scholarly journals Dynamics of fingering convection. Part 1 Small-scale fluxes and large-scale instabilities

2011 ◽  
Vol 677 ◽  
pp. 530-553 ◽  
Author(s):  
A. TRAXLER ◽  
S. STELLMACH ◽  
P. GARAUD ◽  
T. RADKO ◽  
N. BRUMMELL
Keyword(s):  
Large Scale ◽  
Molecular Diffusion ◽  
Turbulent Transport ◽  
Mean Field Theory ◽  
Density Ratio ◽  
Mean Field ◽  
Field Measurements ◽  
Small Scale ◽  
Diapycnal Mixing ◽  
Density Ratios

Double-diffusive instabilities are often invoked to explain enhanced transport in stably stratified fluids. The most-studied natural manifestation of this process, fingering convection, commonly occurs in the ocean's thermocline and typically increases diapycnal mixing by 2 orders of magnitude over molecular diffusion. Fingering convection is also often associated with structures on much larger scales, such as thermohaline intrusions, gravity waves and thermohaline staircases. In this paper, we present an exhaustive study of the phenomenon from small to large scales. We perform the first three-dimensional simulations of the process at realistic values of the heat and salt diffusivities and provide accurate estimates of the induced turbulent transport. Our results are consistent with oceanic field measurements of diapycnal mixing in fingering regions. We then develop a generalized mean-field theory to study the stability of fingering systems to large-scale perturbations using our calculated turbulent fluxes to parameterize small-scale transport. The theory recovers the intrusive instability, the collective instability and the γ-instability as limiting cases. We find that the fastest growing large-scale mode depends sensitively on the ratio of the background gradients of temperature and salinity (the density ratio). While only intrusive modes exist at high density ratios, the collective and γ instabilities dominate the system at the low density ratios where staircases are typically observed. We conclude by discussing our findings in the context of staircase-formation theory.

scholarly journals On the helicity characteristics and induced emf of magnetic-Coriolis wave packets

2020 ◽  
Vol 223 (2) ◽  
pp. 1398-1411
Author(s):  
B R McDermott ◽  
P A Davidson
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Rotation Axis ◽  
Wave Packets ◽  
Mean Field Theory ◽  
Mean Field ◽  
Low Frequency ◽  
Dynamo Model ◽  
Small Scale ◽  
Inertial Wave

SUMMARY In a rapidly rotating Boussinesq fluid, buoyant anomalies radiate low-frequency inertial wave packets that disperse along the rotation axis. The wave packets lead to axially elongated vortices, which propagate negative (positive) kinetic helicity upwards (downwards) with respect to the rotation vector. The kinetic helicity carried by the inertial wave packets is near-maximal relative to the velocity and vorticity fields. In classical mean-field theory, kinetic helicity is often associated with the α-effect, which is thought to be an important ingredient for planetary dynamos. The modification of inertial wave packets in the presence of a transverse uniform magnetic field is investigated here, motivated by small-scale dynamics in planetary cores, where a large-scale magnetic field affects fluid motions. We study numerically the dispersion of wave packets from an isolated buoyant source and from a random layer of buoyant anomalies, while varying the Lehnert number Le—the ratio of the frequencies of Alfvén and inertial waves. We find that for Le < 0.1, the vortices are columnar and continue to segregate kinetic helicity so that it is negative (positive) above (below) the buoyant source. Importantly, the wave packets induce an α-effect, which remains strong and coherent for Earth-like values of the Lehnert number (Le < 0.1). The interaction of wave packets emitted by multiple neighbouring buoyant sources results in an α-effect that is stronger than the α-effect induced by wave packets launched from an isolated buoyant source, and we provide an analytical explanation for this. The coherence of the α-effect induced by the wave packets, for Earth-like values of the Lehnert number, lends support to the α2 dynamo model driven by helical waves.

scholarly journals Energy transfer in Hall-MHD turbulence: cascades, backscatter, and dynamo action

2007 ◽  
Vol 73 (3) ◽  
pp. 377-401 ◽  
Author(s):  
PABLO D. MININNI ◽  
ALEXANDROS ALEXAKIS ◽  
ANNICK POUQUET
Keyword(s):  
Large Scale ◽  
Magnetic Energy ◽  
Transport Coefficients ◽  
Mean Field Theory ◽  
Mean Field ◽  
Small Scale ◽  
Mhd Turbulence ◽  
Dynamo Action ◽  
Large Scale Magnetic Field ◽  
Hall Mhd

