Anisotropic diffusivities' effects in rotating magnetoconvection and geodynamo problems

2021 ◽  
Author(s):  
Enrico Filippi ◽  
Jozef Brestenský
Keyword(s):  
Growth Rate ◽  
Normal Modes ◽  
Maximum Growth ◽  
Outer Core ◽  
Maximum Growth Rate ◽  
Dynamo Action ◽  
Anisotropic Parameter ◽  
Anisotropic Models ◽  
The Earth ◽  
Prandtl Numbers

<p>There are many examples which show how the anisotropic diffusive coefficients crucially influence geophysical and astrophysical flows and in particular flows in the Earth’s outer core. Thus, many models concerning rotating magnetoconvection with anisotropy in the viscosity, thermal and magnetic diffusivities have been developed.  </p><p>Different models correspond to different cases of anisotropic diffusivities. For example, we consider several anisotropic models: one with anisotropy in all diffusivities and other models with various combinations of anisotropic and isotropic diffusivities.  </p><p>Firstly, all kind of anisotropies are reminded and described. Then, a thorough comparison of these anisotropies, especially of the physical differences among them is done. All physical systems with the above mentioned anisotropies are prone to the occurrence of convection and other instabilities. We show how different types of anisotropy cause a different convection and a different balance among the main forces in the Earth’s Outer Core (Magnetic, Archimedean, Coriolis).  </p><p>As usually, to study instabilities in such systems, we use analysis in term of normal modes and search for preferred modes. In all our models, only marginal modes with zero growth rate have so far been studied. Now, we present the bravest modes, i.e. the ones with maximum growth rate. The comparison of the modes dependent on basic input parameters - Prandtl numbers, anisotropic parameter, Ekman and Elsasser numbers - is made mainly for values corresponding to the Earth’s outer core. In all our models the anisotropic diffusive coefficients are represented as diagonal tensors with two equal components different from the third one giving the chance to define simply the anisotropic parameter.  </p><p>We stress how magnetoconvection problems with the anisotropy included, became more and more important among the geodynamo problems in the last years; indeed, the origin of flows necessary for dynamo action, as studied in magnetoconvection with resulting instabilities, is important, as well as the problem of the origin of magnetic fields.  </p>

Anisotropic turbulent diffusivities and rotating magnetoconvection problems

2020 ◽  
Author(s):  
Enrico Filippi ◽  
Jozef Brestenský
Keyword(s):  
Magnetic Field ◽  
Rotation Axis ◽  
Normal Modes ◽  
Vertical Direction ◽  
Plane Layer ◽  
Isotropic Case ◽  
Dynamo Action ◽  
Anisotropic Models ◽  
The Earth ◽  
Magnetic Diffusivity

<p>Earth’s core Physics inspires the magnetoconvection models. Turbulent state of the core can increase the viscosity, the thermal diffusivity and also the magnetic diffusivity. The change of magnetic diffusivity is also called β-effect and it is important in dynamo mechanisms. Moreover, the turbulence suggests that the dynamics can be more complicated than it is usually presented. For instance, due to turbulence the diffusivity coefficients could be anisotropic as it was described in some recent studies, which stress how anisotropy in many cases facilitate convection and in other cases inhibits it. For example, if there is anisotropy some types of convection can occur also with very small values of Ekman numbers, which are usual for the Earth’s core. This is important because the convection can be the main cause of dynamo action. We present several rotating magnetoconvection models in horizontal plane layer with gravity and rotation axis in vertical direction and homogeneous magnetic field in horizontal direction. Different models correspond to different cases of anisotropic diffusivities. In other words, we consider several anisotropic models: one with anisotropy in all diffusivities and other models with various combinations of anisotropic and isotropic diffusivities. Comparisons with other former models (e.g. with isotropic case, <em>p</em>-case, partial anisotropy case when only magnetic diffusivity is isotropic, and <em>f</em>-case, full anisotropy case with all diffusivities anisotropic) are thoroughly performed. In all models we consider two distinct kinds of anisotropy, Stratification Anisotropy – SA, determined by direction of single gravity (buoyancy) force and Braginsky-Meytlis one – BM, determined by directions of magnetic field and rotation axis. All systems described by these models are prone to instabilities, so analysis in term of normal modes and search for preferred modes are very useful to study such systems. We focus our attention on stationary modes and SA anisotropies. Furthermore, we distinguish two sub-cases of SA anisotropy: atmospheric – Sa, if the diffusion in the vertical direction is greater than in the horizontal ones and oceanic – So, if opposite holds. In Sa (So) anisotropy the convection is in major cases facilitated (inhibited). This fact suggests that it is important to study Sa as well as So anisotropies in the Earth’s core. Our main results concern cases of anisotropic diffusivities, when preferred modes give new dynamics (unexpected in isotropic case) in the system in which geodynamo can work. </p>

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.

