scholarly journals Kazantsev dynamo in turbulent compressible flows

2019 ◽  
Vol 475 (2223) ◽  
pp. 20180591 ◽  
Author(s):  
Marco Martins Afonso ◽  
Dhrubaditya Mitra ◽  
Dario Vincenzi
Keyword(s):  
Growth Rate ◽  
Reynolds Number ◽  
Critical Exponent ◽  
Compressible Flows ◽  
Critical Value ◽  
Magnetic Reynolds Number ◽  
Scaling Exponent ◽  
Scaling Exponents ◽  
Potential Part

We consider the kinematic fluctuation dynamo problem in a flow that is random, white-in-time, with both solenoidal and potential components. This model is a generalization of the well-studied Kazantsev model. If both the solenoidal and potential parts have the same scaling exponent, then, as the compressibility of the flow increases, the growth rate decreases but remains positive. If the scaling exponents for the solenoidal and potential parts differ, in particular if they correspond to typical Kolmogorov and Burgers values, we again find that an increase in compressibility slows down the growth rate but does not turn it off. The slow down is, however, weaker and the critical magnetic Reynolds number is lower than when both the solenoidal and potential components display the Kolmogorov scaling. Intriguingly, we find that there exist cases, when the potential part is smoother than the solenoidal part, for which an increase in compressibility increases the growth rate. We also find that the critical value of the scaling exponent above which a dynamo is seen is unity irrespective of the compressibility. Finally, we realize that the dimension d  = 3 is special, as for all other values of d the critical exponent is higher and depends on the compressibility.

scholarly journals Small-scale dynamo action in rotating compressible convection

2011 ◽  
Vol 690 ◽  
pp. 262-287 ◽  
Author(s):  
B. Favier ◽  
P. J. Bushby
Keyword(s):  
Reynolds Number ◽  
Energy Density ◽  
Thermal Stratification ◽  
Magnetic Energy ◽  
Critical Value ◽  
Magnetic Reynolds Number ◽  
Small Scale ◽  
Dynamo Action ◽  
Lower Bounding ◽  
The Mean

AbstractWe study dynamo action in a convective layer of electrically conducting, compressible fluid, rotating about the vertical axis. At the upper and lower bounding surfaces, perfectly conducting boundary conditions are adopted for the magnetic field. Two different levels of thermal stratification are considered. If the magnetic diffusivity is sufficiently small, the convection acts as a small-scale dynamo. Using a definition for the magnetic Reynolds number ${R}_{M} $ that is based upon the horizontal integral scale and the horizontally averaged velocity at the mid-layer of the domain, we find that rotation tends to reduce the critical value of ${R}_{M} $ above which dynamo action is observed. Increasing the level of thermal stratification within the layer does not significantly alter the critical value of ${R}_{M} $ in the rotating calculations, but it does lead to a reduction in this critical value in the non-rotating cases. At the highest computationally accessible values of the magnetic Reynolds number, the saturation levels of the dynamo are similar in all cases, with the mean magnetic energy density somewhere between 4 and 9 % of the mean kinetic energy density. To gain further insights into the differences between rotating and non-rotating convection, we quantify the stretching properties of each flow by measuring Lyapunov exponents. Away from the boundaries, the rate of stretching due to the flow is much less dependent upon depth in the rotating cases than it is in the corresponding non-rotating calculations. It is also shown that the effects of rotation significantly reduce the magnetic energy dissipation in the lower part of the layer. We also investigate certain aspects of the saturation mechanism of the dynamo.

scholarly journals Two-dimensional compressible viscous flow around a circular cylinder

2015 ◽  
Vol 785 ◽  
pp. 349-371 ◽  
Author(s):  
Daniel Canuto ◽  
Kunihiko Taira
Keyword(s):  
Growth Rate ◽  
Reynolds Number ◽  
Mach Number ◽  
Critical Reynolds Number ◽  
Free Stream ◽  
Critical Value ◽  
Dominant Frequency ◽  
Two Dimensional ◽  
Free Stream Mach Number ◽  
Compressibility Effects

Direct numerical simulation is performed to study compressible viscous flow around a circular cylinder. The present study considers two-dimensional shock-free continuum flow by varying the Reynolds number between 20 and 100 and the free-stream Mach number between 0 and 0.5. The results indicate that compressibility effects elongate the near wake for cases above and below the critical Reynolds number for two-dimensional flow under shedding. The wake elongation becomes more pronounced as the Reynolds number approaches this critical value. Moreover, we determine the growth rate and frequency of linear instability for cases above the critical Reynolds number. From the analysis, it is observed that the frequency of the Bénard–von Kármán vortex street in the time-periodic fully saturated flow increases from the dominant unstable frequency found from the linear stability analysis as the Reynolds number increases from its critical value, even for the low range of Reynolds numbers considered. We also find that the compressibility effects reduce the growth rate and dominant frequency in the linear growth stage. Semi-empirical functional relationships for the growth rate and the dominant frequency in linearized flow around the cylinder in terms of the Reynolds number and free-stream Mach number are presented.