AbstractScale interactions in Hall magnetohydrodynamics (MHDs) are studied using both the mean field theory derivation of transport coefficients, and direct numerical simulations in three space dimensions. In the magnetically dominated regime, the eddy resistivity is found to be negative definite, leading to large-scale instabilities. A direct cascade of the total energy is observed, although as the amplitude of the Hall effect is increased, backscatter of magnetic energy to large scales is found, a feature not present in MHD flows. The coupling between the magnetic and velocity fields is different than in the MHD case, and backscatter of energy from small-scale magnetic fields to large-scale flows is also observed. For the magnetic helicity, a strong quenching of its transfer is found. We also discuss non-helical magnetically forced Hall-MHD simulations where growth of a large-scale magnetic field is observed.

scholarly journals Generation of large-scale vorticity in rotating stratified turbulence with inhomogeneous helicity: mean-field theory

2018 ◽  
Vol 84 (3) ◽  
Author(s):  
N. Kleeorin ◽  
I. Rogachevskii
Keyword(s):  
Field Theory ◽  
Reynolds Stress ◽  
Large Scale ◽  
Mean Field Theory ◽  
Mean Field ◽  
Combined Effect ◽  
Small Scale ◽  
Stratified Turbulence ◽  
Developed Turbulence ◽  
Scale Shear

We discuss a mean-field theory of the generation of large-scale vorticity in a rotating density stratified developed turbulence with inhomogeneous kinetic helicity. We show that the large-scale non-uniform flow is produced due to either a combined action of a density stratified rotating turbulence and uniform kinetic helicity or a combined effect of a rotating incompressible turbulence and inhomogeneous kinetic helicity. These effects result in the formation of a large-scale shear, and in turn its interaction with the small-scale turbulence causes an excitation of the large-scale instability (known as a vorticity dynamo) due to a combined effect of the large-scale shear and Reynolds stress-induced generation of the mean vorticity. The latter is due to the effect of large-scale shear on the Reynolds stress. A fast rotation suppresses this large-scale instability.

scholarly journals On the dynamical interaction between overshooting convection and an underlying dipole magnetic field – I. The non-dynamo regime

2021 ◽  
Vol 503 (1) ◽  
pp. 362-375
Author(s):  
L Korre ◽  
NH Brummell ◽  
P Garaud ◽  
C Guervilly
Keyword(s):  
Magnetic Field ◽  
Turbulent Diffusion ◽  
Large Scale ◽  
Molecular Diffusion ◽  
Mean Field ◽  
Stable Region ◽  
Turbulent Regime ◽  
Poloidal Magnetic Field ◽  
Dynamical Interaction ◽  
Large Scale Field

ABSTRACT Motivated by the dynamics in the deep interiors of many stars, we study the interaction between overshooting convection and the large-scale poloidal fields residing in radiative zones. We have run a suite of 3D Boussinesq numerical calculations in a spherical shell that consists of a convection zone with an underlying stable region that initially compactly contains a dipole field. By varying the strength of the convective driving, we find that, in the less turbulent regime, convection acts as turbulent diffusion that removes the field faster than solely molecular diffusion would do. However, in the more turbulent regime, turbulent pumping becomes more efficient and partially counteracts turbulent diffusion, leading to a local accumulation of the field below the overshoot region. These simulations suggest that dipole fields might be confined in underlying stable regions by highly turbulent convective motions at stellar parameters. The confinement is of large-scale field in an average sense and we show that it is reasonably modelled by mean-field ideas. Our findings are particularly interesting for certain models of the Sun, which require a large-scale, poloidal magnetic field to be confined in the solar radiative zone in order to explain simultaneously the uniform rotation of the latter and the thinness of the solar tachocline.

The Fully Developed Wake of a Circular Cylinder

1949 ◽  
Vol 2 (4) ◽  
pp. 451 ◽  
Author(s):  
AA Townsend
Keyword(s):  
Circular Cylinder ◽  
Diffusion Coefficients ◽  
Large Scale ◽  
Turbulent Transport ◽  
Turbulent Energy ◽  
Small Scale ◽  
Mean Velocity ◽  
Turbulent Fluid ◽  
Air Stream ◽  
Scale Motion

