scholarly journals Synthesis of Small and Large Scale Dynamos

2002 ◽  
Vol 12 ◽  
pp. 739-741
Author(s):  
Kandaswamy Subramanian
Keyword(s):  
Reynolds Number ◽  
Large Scale ◽  
Magnetic Reynolds Number ◽  
Mhd Equations ◽  
Magnetic Helicity ◽  
Small Scale ◽  
Quantum Mechanical ◽  
Closure Model ◽  
Scale Fluctuation ◽  
Small Scale Fluctuation

AbstractUsing a closure model for the evolution of magnetic correlations, we uncover an interesting plausible saturated state of the small-scale fluctuation dynamo (SSD) and a novel anology between quantum mechanical tunnelling and the generation of large-scale fields. Large scale fields develop via the α-effect, but as magnetic helicity can only change on a resistive timescale, the time it takes to organize the field into large scales increases with magnetic Reynolds number. This is very similar to the results which obtain from simulations using the full MHD equations.

A numerical study of the transition of jet diffusion flames

1990 ◽  
Vol 431 (1882) ◽  
pp. 301-314 ◽  
Keyword(s):  
Reynolds Number ◽  
Diffusion Coefficient ◽  
Large Scale ◽  
Numerical Study ◽  
Small Scale ◽  
Surface Model ◽  
Flame Surface ◽  
Transition Mechanism ◽  
Air Stream ◽  
Scale Fluctuation

A numerical study on the transition from laminar to turbulent of two-dimensional fuel jet flames developed in a co-flowing air stream was made by adopting the flame surface model of infinite chemical reaction rate and unit Lewis number. The time dependent compressible Navier–Stokes equation was solved numerically with the equation for coupling function by using a finite difference method. The temperature-dependence of viscosity and diffusion coefficient were taken into account so as to study effects of increases of these coefficients on the transition. The numerical calculation was done for the case when methane is injected into a co-flowing air stream with variable injection Reynolds number up to 2500. When the Reynolds number was smaller than 1000 the flame, as well as the flow, remained laminar in the calculated domain. As the Reynolds number was increased above this value, a transition point appeared along the flame, downstream of which the flame and flow began to fluctuate. Two kinds of fluctuations were observed, a small scale fluctuation near the jet axis and a large scale fluctuation outside the flame surface, both of the same origin, due to the Kelvin–Helmholtz instability. The radial distributions of density and transport coefficients were found to play dominant roles in this instability, and hence in the transition mechanism. The decreased density in the flame accelerated the instability, while the increase in viscosity had a stabilizing effect. However, the most important effect was the increase in diffusion coefficient. The increase shifted the flame surface, where the large density decrease occurs, outside the shear layer of the jet and produced a thick viscous layer surrounding the jet which effectively suppressed the instability.

scholarly journals The electromotive force in multi-scale flows at high magnetic Reynolds number

2015 ◽  
Vol 81 (6) ◽  
Author(s):  
Steven M. Tobias ◽  
Fausto Cattaneo
Keyword(s):  
Reynolds Number ◽  
Electromotive Force ◽  
Large Scale ◽  
Magnetic Reynolds Number ◽  
Small Scale ◽  
Dynamo Theory ◽  
Multi Scale ◽  
The Mean ◽  
Scale Shear

Recent advances in dynamo theory have been made by examining the competition between small- and large-scale dynamos at high magnetic Reynolds number $\mathit{Rm}$. Small-scale dynamos rely on the presence of chaotic stretching whilst the generation of large-scale fields occurs in flows lacking reflectional symmetry via a systematic electromotive force (EMF). In this paper we discuss how the statistics of the EMF (at high $\mathit{Rm}$) depend on the properties of the multi-scale velocity that is generating it. In particular, we determine that different scales of flow have different contributions to the statistics of the EMF, with smaller scales contributing to the mean without increasing the variance. Moreover, we determine when scales in such a flow act independently in their contribution to the EMF. We further examine the role of large-scale shear in modifying the EMF. We conjecture that the distribution of the EMF, and not simply the mean, largely determines the dominant scale of the magnetic field generated by the flow.

scholarly journals On magnetic helicity generation and transport in a nonlinear dynamo driven by a helical flow

2020 ◽  
Vol 86 (4) ◽  
Author(s):  
F. Cattaneo ◽  
G. Bodo ◽  
S. M. Tobias
Keyword(s):  
Reynolds Number ◽  
Large Scale ◽  
Travelling Waves ◽  
Magnetic Reynolds Number ◽  
Magnetic Helicity ◽  
Dynamo Action ◽  
Strong Constraint ◽  
Sheared Flow ◽  
The Relationship ◽  
The Magnetic Field