Examination of hypotheses in the Kolmogorov refined turbulence theory through high-resolution simulations. Part 2. Passive scalar field

1999 ◽  
Vol 400 ◽  
pp. 163-197 ◽  
Author(s):  
LIAN-PING WANG ◽  
SHIYI CHEN ◽  
JAMES G. BRASSEUR
Keyword(s):  
Reynolds Number ◽  
Scalar Field ◽  
Velocity Field ◽  
Scalar Fields ◽  
Passive Scalar ◽  
Experimental Results ◽  
Inertial Subrange ◽  
Scalar Dissipation ◽  
Scaling Exponent ◽  
Scaling Exponents

Using direct numerical simulations (DNS) and large-eddy simulations (LES) of velocity and passive scalar in isotropic turbulence (up to 5123 grid points), we examine directly and quantitatively the refined similarity hypotheses as applied to passive scalar fields (RSHP) with Prandtl number of order one. Unlike previous experimental investigations, exact energy and scalar dissipation rates were used and scaling exponents were quantified as a function of local Reynolds number. We first demonstrate that the forced DNS and LES scalar fields exhibit realistic inertial-range dynamics and that the statistical characteristics compare well with other numerical, theoretical and experimental studies. The Obukhov–Corrsin constant for the k−5/3 scalar variance spectrum obtained from the 5123 mesh is 0.87±0.10. Various statistics indicated that the scalar field is more intermittent than the velocity field. The joint probability distribution of locally-averaged energy dissipation εr and scalar dissipation χr is close to log-normal with a correlation coefficient of 0.25±0.01 between the logarithmic dissipations in the inertial subrange. The intermittency parameter for scalar dissipation is estimated to be in the range 0.43≈0.77, based on direct calculations of the variance of lnχr. The scaling exponents of the conditional scalar increment δrθ[mid ] χr,εr suggest a tendency to follow RSHP. Most significantly, the scaling exponent of δrθ[mid ] χr,εr over εr was shown to be approximately −⅙ in the inertial subrange, confirming a dynamical aspect of RSHP. In agreement with recent experimental results (Zhu et al. 1995; Stolovitzky et al. 1995), the probability distributions of the random variable βs = δrθ[mid ] χr,εr/ (χ1/2r ε−⅙rr1/3) were found to be nearly Gaussian. However, contrary to the experimental results, we find that the moments of βs are almost identical to those for the velocity field found in Part 1 of this study (Wang et al. 1996) and are insensitive to Reynolds number, large-scale forcing, and subgrid modelling.

scholarly journals Adaptive diversification of growth allometry in the plant Arabidopsis thaliana

2018 ◽  
Vol 115 (13) ◽  
pp. 3416-3421 ◽  
Author(s):  
François Vasseur ◽  
Moises Exposito-Alonso ◽  
Oscar J. Ayala-Garay ◽  
George Wang ◽  
Brian J. Enquist ◽  
...  
Keyword(s):  
Growth Rate ◽  
Arabidopsis Thaliana ◽  
Abiotic Stress ◽  
Seed Production ◽  
Stress Resistance ◽  
Allometric Scaling ◽  
Hydrodynamic Resistance ◽  
Scaling Exponent ◽  
Scaling Exponents ◽  
Growth Scaling

Seed plants vary tremendously in size and morphology; however, variation and covariation in plant traits may be governed, at least in part, by universal biophysical laws and biological constants. Metabolic scaling theory (MST) posits that whole-organismal metabolism and growth rate are under stabilizing selection that minimizes the scaling of hydrodynamic resistance and maximizes the scaling of resource uptake. This constrains variation in physiological traits and in the rate of biomass accumulation, so that they can be expressed as mathematical functions of plant size with near-constant allometric scaling exponents across species. However, the observed variation in scaling exponents calls into question the evolutionary drivers and the universality of allometric equations. We have measured growth scaling and fitness traits of 451 Arabidopsis thaliana accessions with sequenced genomes. Variation among accessions around the scaling exponent predicted by MST was correlated with relative growth rate, seed production, and stress resistance. Genomic analyses indicate that growth allometry is affected by many genes associated with local climate and abiotic stress response. The gene with the strongest effect, PUB4, has molecular signatures of balancing selection, suggesting that intraspecific variation in growth scaling is maintained by opposing selection on the trade-off between seed production and abiotic stress resistance. Our findings suggest that variation in allometry contributes to local adaptation to contrasting environments. Our results help reconcile past debates on the origin of allometric scaling in biology and begin to link adaptive variation in allometric scaling to specific genes.

