scholarly journals A multiscale dynamo model driven by quasi-geostrophic convection

2015 ◽  
Vol 780 ◽  
pp. 143-166 ◽  
Author(s):  
Michael A. Calkins ◽  
Keith Julien ◽  
Steven M. Tobias ◽  
Jonathan M. Aurnou
Keyword(s):  
Prandtl Number ◽  
Viscous Dissipation ◽  
Time Scale ◽  
Large Scale ◽  
Force Balance ◽  
Dynamo Model ◽  
Small Scale ◽  
Ohmic Dissipation ◽  
Evolution Time ◽  
Magnetic Prandtl Number

A convection-driven multiscale dynamo model is developed in the limit of low Rossby number for the plane layer geometry in which the gravity and rotation vectors are aligned. The small-scale fluctuating dynamics are described by a magnetically modified quasi-geostrophic equation set, and the large-scale mean dynamics are governed by a diagnostic thermal wind balance. The model utilizes three time scales that respectively characterize the convective time scale, the large-scale magnetic evolution time scale and the large-scale thermal evolution time scale. Distinct equations are derived for the cases of order one and low magnetic Prandtl number. It is shown that the low magnetic Prandtl number model is characterized by a magnetic to kinetic energy ratio that is asymptotically large, with ohmic dissipation dominating viscous dissipation on the large scale. For the order one magnetic Prandtl number model, the magnetic and kinetic energies are equipartitioned and both ohmic and viscous dissipation are weak on the large scales; large-scale ohmic dissipation occurs in thin magnetic boundary layers adjacent to the horizontal boundaries. For both magnetic Prandtl number cases the Elsasser number is small since the Lorentz force does not enter the leading order force balance. The new models can be considered fully nonlinear, generalized versions of the dynamo model originally developed by Childress & Soward (Phys. Rev. Lett., vol. 29, 1972, pp. 837–839), and provide a new theoretical framework for understanding the dynamics of convection-driven dynamos in regimes that are only just becoming accessible to direct numerical simulations.

scholarly journals Hydromagnetic dynamos at the low Ekman and magnetic Prandtl numbers

2016 ◽  
Vol 46 (3) ◽  
pp. 221-244 ◽  
Author(s):  
Ján Šimkanin
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Prandtl Number ◽  
Large Scale ◽  
Small Scale ◽  
Polar Regions ◽  
Magnetic Diffusion ◽  
Magnetic Prandtl Number ◽  
Prandtl Numbers ◽  
The Magnetic Field

Abstract Hydromagnetic dynamos are numerically investigated at low Prandtl, Ekman and magnetic Prandtl numbers using the PARODY dynamo code. In all the investigated cases, the generated magnetic fields are dominantly-dipolar. Convection is small-scale and columnar, while the magnetic field maintains its large-scale structure. In this study the generated magnetic field never becomes weak in the polar regions, neither at large magnetic Prandtl numbers (when the magnetic diffusion is weak), nor at low magnetic Prandtl numbers (when the magnetic diffusion is strong), which is a completely different situation to that observed in previous studies. As magnetic fields never become weak in the polar regions, then the magnetic field is always regenerated in the tangent cylinder. At both values of the magnetic Prandtl number, strong polar magnetic upwellings and weaker equatorial upwellings are observed. An occurrence of polar magnetic upwellings is coupled with a regenaration of magnetic fields inside the tangent cylinder and then with a not weakened intensity of magnetic fields in the polar regions. These new results indicate that inertia and viscosity are probably negligible at low Ekman numbers.

scholarly journals Turbulent viscosity and magnetic Prandtl number from simulations of isotropically forced turbulence

2020 ◽  
Vol 636 ◽  
pp. A93 ◽  
Author(s):  
P. J. Käpylä ◽  
M. Rheinhardt ◽  
A. Brandenburg ◽  
M. J. Käpylä
Keyword(s):  
Magnetic Fields ◽  
Prandtl Number ◽  
Large Scale ◽  
Turbulent Viscosity ◽  
Scale Dependence ◽  
Scale Separation ◽  
Separation Ratio ◽  
Magnetic Prandtl Number ◽  
Magnetic Diffusivity ◽  
Forced Turbulence

Context. Turbulent diffusion of large-scale flows and magnetic fields plays a major role in many astrophysical systems, such as stellar convection zones and accretion discs. Aims. Our goal is to compute turbulent viscosity and magnetic diffusivity which are relevant for diffusing large-scale flows and magnetic fields, respectively. We also aim to compute their ratio, which is the turbulent magnetic Prandtl number, Pmt, for isotropically forced homogeneous turbulence. Methods. We used simulations of forced turbulence in fully periodic cubes composed of isothermal gas with an imposed large-scale sinusoidal shear flow. Turbulent viscosity was computed either from the resulting Reynolds stress or from the decay rate of the large-scale flow. Turbulent magnetic diffusivity was computed using the test-field method for a microphysical magnetic Prandtl number of unity. The scale dependence of the coefficients was studied by varying the wavenumber of the imposed sinusoidal shear and test fields. Results. We find that turbulent viscosity and magnetic diffusivity are in general of the same order of magnitude. Furthermore, the turbulent viscosity depends on the fluid Reynolds number (Re) and scale separation ratio of turbulence. The scale dependence of the turbulent viscosity is found to be well approximated by a Lorentzian. These results are similar to those obtained earlier for the turbulent magnetic diffusivity. The results for the turbulent transport coefficients appear to converge at sufficiently high values of Re and the scale separation ratio. However, a weak trend is found even at the largest values of Re, suggesting that the turbulence is not in the fully developed regime. The turbulent magnetic Prandtl number converges to a value that is slightly below unity for large Re. For small Re we find values between 0.5 and 0.6 but the data are insufficient to draw conclusions regarding asymptotics. We demonstrate that our results are independent of the correlation time of the forcing function. Conclusions. The turbulent magnetic diffusivity is, in general, consistently higher than the turbulent viscosity, which is in qualitative agreement with analytic theories. However, the actual value of Pmt found from the simulations (≈0.9−0.95) at large Re and large scale separation ratio is higher than any of the analytic predictions (0.4−0.8).

