs from previous predictions. For all but the second structure functions the anomalous exponents are nonvanishing.

8 pages, latex

References in corpus (2)

• Anomalous Scaling in a Model of Passive Scalar Advection: Exact Results
• Universality in Turbulence: an Exactly Soluble Model

Cited by in corpus (152)

• Particles and fields in fluid turbulence
• Burgers Turbulence
• Anisotropy in Turbulent Flows and in Turbulent Transport
• Normal and Anomalous Scaling of the Fourth-Order Correlation Function of a Randomly Advected Passive Scalar
• Lagrangian Tetrad Dynamics and the Phenomenology of Turbulence
• Slow modes in passive advection
• Anomalous Scaling Exponents of a White-Advected Passive Scalar
• Fluid flow dynamics under location uncertainty
• Magnetic fluctuations in the classical XY model: the origin of an exponential tail in a complex system
• Renormalization Group, Operator Product Expansion, and Anomalous Scaling in a Model of Advected Passive Scalar
• Influence of compressibility on scaling regimes of strongly anisotropic fully developed turbulence
• Anomalous Scaling in the N-Point Functions of Passive Scalar
• Intermittency in passive scalar advection
• Universality and saturation of intermittency in passive scalar turbulence
• Non-locality and Intermittency in 3D Turbulence
• Anomalous scaling regimes of a passive scalar advected by the synthetic velocity field
• Fronts in passive scalar turbulence
• Geophysical flows under location uncertainty, Part II: Quasi-geostrophy and efficient ensemble spreading
• Symmetry and Scaling of Turbulent Mixing
• Geophysical flows under location uncertainty, Part I Random transport and general models
• Active and passive fields face to face
• Mean- Field Approximation and a Small Parameter in Turbulence Theory
• Instanton for random advection
• Renormalization group and anomalous scaling in a simple model of passive scalar advection in compressible flow
• Statistical geometry in scalar turbulence
• SLE_k growth processes and conformal field theories
• Persistence of small-scale anisotropies and anomalous scaling in a model of magnetohydrodynamics turbulence
• Probability Densities in Strong Turbulence
• Anisotropic Homogeneous Turbulence: hierarchy and intermittency of scaling exponents in the anisotropic sectors
• Fully developed isotropic turbulence: nonperturbative renormalization group formalism and fixed point solution
• Instanton for the Kraichnan Passive Scalar Problem
• Anomalous scaling of a passive scalar advected by the synthetic compressible flow
• Turbulence with Pressure: Anomalous Scaling of a Passive Vector Field
• Multiscaling and Structure Functions in Turbulence: An Alternative Approach
• Lagrangian method for multiple correlations in passive scalar advection
• Nonperturbative Spectrum of Anomalous Scaling Exponents in the Anisotropic Sectors of Passively Advected Magnetic Fields
• Turbulent Decay of a Passive Scalar in Batchelor Limit: Exact Results from a Quantum-Mechanical Approach
• Calculation of the anomalous exponents in the rapid-change model of passive scalar advection to order ${\epsilon }^3$
• Non-universality of the scaling exponents of a passive scalar convected by a random flow
• Scaling and universality in turbulent convection
• Inverse versus direct cascades in turbulent advection
• Anomalous exponents in the rapid-change model of the passive scalar advection in the order ${\epsilon }^3$
• Anomalous scaling of a passive scalar advected by the turbulent velocity field with finite correlation time: Two-loop approximation
• Inverse cascade and intermittency of passive scalar in 1d smooth flow
• Statistical conservation laws in turbulent transport
• Anomalous scaling of a passive scalar advected by the Navier--Stokes velocity field: Two-loop approximation
• Anomalous scaling in passive scalar advection: Monte-Carlo Lagrangian trajectories
• Probability density and scaling exponents of the moments of longitudinal velocity difference in strong turbulence
• Intermittency and Anomalous Scaling of Passive Scalars in Any Space Dimension
• Anomalous scaling, nonlocality and anisotropy in a model of the passively advected vector field
• Anomalous Scaling and Structure Instability in Three-Dimensional Passive Scalar Turbulence
• Passive Scalar: Scaling Exponents and Realizability
• Pressure and intermittency in passive vector turbulence
• Manifestation of anisotropy persistence in the hierarchies of MHD scaling exponents
• Anomalous scaling of a passive scalar in the presence of strong anisotropy
• Averaging versus Chaos in Turbulent Transport?
• Anomalous scaling in two models of the passive scalar advection: Effects of anisotropy and compressibility
• Passive Scalar Evolution in Peripheral Region
• Computing the Scaling Exponents in Fluid Turbulence from First Principles: Demonstration of Multi-scaling
• Structures and intermittency in a passive scalar model
• Spectrum of Anisotropic Exponents in Hydrodynamic Systems with Pressure
• Eddy heat exchange at the boundary under white noise turbulence
• Functional renormalisation group for turbulence
• Langevin approach to generate synthetic turbulence
• Influence of helicity on anomalous scaling of a passive scalar advected by the turbulent velocity field with finite correlation time: Two-loop approximation
• Anomalous scaling and universality in hydrodynamic systems with power-law forcing
• Fully developed turbulence and the multifractal conjecture
• Analytic Calculation of the Anomalous Exponents in Turbulence: Using the Fusion Rules to Flush Out a Small Parameter
• Scaling, renormalization and statistical conservation laws in the Kraichnan model of turbulent advection
• Anomalous scaling and anisotropy in models of passively advected vector fields
• Anomalous scaling of passive scalar fields advected by the Navier-Stokes velocity ensemble: Effects of strong compressibility and large-scale anisotropy
• On how a joint interaction of two innocent partners (smooth advection & linear damping) produces a strong intermittency