The relationship between nonlinear large-scale dynamo action and the generation and transport of magnetic helicity is investigated at moderate values of the magnetic Reynolds number ( $Rm$ ). The model consists of a helically forced, sheared flow in a Cartesian domain. The boundary conditions are periodic in the horizontal and impenetrable for the vertical. The magnetic field is required to be vertical at the upper and lower boundaries. There are two consequences of this choice; one is that the magnetic helicity is not gauge invariant, the second is that fluxes of magnetic helicity are allowed in and out of the domain. We select the winding gauge, define all the contributions to the evolution of the helicity in this gauge and measure these contributions for various solutions of the dynamo equations. We vary $Rm$ and the shear strength, and find a rich landscape of dynamo solutions including travelling waves, pulsating waves and non-wave-like solutions. We find that, at the $Rm$ considered, the main contribution to the growth of magnetic helicity comes from processes throughout the volume of the fluid and that boundary terms respond by limiting the growth. We find that, in this magnetic Reynolds number regime, helicity conservation is not a strong constraint on large-scale dynamo action. We speculate on what may happen at higher $Rm$ .

Turbulent dynamo action at low magnetic Reynolds number

1970 ◽  
Vol 41 (2) ◽  
pp. 435-452 ◽  
Author(s):  
H. K. Moffatt
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Magnetic Energy ◽  
Magnetic Reynolds Number ◽  
Dynamo Action ◽  
Ohmic Dissipation ◽  
Magnetic Energy Density ◽  
Magnetic Diffusivity

The effect of turbulence on a magnetic field whose length-scale L is initially large compared with the scale l of the turbulence is considered. There are no external sources for the field, and in the absence of turbulence it decays by ohmic dissipation. It is assumed that the magnetic Reynolds number Rm = u0l/λ (where u0 is the root-mean-square velocity and λ the magnetic diffusivity) is small. It is shown that to lowest order in the small quantities l/L and Rm, isotropic turbulence has no effect on the large-scale field; but that turbulence that lacks reflexional symmetry is capable of amplifying Fourier components of the field on length scales of order Rm−2l and greater. In the case of turbulence whose statistical properties are invariant under rotation of the axes of reference, but not under reflexions in a point, it is shown that the magnetic energy density of a magnetic field which is initially a homogeneous random function of position with a particularly simple spectrum ultimately increases as t−½exp (α2t/2λ3) where α(= O(u02l)) is a certain linear functional of the spectrum tensor of the turbulence. An analogous result is obtained for an initially localized field.

Pressure gradient effects on the large-scale structure of turbulent boundary layers

2013 ◽  
Vol 715 ◽  
pp. 477-498 ◽  
Author(s):  
Zambri Harun ◽  
Jason P. Monty ◽  
Romain Mathis ◽  
Ivan Marusic
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Amplitude Modulation ◽  
Large Scale ◽  
Outer Region ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Small Scale

AbstractResearch into high-Reynolds-number turbulent boundary layers in recent years has brought about a renewed interest in the larger-scale structures. It is now known that these structures emerge more prominently in the outer region not only due to increased Reynolds number (Metzger & Klewicki, Phys. Fluids, vol. 13(3), 2001, pp. 692–701; Hutchins & Marusic, J. Fluid Mech., vol. 579, 2007, pp. 1–28), but also when a boundary layer is exposed to an adverse pressure gradient (Bradshaw, J. Fluid Mech., vol. 29, 1967, pp. 625–645; Lee & Sung, J. Fluid Mech., vol. 639, 2009, pp. 101–131). The latter case has not received as much attention in the literature. As such, this work investigates the modification of the large-scale features of boundary layers subjected to zero, adverse and favourable pressure gradients. It is first shown that the mean velocities, turbulence intensities and turbulence production are significantly different in the outer region across the three cases. Spectral and scale decomposition analyses confirm that the large scales are more energized throughout the entire adverse pressure gradient boundary layer, especially in the outer region. Although more energetic, there is a similar spectral distribution of energy in the wake region, implying the geometrical structure of the outer layer remains universal in all cases. Comparisons are also made of the amplitude modulation of small scales by the large-scale motions for the three pressure gradient cases. The wall-normal location of the zero-crossing of small-scale amplitude modulation is found to increase with increasing pressure gradient, yet this location continues to coincide with the large-scale energetic peak wall-normal location (as has been observed in zero pressure gradient boundary layers). The amplitude modulation effect is found to increase as pressure gradient is increased from favourable to adverse.