A note on growth curves of rabbit lines selected on growth rate or litter size

1993 ◽  
Vol 57 (2) ◽  
pp. 332-334 ◽  
Author(s):  
A. Blasco ◽  
E. Gómez
Keyword(s):  
Growth Rate ◽  
Litter Size ◽  
Growth Curves ◽  
Live Weight ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Standard Errors ◽  
Adult Weight ◽  
Weight Growth ◽  
Using Data

Two synthetic lines of rabbits were used in the experiment. Line V, selected on litter size, and line R, selected on growth rate. Ninety-six animals were randomly collected from 48 litters, taking a male and a female each time. Richards and Gompertz growth curves were fitted. Sexual dimorphism appeared in the line V but not in the R. Values for b and k were similar in all curves. Maximum growth rate took place in weeks 7 to 8. A break due to weaning could be observed in weeks 4 to 5. Although there is a remarkable similarity of the values of all the parameters using data from the first 20 weeks only, the higher standard errors on adult weight would make 30 weeks the preferable time to take data for live-weight growth curves.

Reassessment of Maximum Growth Rates for C3 and C4 Crops

1978 ◽  
Vol 14 (1) ◽  
pp. 1-5 ◽  
Author(s):  
J. L. Monteith
Keyword(s):  
Growth Rate ◽  
Growth Rates ◽  
Growing Season ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Crop Growth ◽  
Close Inspection ◽  
Similar Difference ◽  
Photosynthetic Efficiencies

SUMMARYFigures for maximum crop growth rates, reviewed by Gifford (1974), suggest that the productivity of C3 and C4 species is almost indistinguishable. However, close inspection of these figures at source and correspondence with several authors revealed a number of errors. When all unreliable figures were discarded, the maximum growth rate for C3 stands fell in the range 34–39 g m−2 d−1 compared with 50–54 g m−2 d−1 for C4 stands. Maximum growth rates averaged over the whole growing season showed a similar difference: 13 g m−2 d−1 for C3 and 22 g m−2 d−1 for C4. These figures correspond to photosynthetic efficiencies of approximately 1·4 and 2·0%.

Tidal excitation of hydromagnetic waves and their damping in the Earth

1994 ◽  
Vol 274 ◽  
pp. 219-241 ◽  
Author(s):  
R. R. Kerswell
Keyword(s):  
Growth Rate ◽  
Growth Rates ◽  
Outer Core ◽  
Decay Rates ◽  
Wave Disturbance ◽  
Instability Mechanism ◽  
The Earth ◽  
Elliptical Instability ◽  
Hydromagnetic Waves

We examine the possibility that the Earth's outer core, as a tidally distorted fluid-filled rotating spheroid, may be the seat of an elliptical instability. The instability mechanism is described within the framework of a simple Earth-like model. The preferred forms of wave disturbance are explored and a likely growth rate supremum deduced. Estimates are made of the Ohmic and viscous decay rates of such hydromagnetic waves in the outer core. Rather than a conclusive disparity of scales, we find that typical elliptical growth rates, Ohmic decay rates and viscous decay rates all have the same order for plausible core fields and core-to-mantle conductivities. This study is all the more timely considering the recent realization that the Earth's precession may also drive similar instabilities at comparable strengths in the outer core.

Interpretation of Experimental Data with Regard to the Activated Sludge Model No.1 and Calibration of the Model for Municipal Wastewater Treatment Plants

1992 ◽  
Vol 25 (6) ◽  
pp. 167-183 ◽  
Author(s):  
H. Siegrist ◽  
M. Tschui
Keyword(s):  
Experimental Data ◽  
Growth Rate ◽  
Activated Sludge ◽  
Municipal Wastewater ◽  
Wastewater Treatment Plants ◽  
Treatment Plant ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Municipal Wastewater Treatment ◽  
Activated Sludge Model