Extending previous work on turbulent diffusion in the wake of a circular-cylinder, a series of measurements have been made of the turbulent transport of mean stream momentum, turbulent energy, and heat in the wake of a cylinder of 0.169 cm. diameter, placed in an air-stream of velocity 1280 cm. sec.-1. It has been possible to extend the measurements to 960 diameters down-stream from the cylinder, and it 1s found that, at distances in excess of 600 diameters, the requirements of dynamical similarity are very nearly satisfied. To account for the observed rates of transport of turbulent energy and heat, it is necessary that only part of this transport be due to bulk convection by the slow large-scale motion of the jets of turbulent fluid emitted by the central, fully turbulent core of the wake, which had been supposed previously to perform most of the transport. The remainder of the transport is carried out by the small-scale diffusive motion of the turbulent eddies within the jets, and may be described by assigning diffusion coefficients to the turbulent fluid. It is found that the diffusion coefficients for momentum and heat are approximately equal, but that for turbulent energy is considerably smaller. On the basis of these hypotheses, it is possible to calculate $he form of the mean velocity distribution in good agreement with experiment, and to give a qualitative explanation of the apparently more rapid diffusion of heat.

scholarly journals Convection and Dynamo in Newly Born Neutron Stars

2022 ◽  
Vol 924 (2) ◽  
pp. 75
Author(s):  
Youhei Masada ◽  
Tomoya Takiwaki ◽  
Kei Kotake
Keyword(s):  
Spherical Shell ◽  
Neutron Stars ◽  
Large Scale ◽  
Convection Zone ◽  
Turbulent Transport ◽  
Mean Field ◽  
Magnetic Component ◽  
Large Scale Structures ◽  
Scale Structures ◽  
Convective Model

Abstract To study properties of magnetohydrodynamic (MHD) convection and resultant dynamo activities in proto-neutron stars (PNSs), we construct a “PNS in a box” simulation model and solve the compressible MHD equation coupled with a nuclear equation of state (EOS) and simplified leptonic transport. As a demonstration, we apply it to two types of PNS model with different internal structures: a fully convective model and a spherical-shell convection model. By varying the spin rate of the models, the rotational dependence of convection and the dynamo that operate inside the PNS is investigated. We find that, as a consequence of turbulent transport by rotating stratified convection, large-scale structures of flow and thermodynamic fields are developed in all models. Depending on the spin rate and the depth of the convection zone, various profiles of the large-scale structures are obtained, which can be physically understood as steady-state solutions to the “mean-field” equation of motion. Additionally to those hydrodynamic structures, a large-scale magnetic component of  ( 10 15 ) G is also spontaneously organized in disordered tangled magnetic fields in all models. The higher the spin rate, the stronger the large-scale magnetic component grows. Intriguingly, as an overall trend, the fully convective models have a stronger large-scale magnetic component than that in the spherical-shell convection models. The deeper the convection zone extends, the larger the size of the convective eddies becomes. As a result, rotationally constrained convection seems to be more easily achieved in the fully convective model, resulting in a higher efficiency of the large-scale dynamo there. To gain a better understanding of the origin of the diversity of a neutron star’s magnetic field, we need to study the PNS dynamo in a wider parameter range.

Multiscale Simulations of Domains in Ferroelectrics

Domain Walls ◽  
2020 ◽  
pp. 311-339
Author(s):  
S. Liu ◽  
I. Grinberg ◽  
A. M. Rappe
Keyword(s):  
Density Functional ◽  
Large Scale ◽  
Mean Field Theory ◽  
Mean Field ◽  
Md Simulations ◽  
Relaxor Ferroelectrics ◽  
Ferroelectric Materials ◽  
Multiscale Simulations ◽  
Challenges And Opportunities ◽  
Physically Based

This chapter focuses on recent studies of ferroelectrics, where large-scale molecular dynamics (MD) simulations using first-principles-based force fields played a central role in revealing important physics inaccessible to direct density functional theory (DFT) calculations but critical for developing physically-based free energy functional for coarse-grained phase-field-type simulations. After reviewing typical atomistic potentials of ferroelectrics for MD simulations, the chapter describes a progressive theoretical framework that combines DFT, MD, and a mean-field theory. It then focuses on relaxor ferroelectrics. By examining the spatial and temporal polarization correlations in prototypical relaxor ferroelectrics with million-atom MD simulations and novel analysis techniques, this chapter shows that the widely accepted model of polar nanoregions embedded in a non-polar matrix is incorrect for Pb-based relaxors. Rather, the unusual properties of theses relaxor ferroelectrics stem from the presence of a multi-domain state with extremely small domain sizes (2–10 nanometers), giving rise to a greater flexibility for polarization rotations and the ultrahigh dielectric and piezoelectric responses. Finally, this chapter discusses the challenges and opportunities for multiscale simulations of ferroelectric materials.

scholarly journals Mean-Field Magnetohydrodynamics as a Basis of Solar Dynamo Theory

1976 ◽  
Vol 71 ◽  
pp. 323-344 ◽  
Author(s):  
K.-H. Rädler
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Mean Field ◽  
Strong Relationship ◽  
Solar Radius ◽  
Small Scale ◽  
Dynamo Theory ◽  
The Magnetic Field ◽  
Complicated Situation ◽  
Insight Into