Fully developed MHD turbulence near critical magnetic Reynolds number

1981 ◽  
Vol 104 ◽  
pp. 419-443 ◽  
Author(s):  
J. Léorat ◽  
A. Pouquet ◽  
U. Frisch
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Isotropic Turbulence ◽  
Magnetic Energy ◽  
Reynolds Numbers ◽  
Magnetic Reynolds Number ◽  
Mhd Equations ◽  
Liquid Sodium ◽  
Turbulent Heat ◽  
Mhd Turbulence

Liquid-sodium-cooled breeder reactors may soon be operating at magnetic Reynolds numbers RM where magnetic fields can be self-excited by a dynamo mechanism (as first suggested by Bevir 1973). Such flows have kinetic Reynolds numbers RV of the order of 107 and are therefore highly turbulent.This leads us to investigate the behaviour of MHD turbulence with high RV and low magnetic Prandtl numbers. We use the eddy-damped quasi-normal Markovian closure applied to the MHD equations. For simplicity we restrict ourselves to homogeneous and isotropic turbulence, but we do include helicity.We obtain a critical magnetic Reynolds number RMc of the order of a few tens (non-helical case) above which magnetic energy is present. RMc is practically independent of RV (in the range 40 to 106). RMc can be considerably decreased by the presence of helicity: when the overall size of the flow L is much larger than the integral scale l0, RMc can drop below unity as suggested by an α-effect argument. When L ≈ l0 the drop can still be substantial (factor of 6) when helicity is a maximum. We examine how the turbulence is modified when RM crosses RMc: presence of magnetic energy, decreased kinetic energy, steepening of kinetic-energy spectrum, etc.We make no attempt to obtain quantitative estimates for a breeder reactor, but discuss some of the possible consequences of exceeding RMc, such as decreased turbulent heat transport. More precise information may be obtained from numerical simulations and experiments (including some in the subcritical regime).

scholarly journals Combined measurement of velocity and temperature in liquid metal convection

2019 ◽  
Vol 876 ◽  
pp. 1108-1128 ◽  
Author(s):  
Till Zürner ◽  
Felix Schindler ◽  
Tobias Vogt ◽  
Sven Eckert ◽  
Jörg Schumacher
Keyword(s):  
Reynolds Number ◽  
Liquid Metal ◽  
Large Scale ◽  
Scale Up ◽  
Convection Cell ◽  
Small Scale ◽  
Convection Flow ◽  
Large Scale Circulation ◽  
Large Scale Flow ◽  
The Impact

Combined measurements of velocity components and temperature in a turbulent Rayleigh–Bénard convection flow at a low Prandtl number of $Pr=0.029$ and Rayleigh numbers of $10^{6}\leqslant Ra\leqslant 6\times 10^{7}$ are conducted in a series of experiments with durations of more than a thousand free-fall time units. Multiple crossing ultrasound beam lines and an array of thermocouples at mid-height allow for a detailed analysis and characterization of the complex three-dimensional dynamics of the single large-scale circulation roll in a cylindrical convection cell of unit aspect ratio which is filled with the liquid metal alloy GaInSn. We measure the internal temporal correlations of the complex large-scale flow and distinguish between short-term oscillations associated with a sloshing motion in the mid-plane as well as varying orientation angles of the velocity close to the top/bottom plates and the slow azimuthal drift of the mean orientation of the roll as a whole that proceeds on a time scale up to a hundred times slower. The coherent large-scale circulation drives a vigorous turbulence in the whole cell that is quantified by direct Reynolds number measurements at different locations in the cell. The velocity increment statistics in the bulk of the cell displays characteristic properties of intermittent small-scale fluid turbulence. We also show that the impact of the symmetry-breaking large-scale flow persists to small-scale velocity fluctuations thus preventing the establishment of fully isotropic turbulence in the cell centre. Reynolds number amplitudes depend sensitively on beam-line position in the cell such that different definitions have to be compared. The global momentum and heat transfer scalings with Rayleigh number are found to agree with those of direct numerical simulations and other laboratory experiments.

scholarly journals Inverse Energy Cascade in Advanced MHD Turbulence (the RNG Method)

1993 ◽  
Vol 157 ◽  
pp. 255-261
Author(s):  
N. Kleeorin ◽  
I. Rogachevskii
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Magnetic Field Effect ◽  
Magnetic Reynolds Number ◽  
Energy Cascade ◽  
Small Scale ◽  
Magnetic Fluctuations ◽  
Mhd Turbulence ◽  
Inverse Energy Cascade ◽  
Large Scale Magnetic Field

