Book contents
- Frontmatter
- Contents
- Preface
- List of Participants
- Magnetic Noise and the Galactic Dynamo
- On the Oscillation in Model Z
- Nonlinear Dynamos in a Spherical Shell
- The Onset of Dynamo Action in Alpha-lambda Dynamos
- Multifractality, Near-singularities and the Role of Stretching in Turbulence
- Note on Perfect Fast Dynamo Action in a Large-amplitude SFS Map
- A Thermally Driven Disc Dynamo
- Magnetic Instabilities in Rapidly Rotating Systems
- Modes of a Flux Ring Lying in the Equator of a Star
- A Nonaxisymmetric Dynamo in Toroidal Geometry
- Simulating the Interaction of Convection with Magnetic Fields in the Sun
- Experimental Aspects of a Laboratory Scale Liquid Sodium Dynamo Model
- Influence of the Period of an ABC Flow on its Dynamo Action
- Numerical Calculations of Dynamos for ABC and Related Flows
- Local Helicity, a Material Invariant for the Odd-dimensional Incompressible Euler Equations
- On the Quasimagnetostrophic Asymptotic Approximation Related to Solar Activity
- Simple Dynamical Fast Dynamos
- A Numerical Study of Dynamos in Spherical Shells with Conducting Boundaries
- Non-axisymmetric Shear Layers in a Rotating Spherical Shell
- Testing for Dynamo Action
- Alpha-quenching in Cylindrical Magnetoconvection
- On the Stretching of Line Elements in Fluids: an Approach from Differential Geometry
- Instabilities of Tidally and Precessionally Induced Flows
- Probability Distribution of Passive Scalars with Nonlinear Mean Gradient
- Magnetic Fluctuations in Fast Dynamos
- A Statistical Description of MHD Turbulence in Laboratory Plasmas
- Compressible Magnetoconvection in Three Dimensions
- The Excitation of Nonaxisymmetric Magnetic Fields in Galaxies
- Localized Magnetic Fields in a Perfectly Conducting Fluid
- Turbulent Dynamo and the Geomagnetic Secular Variation
- On-Off Intermittency: General Description and Feedback Model
- Dynamo Action in a Nearly Integrable Chaotic Flow
- The Dynamo Mechanism in the Deep Convection Zone of the Sun
- Shearing Instabilities in Magnetoconvection
- On the Role of Rotation of the Internal Core Relative to the Mantle
- Evolution of Magnetic Fields in a Swirling Jet
- Analytic Fast Dynamo Solution for a Two-dimensional Pulsed Flow
- On Magnetic Dynamos in Thin Accretion Disks Around Compact and Young Stars
- The Strong Field Branch of the Childress–Soward Dynamo
- Evidence for the Suppression of the Alpha-effect by Weak Magnetic Fields
- Turbulent Magnetic Transport Effects and their Relation to Magnetic Field Intermittency
- Proving the Existence of Negative Isotropic Eddy Viscosity
- Dynamo Action Induced by Lateral Variation of Electrical Conductivity
- Spherical Inertial Oscillation and Convection
- Hydrodynamic Stability of the ABC Flow
- Dynamos with Ambipolar Diffusion
- Subject Index
Probability Distribution of Passive Scalars with Nonlinear Mean Gradient
Published online by Cambridge University Press: 11 May 2010
- Frontmatter
- Contents
- Preface
- List of Participants
- Magnetic Noise and the Galactic Dynamo
- On the Oscillation in Model Z
- Nonlinear Dynamos in a Spherical Shell
- The Onset of Dynamo Action in Alpha-lambda Dynamos
- Multifractality, Near-singularities and the Role of Stretching in Turbulence
- Note on Perfect Fast Dynamo Action in a Large-amplitude SFS Map
- A Thermally Driven Disc Dynamo
- Magnetic Instabilities in Rapidly Rotating Systems
- Modes of a Flux Ring Lying in the Equator of a Star
- A Nonaxisymmetric Dynamo in Toroidal Geometry
- Simulating the Interaction of Convection with Magnetic Fields in the Sun
- Experimental Aspects of a Laboratory Scale Liquid Sodium Dynamo Model
- Influence of the Period of an ABC Flow on its Dynamo Action
- Numerical Calculations of Dynamos for ABC and Related Flows