Dynamo action in complex flows: the quick and the fast

2008 ◽  
Vol 601 ◽  
pp. 101-122 ◽  
Author(s):  
STEVEN M. TOBIAS ◽  
FAUSTO CATTANEO
Keyword(s):  
Growth Rate ◽  
Reynolds Number ◽  
Coherent Structures ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Magnetic Reynolds Number ◽  
Flow Structures ◽  
Dynamo Action ◽  
Spatial And Temporal Scales ◽  
Active Scalar Equations

We consider the kinematic dynamo problem for a velocity field consisting of a mixture of turbulence and coherent structures. For these flows the dynamo growth rate is determined by a competition between the large flow structures that have large magnetic Reynolds number but long turnover times and the small ones that have low magnetic Reynolds number but short turnover times. We introduce the concept of a quick dynamo as one that reaches its maximum growth rate in some (small) neighbourhood of its critical magnetic Reynolds number. We argue that if the coherent structures are quick dynamos, the overall dynamo growth rate can be predicted by looking at those flow structures that have spatial and temporal scales such that their magnetic Reynolds number is just above critical. We test this idea numerically by studying 2.5-dimensional dynamo action which allows extreme parameter values to be considered. The required velocities, consisting of a mixture of turbulence with a given spectrum and long-lived vortices (coherent structures), are obtained by solving the active scalar equations. By using spectral filtering we demonstrate that the scales responsible for dynamo action are consistent with those predicted by the theory.

scholarly journals Biological scaling in green algae: the role of cell size and geometry

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Helena Bestová ◽  
Jules Segrestin ◽  
Klaus von Schwartzenberg ◽  
Pavel Škaloud ◽  
Thomas Lenormand ◽  
...  
Keyword(s):  
Growth Rate ◽  
Population Growth ◽  
Population Growth Rate ◽  
Internal Diffusion ◽  
Scaling Exponent ◽  
Power Scaling ◽  
Nutrient Distribution ◽  
Metabolic Scaling ◽  
Key Factor ◽  
Size And Morphology

AbstractThe Metabolic Scaling Theory (MST), hypothesizes limitations of resource-transport networks in organisms and predicts their optimization into fractal-like structures. As a result, the relationship between population growth rate and body size should follow a cross-species universal quarter-power scaling. However, the universality of metabolic scaling has been challenged, particularly across transitions from bacteria to protists to multicellulars. The population growth rate of unicellulars should be constrained by external diffusion, ruling nutrient uptake, and internal diffusion, operating nutrient distribution. Both constraints intensify with increasing size possibly leading to shifting in the scaling exponent. We focused on unicellular algae Micrasterias. Large size and fractal-like morphology make this species a transitional group between unicellular and multicellular organisms in the evolution of allometry. We tested MST predictions using measurements of growth rate, size, and morphology-related traits. We showed that growth scaling of Micrasterias follows MST predictions, reflecting constraints by internal diffusion transport. Cell fractality and density decrease led to a proportional increase in surface area with body mass relaxing external constraints. Complex allometric optimization enables to maintain quarter-power scaling of population growth rate even with a large unicellular plan. Overall, our findings support fractality as a key factor in the evolution of biological scaling.

The flattening phase transition in systems of trapped ions

2009 ◽  
Vol 87 (10) ◽  
pp. 1425-1435 ◽  
Author(s):  
Taunia L. L. Closson ◽  
Marc R. Roussel
Keyword(s):  
Phase Transition ◽  
Critical Exponent ◽  
Order Parameter ◽  
Ion Trap ◽  
Anisotropy Parameter ◽  
Critical Value ◽  
Trapped Ions ◽  
Dimensional Structure ◽  
Flattening Process ◽  
Second Order Phase Transition

When the anisotropy of a harmonic ion trap is increased, the ions eventually collapse into a two-dimensional structure consisting of concentric shells of ions. This collapse generally behaves like a second-order phase transition. A graph of the critical value of the anisotropy parameter vs. the number of ions displays substructure closely related to the inner-shell configurations of the clusters. The critical exponent for the order parameter of this phase transition (maximum extent in the z direction) was found computationally to have the value β = 1/2. A second critical exponent related to displacements perpendicular to the z axis was found to have the value δ = 1. Using these estimates of the critical exponents, we derive an equation that relates the amplitudes of the displacements of the ions parallel to the x–y plane to the amplitudes along the z axis during the flattening process.

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.

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