The wastewater of the municipal treatment plants Zürich-Werdhölzli (350000 population equivalents), Zürich-Glatt (110000), and Wattwil (20000) have been characterized with regard to the activated sludge model Nr.1 of the IAWPRC task group. Zürich-Glatt and Wattwil are partly nitrifying treatment plants and Zürich-Werdhölzli is fully nitrifying. The mixing characteristics of the aeration tanks at Werdhölzli and Glatt were determined with sodium bromide as a tracer. The experimental data were used to calibrate hydrolysis, heterotrophic growth and nitrification. Problems arising by calibrating hydrolysis of the paniculate material and by measuring oxygen consumption of heterotrophic and nitrifying microorganisms are discussed. For hydrolysis the experimental data indicate first-order kinetics. For nitrification a maximum growth rate of 0.40±0.07 d−1, corresponding to an observed growth rate of 0.26±0.04 d−1 was calculated at 10°C. The half velocity constant found for 12 and 20°C was 2 mg NH4-N/l. The calibrated model was verified with experimental dam of me Zürich-Werdhölzli treatment plant during ammonia shock load.

Dietary Protein Requirements of Fishes — A Reassessment

1987 ◽  
Vol 44 (11) ◽  
pp. 1995-2001 ◽  
Author(s):  
Stephen H. Bowen
Keyword(s):  
Growth Rate ◽  
Dietary Protein ◽  
Protein Concentration ◽  
Trophic Ecology ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Intake Rate ◽  
Protein Requirement ◽  
Fish Physiology ◽  
Protein Retention

It is widely believed that fishes require more dietary protein than other vertebrates. Many aspects of fish physiology, nutrition, and trophic ecology have been interpreted within the context of this high protein requirement. Here, fishes are compared with terrestrial homeotherms in terms of (1) protein requirement for maintenance, (2) relative protein concentration in the diet required for maximum growth rate, (3) protein intake rate required for maximum growth rate, (4) efficiency of protein retention in growth, and (5) weight of growth achieved per weight of protein ingested. The two animal groups compared differ only in relative protein concentration in the diet required for maximum growth rate. This difference is explained in terms of homeotherms' greater requirement for energy and does not reflect absolute differences in protein requirement. The remaining measures of protein requirement suggest that fishes and terrestrial homeotherms are remarkably similar in their use of protein as a nutritional resource. Reinterpretation of the role of protein in fish physiology, nutrition, and trophic ecology is perhaps in order.

Allometric scaling and taxonomic variation in nutrient utilization traits and maximum growth rate of phytoplankton

2012 ◽  
Vol 57 (2) ◽  
pp. 554-566 ◽  
Author(s):  
Kyle F. Edwards ◽  
Mridul K. Thomas ◽  
Christopher A. Klausmeier ◽  
Elena Litchman
Keyword(s):  
Growth Rate ◽  
Allometric Scaling ◽  
Maximum Growth ◽  
Nutrient Utilization ◽  
Maximum Growth Rate

Instability waves on the air–sea interface

1993 ◽  
Vol 248 ◽  
pp. 363-381 ◽  
Author(s):  
G. H. Wheless ◽  
G. T. Csanady
Keyword(s):  
Surface Tension ◽  
Growth Rate ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Surface Velocity ◽  
Instability Waves ◽  
Interface Surface ◽  
Fluid Properties ◽  
Compound Matrix Method ◽  
Order Of Magnitude

We used a compound matrix method to integrate the Orr–Sommerfeld equation in an investigation of short instability waves (λ < 6 cm) on the coupled shear flow at the air–sea interface under suddenly imposed wind (a gust model). The method is robust and fast, so that the effects of external variables on growth rate could easily be explored. As expected from past theoretical studies, the growth rate proved sensitive to air and water viscosity, and to the curvature of the air velocity profile very close to the interface. Surface tension had less influence, growth rate increasing somewhat with decreasing surface tension. Maximum growth rate and minimum wave speed nearly coincided for some combinations of fluid properties, but not for others.The most important new finding is that, contrary to some past order of magnitude estimates made on theoretical grounds, the eigenfunctions at these short wavelengths are confined to a distance of the order of the viscous wave boundary-layer thickness from the interface. Correspondingly, the perturbation vorticity is high, the streamwise surface velocity perturbation in typical cases being five times the orbital velocity of free waves on an undisturbed water surface. The instability waves should therefore be thought of as fundamentally different flow structures from free waves: given their high vorticity, they are akin to incipient turbulent eddies. They may also be expected to break at a much lower steepness than free waves.

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