One of the most striking features of both the magnetic field and the motions observed at the Sun is their highly irregular or random character which indicates the presence of rather complicated magnetohydrodynamic processes. Of great importance in this context is a comprehension of the behaviour of the large scale components of the magnetic field; large scales are understood here as length scales in the order of the solar radius and time scales of a few years. Since there is a strong relationship between these components and the solar 22-years cycle, an insight into the mechanism controlling these components also provides for an insight into the mechanism of the cycle. The large scale components of the magnetic field are determined not only by their interaction with the large scale components of motion. On the contrary, a very important part is played also by an interaction between the large and the small scale components of magnetic field and motion so that a very complicated situation has to be considered.

scholarly journals Characterising the surface magnetic fields of T Tauri stars with high-resolution near-infrared spectroscopy

2019 ◽  
Vol 630 ◽  
pp. A99 ◽  
Author(s):  
A. Lavail ◽  
O. Kochukhov ◽  
G. A. J. Hussain
Keyword(s):  
Magnetic Field ◽  
High Resolution ◽  
Magnetic Fields ◽  
Large Scale ◽  
Near Infrared ◽  
Field Measurements ◽  
T Tauri Stars ◽  
Small Scale ◽  
Surface Magnetic Field ◽  
T Tauri

Aims. In this paper, we aim to characterise the surface magnetic fields of a sample of eight T Tauri stars from high-resolution near-infrared spectroscopy. Some stars in our sample are known to be magnetic from previous spectroscopic or spectropolarimetric studies. Our goals are firstly to apply Zeeman broadening modelling to T Tauri stars with high-resolution data, secondly to expand the sample of stars with measured surface magnetic field strengths, thirdly to investigate possible rotational or long-term magnetic variability by comparing spectral time series of given targets, and fourthly to compare the magnetic field modulus ⟨B⟩ tracing small-scale magnetic fields to those of large-scale magnetic fields derived by Stokes V Zeeman Doppler Imaging (ZDI) studies. Methods. We modelled the Zeeman broadening of magnetically sensitive spectral lines in the near-infrared K-band from high-resolution spectra by using magnetic spectrum synthesis based on realistic model atmospheres and by using different descriptions of the surface magnetic field. We developped a Bayesian framework that selects the complexity of the magnetic field prescription based on the information contained in the data. Results. We obtain individual magnetic field measurements for each star in our sample using four different models. We find that the Bayesian Model 4 performs best in the range of magnetic fields measured on the sample (from 1.5 kG to 4.4 kG). We do not detect a strong rotational variation of ⟨B⟩ with a mean peak-to-peak variation of 0.3 kG. Our confidence intervals are of the same order of magnitude, which suggests that the Zeeman broadening is produced by a small-scale magnetic field homogeneously distributed over stellar surfaces. A comparison of our results with mean large-scale magnetic field measurements from Stokes V ZDI show different fractions of mean field strength being recovered, from 25–42% for relatively simple poloidal axisymmetric field topologies to 2–11% for more complex fields.

scholarly journals The physical impact of towed demersal fishing gears on soft sediments

2015 ◽  
Vol 73 (suppl_1) ◽  
pp. i5-i14 ◽  
Author(s):  
F. G. O'Neill ◽  
A. Ivanović
Keyword(s):  
Mathematical Modelling ◽  
Large Scale ◽  
Lateral Displacement ◽  
Field Measurements ◽  
Small Scale ◽  
Physical Interaction ◽  
Soft Sediments ◽  
Fishing Gears ◽  
Scale Modelling ◽  
Physical Impact

Abstract An improved understanding of the physical interaction of towed demersal fishing gears with the seabed has been developed in recent years, and there is a clearer view of the underpinning mechanical processes that lead to the modification and alteration of the benthic environment. The physical impact of these gears on soft sediments can be classified broadly as being either geotechnical or hydrodynamic in nature: penetration and piercing of the substrate, lateral displacement of sediment, and the influence of the pressure field transmitted through the sediment can be considered geotechnical, whereas the mobilization of sediment into the water column can be considered hydrodynamic. A number of experimental and numerical approaches have been used to gain better insights of these physical processes. These include small-scale modelling in towing tanks and sand channels; large-scale modelling in the field; measurements behind full-scale towed gears at sea; numerical/mathematical modelling of sediment mechanics; and numerical/mathematical modelling of hydrodynamics. Here, we will review this research, and that in associated fields, and show how it can form the basis of predictive models of the benthic impact of trawl gears.

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