- Local Helicity, a Material Invariant for the Odd-dimensional Incompressible Euler Equations
- On the Quasimagnetostrophic Asymptotic Approximation Related to Solar Activity
- Simple Dynamical Fast Dynamos
- A Numerical Study of Dynamos in Spherical Shells with Conducting Boundaries
- Non-axisymmetric Shear Layers in a Rotating Spherical Shell
- Testing for Dynamo Action
- Alpha-quenching in Cylindrical Magnetoconvection
- On the Stretching of Line Elements in Fluids: an Approach from Differential Geometry
- Instabilities of Tidally and Precessionally Induced Flows
- Probability Distribution of Passive Scalars with Nonlinear Mean Gradient
- Magnetic Fluctuations in Fast Dynamos
- A Statistical Description of MHD Turbulence in Laboratory Plasmas
- Compressible Magnetoconvection in Three Dimensions
- The Excitation of Nonaxisymmetric Magnetic Fields in Galaxies
- Localized Magnetic Fields in a Perfectly Conducting Fluid
- Turbulent Dynamo and the Geomagnetic Secular Variation
- On-Off Intermittency: General Description and Feedback Model
- Dynamo Action in a Nearly Integrable Chaotic Flow
- The Dynamo Mechanism in the Deep Convection Zone of the Sun
- Shearing Instabilities in Magnetoconvection
- On the Role of Rotation of the Internal Core Relative to the Mantle
- Evolution of Magnetic Fields in a Swirling Jet
- Analytic Fast Dynamo Solution for a Two-dimensional Pulsed Flow
- On Magnetic Dynamos in Thin Accretion Disks Around Compact and Young Stars
- The Strong Field Branch of the Childress–Soward Dynamo
- Evidence for the Suppression of the Alpha-effect by Weak Magnetic Fields
- Turbulent Magnetic Transport Effects and their Relation to Magnetic Field Intermittency
- Proving the Existence of Negative Isotropic Eddy Viscosity
- Dynamo Action Induced by Lateral Variation of Electrical Conductivity
- Spherical Inertial Oscillation and Convection
- Hydrodynamic Stability of the ABC Flow
- Dynamos with Ambipolar Diffusion
- Subject Index
Summary
Recently Pumir, Shraiman & Siggia (1991) proposed an idea that a nonlinear mean temperature is essential to produce exponentiallike tails for probability density functions (PDFs) of temperature fluctuations in convection. In this paper, results of numerical simulations of the 3D random advection equation with a mean gradient term will be shown. Some theoretical analysis is given based on a transport equation without molecular diffusion. The simplified analysis can capture the characteristic shapes of PDFs well.
INTRODUCTION
The study of passive scalar advection provides fundamental understanding of various phenomena such as convection and mixing that are ubiquitous in nature. In particular, the probability distribution of amplitude and its spatial gradients are of vital importance in relation to recent active studies of non-Gaussian probability density functions (PDFs) endemic in turbulence.
Since Castaing et al. (1989) reported exponential-like tails on the PDF of temperature fluctuations in thermal convection at very high Rayleigh numbers, there has been increasing interest in the mechanism of the non-Gaussian tails on PDFs of amplitudes. In a recent paper, Pumir, Shraiman & Siggia (1991) have suggested that the non-Gaussian tails for an advected passive temperature field may be induced by the presence of a mean-temperature profile. A simple physical mechanism for this is proposed in the present paper. The resultant non-Gaussian statistics will be shown by numerical simulations and theoretical analysis for a transport equation without molecular diffusion. In this paper, the result on PDFs is summarized; other details will be presented elsewhere (Kimura & Kraichnan 1993).
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- Solar and Planetary Dynamos , pp. 189 - 194Publisher: Cambridge University PressPrint publication year: 1994