The nonlinear (in terms of the large-scale magnetic field) effect of the modification of the magnetic force by an advanced small-scale magnetohydrodynamic (MHD) turbulence is considered. The phenomenon is due to the generation of magnetic fluctuations at the expense of hydrodynamic pulsations. It results in a decrease of the elasticity of the large-scale magnetic field.The renormalization group (RNG) method was employed for the investigation of the MHD turbulence at the large magnetic Reynolds number. It was found that the level of the magnetic fluctuations can exceed that obtained from the equipartition assumption due to the inverse energy cascade in advanced MHD turbulence.This effect can excite an instability of the large-scale magnetic field due to the energy transfer from the small-scale turbulent pulsations. This instability is an example of the inverse energy cascade in advanced MHD turbulence. It may act as a mechanism for the large-scale magnetic ropes formation in the solar convective zone and spiral galaxies.

Fully resolved numerical simulation of particle-laden turbulent flow in a horizontal channel at a low Reynolds number

2012 ◽  
Vol 693 ◽  
pp. 319-344 ◽  
Author(s):  
Xueming Shao ◽  
Tenghu Wu ◽  
Zhaosheng Yu
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Large Scale ◽  
Horizontal Channel ◽  
Small Scale ◽  
Channel Height ◽  
Wall Region ◽  
Sediment Layer ◽  
Particle Settling ◽  
Volume Fractions

AbstractA fictitious domain method is used to perform fully resolved numerical simulations of particle-laden turbulent flow in a horizontal channel. The effects of large particles of diameter 0.05 and 0.1 times the channel height on the turbulence statistics and structures are investigated for different settling coefficients and volume fractions (0.79 %–7.08 %) for the channel Reynolds number being 5000. The results indicate the following. (a) When the particle sedimentation effect is negligible (i.e. neutrally buoyant), the presence of particles decreases the maximum r.m.s. of streamwise velocity fluctuation near the wall by weakening the intensity of the large-scale streamwise vortices, while increasing the r.m.s. of the streamwise fluctuating velocity in the region very close to the wall and in the centre region. On the other hand, the particles increase the r.m.s. of transverse and spanwise fluctuating velocities in the near-wall region by inducing the small-scale vortices. (b) When the particle settling effect is so substantial that most particles settle onto the bottom wall and form a particle sediment layer (SL), the SL plays the role of a rough wall and parts of the vortex structures shedding from the SL ascend into the core region and substantially increase the turbulence intensity there. (c) When the particle settling effect is moderate, the effects of particles on the turbulence are a combination of the former two situations, and the Shields number is a good parameter for measuring the particle settling effects (i.e. the particle concentration distribution in the transverse direction). The average velocities of the particle are smaller in the lower half-channel and larger in the upper half-channel compared to the local fluid velocities in the presence of gravity effects. The effects of the smaller particles on the turbulence are found to be stronger at the same particle volume fractions.

Generation mechanism of a hierarchy of vortices in a turbulent boundary layer

2019 ◽  
Vol 865 ◽  
pp. 1085-1109 ◽  
Author(s):  
Yutaro Motoori ◽  
Susumu Goto
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Energy Spectrum ◽  
Turbulent Boundary Layer ◽  
Large Scale ◽  
Generation Mechanism ◽  
Small Scale ◽  
Generation Process ◽  
Mean Flow ◽  
The Mean

To understand the generation mechanism of a hierarchy of multiscale vortices in a high-Reynolds-number turbulent boundary layer, we conduct direct numerical simulations and educe the hierarchy of vortices by applying a coarse-graining method to the simulated turbulent velocity field. When the Reynolds number is high enough for the premultiplied energy spectrum of the streamwise velocity component to show the second peak and for the energy spectrum to obey the$-5/3$power law, small-scale vortices, that is, vortices sufficiently smaller than the height from the wall, in the log layer are generated predominantly by the stretching in strain-rate fields at larger scales rather than by the mean-flow stretching. In such a case, the twice-larger scale contributes most to the stretching of smaller-scale vortices. This generation mechanism of small-scale vortices is similar to the one observed in fully developed turbulence in a periodic cube and consistent with the picture of the energy cascade. On the other hand, large-scale vortices, that is, vortices as large as the height, are stretched and amplified directly by the mean flow. We show quantitative evidence of these scale-dependent generation mechanisms of vortices on the basis of numerical analyses of the scale-dependent enstrophy production rate. We also demonstrate concrete examples of the generation process of the hierarchy of multiscale vortices.

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