• Analytic calculation of anomalous scaling in random shell models for a passive scalar
• Logarithmic violation of scaling in strongly anisotropic turbulent transfer of a passive vector field
• Anomalous scaling in random shell models for passive scalars
• Direct Numerical Simulations of the Kraichnan Model: Scaling Exponents and Fusion Rules
• Anomalous scaling of a passive scalar advected by the turbulent velocity field with finite correlation time and uniaxial small-scale anisotropy
• Multiscaling in passive scalar advection as stochastic shape dynamics
• Anomalous scaling of passive scalar in turbulence and in equilibrium
• Functional Renormalization Group approach to the Kraichnan model
• Anomalous scaling in statistical models of passively advected vector fields
• The State of the Art in Hydrodynamic Turbulence: Past Successes and Future Challenges
• Hidden scale invariance in Navier-Stokes intermittency
• Large Deviations For Sticky Brownian Motions
• Anomalous scaling of a passive vector field in $d$ dimensions: Higher-order structure functions
• Turbulent compressible fluid: renormalization group analysis, scaling regimes, and anomalous scaling of advected scalar fields
• Influence of helicity on scaling regimes in the extended Kraichnan model
• Propagation of a Huygens front through turbulent medium
• Anomalous scaling in two and three dimensions for a passive vector field advected by a turbulent flow
• The passive polymer problem
• Passive scalar turbulence in high dimensions
• Sailing the Deep Blue Sea of Decaying Burgers Turbulence
• Passive scalar intermittency in compressible flow
• An Intermittency Model For Passive-Scalar Turbulence
• Renormalization group in the infinite-dimensional turbulence: third-order results
• Constructive Field Theory and Applications: Perspectives and Open Problems
• Moderate deviations for diffusion in time dependent random media
• Towards a two-fluid picture of intermittency in shell models of turbulence
• Spectrum of the Fokker-Planck operator representing diffusion in a random velocity field
• On Conditional Statistics in Scalar Turbulence: Theory vs. Experiment
• Eulerian spatio-temporal correlations in passive scalar turbulence
• Intermittency in the large N-limit of a spherical shell model for turbulence
• Inertial-range behaviour of a passive scalar field in a random shear flow
• Shell Model for Time-correlated Random Advection of Passive Scalars
• Passive tracer in a slowly decorrelating random flow with a large mean
• Passive advection in nonlinear medium
• Functional renormalization-group approach to decaying turbulence
• Anomalous Scalings and Dynamics of Magnetic Helicity
• Anomalous scaling of triple correlation function of white-advected passive scalar
• Advection of a passive scalar field by turbulent compressible fluid: renormalization group analysis near $d=4$
• Universality of scaling and multiscaling in turbulent symmetric binary fluids
• Spatio-temporal correlation functions in scalar turbulence from functional renormalization group
• KPZ equation limit of sticky Brownian motion
• A fractional Brownian motion model for the turbulent refractive index in lightwave propagation
• About coherent structures in random shell models for passive scalar advection
• Stochastic processes in turbulent transport
• Self-Similar Decay in the Kraichnan Model of a Passive Scalar
• Multiscale theory of turbulence in wavelet representation
• Stochastic Navier-Stokes equation and advection of a tracer field: One-loop renormalization near $d=4$
• Inhomogeneous Anisotropic Passive Scalars
• Shock statistics in higher-dimensional Burgers turbulence
• Existence and Uniqueness of $L^2$-Solutions at Zero-Diffusivity in the Kraichnan Model of a Passive Scalar
• Stationary solution for quasi-homogeneous small-scale magnetic field advected by non-Gaussian turbulent flow
• Renormalization Group in the Problem of Active Scalar Advection
• Perspectives on scaling and multiscaling in passive scalar turbulence
• A Simple Passive Scalar Advection-Diffusion Model
• Density and tracer statistics in compressible turbulence: phase transition to multifractality
• Fluid Dynamics of NSR Strings
• Coarse-grained description of a passive scalar
• Statistics of pressure and of pressure-velocity correlations in isotropic turbulence
• Conditional Averages and Probability Density Functions in the Passive Scalar Field
• Richardson's Laws for Relative Dispersion in Colored-Noise Flows with Kolmogorov-type Spectra
• Statistical properties of stochastic 2D Navier-Stokes equations from linear models
• Turbulence under a magnifying glass
• Scaling Laws in Turbulence
• Theory and Experiments for Disordered Elastic Manifolds, Depinning, Avalanches, and Sandpiles
• Scaling or multiscaling: Varieties of universality in a driven nonlinear model
• Light Propagation in Turbulent Media
• Fixed points, stability and intermittency in a shell model for advection of passive scalars
• The Batchelor--Howells--Townsend spectrum: three-dimensional case
• Anomalous Scaling in a Model of Hydrodynamic Turbulence with a Small Parameter
• Three-dimensional turbulent relative dispersion by the Gledzer-Ohkitani-Yamada shell model
• The Scalings of Scalar Structure Functions in a Velocity Field with Coherent Vortical Structures
• Towards a geometrical classification of statistical conservation laws in turbulent advection
• Symmetries and novel universal properties of turbulent hydrodynamics in a symmetric binary fluid mixture
• Spinless particle in rapidly fluctuating random magnetic field
• Particle transport in a random velocity field with Lagrangian statistics
• Soluble models of turbulent advection
• Remark on the relation between passive scalars and diffusion backward in time
• Advection by Compressible Turbulent Flows: Renormalization Group Study of Vector and Tracer Admixture
• Perturbative anomalous exponents from Kolmogorov multipliers
• Heat equilibrium distribution in a turbulent flow