scholarly journals MaBμlS-2: high-precision microlensing modelling for the large-scale survey era

2020 ◽  
Vol 498 (2) ◽  
pp. 2196-2218
Author(s):  
David Specht ◽  
Eamonn Kerins ◽  
Supachai Awiphan ◽  
Annie C Robin
Keyword(s):  
Proper Motion ◽  
Time Scale ◽  
Large Scale ◽  
Near Infrared ◽  
Event Rate ◽  
Structural Features ◽  
Small Scale ◽  
Stellar Kinematics ◽  
Full Account ◽  
Space Telescope

ABSTRACT Galactic microlensing datasets now comprise in excess of 104 events and, with the advent of next-generation microlensing surveys that may be undertaken with facilities such as the Rubin Observatory (formerly LSST) and Roman Space Telescope (formerly WFIRST), this number will increase significantly. So too will the fraction of events with measurable higher order information, such as finite-source effects and lens–source relative proper motion. Analysing such data requires a more sophisticated Galactic microlens modelling approach. We present a new second-generation Manchester–Besançon Microlensing Simulator (MaBμlS-2), which uses a version of the Besançon population synthesis Galactic model that provides good agreement with stellar kinematics observed by the Hubble Space Telescope (HST) towards the bulge. MaBμlS-2 provides high-fidelity signal-to-noise limited maps of the microlensing optical depth, rate and average time-scale towards a 400 deg2 region of the Galactic bulge in several optical to near-infrared pass-bands. The maps take full account of the unresolved stellar background, as well as limb-darkened source profiles. Comparing MaBμlS-2 with the efficiency-corrected OGLE-IV 8000 event sample shows a much improved agreement over the previous version of MaBμlS and succeeds in matching even small-scale structural features in the OGLE-IV event rate map. However, evidence remains for a small underprediction of the event rate per source and overprediction of the time-scale. MaBμlS-2 is available online (www.mabuls.net, Specht & Kerins) to provide on-the-fly maps for user-supplied cuts in survey magnitude, event time-scale and relative proper motion.

Investigation of Inverse-Turbulent-Prandtl Number with Four RNG k-ε Turbulence Models on Compressor Discharge Pipe of Bioenergy Micro Gas Turbine

2016 ◽  
Vol 819 ◽  
pp. 392-400 ◽  
Author(s):  
Ahmad Indra Siswantara ◽  
Budiarso ◽  
Steven Darmawan
Keyword(s):  
Prandtl Number ◽  
Turbulence Model ◽  
Large Scale ◽  
Swirling Flow ◽  
Turbulent Viscosity ◽  
Turbulence Models ◽  
Small Scale ◽  
Turbulent Prandtl Number ◽  
Curved Pipe ◽  
Molecular Viscosity

Inverse-Turbulent Prandtl number (α) is an important parameter in RNG k-ε turbulence models since it affects the ratio of molecular viscosity and turbulent viscosity. In curved pipe, this highly affects the model prediction to a large range eddy-scale flow. According to Yakhot & Orzag, the α range from 1-1.3929 has not been investigated in detail in curved pipe flow (Yakhot & Orszag, 1986) and specific Re. This paper varied inverse-turbulent Prandtl number α to 1-1.3 in RNG k-ε turbulence model on cylindrical curved pipe in order to obtain the optimum value of α to predict unfully-developed flow in the curve with curve ratio R/D of 1.607. Analysis was conducted numericaly with inlet specified Re of 40900 which was generated from the experiment at α 1, 1.1, 1.2, 1.3. Wall surface roughness is not considered in this paper. With assumption that thermal diffusivity is always dominant to turbulent viscosity, higher Inverse-turbulent Prandtl number represent domination of turbulent viscosity to molecular viscosity of the flow and predict to have more interaction between large scale eddy to small scale eddy as well. The results show the use of α = 1.3 has increased the turbulent kinetic energy by 7% and the turbulent dissipation by 5% compared to general inverse-turbulent Prandtl number of 1. The value difference shows that the use of higher α on RNG turbulence model described more interaction between eddies in secondary and swirling flow at pipe curve at Re = 40900.

scholarly journals A severe blizzard event in Romania – a case study

2009 ◽  
Vol 9 (2) ◽  
pp. 623-634 ◽  
Author(s):  
F. Georgescu ◽  
S. Tascu ◽  
M. Caian ◽  
D. Banciu
Keyword(s):  
Numerical Simulations ◽  
Time Scale ◽  
Large Scale ◽  
Forecast Accuracy ◽  
Horizontal Resolution ◽  
Maximum Temperature ◽  
Small Scale ◽  
Relative Role ◽  
Snow Layer ◽  
Strong Winds

Abstract. During winter cold strong winds associated with snowfalls are not unusual for South and Southeastern Romania. The episode of 2–4 January 2008 was less usual due to its intensity and persistence. It happened after a long period (autumn 2006–autumn 2007) of mainly southerly circulations inducing warm weather, when the absolute record of the maximum temperature was registered. The important snowfalls and snowdrifts, leading to a consistent snow layer (up to 100 cm), produced serious transport and electricity supply perturbations. Since this atypical local weather event was not correctly represented by the operational numerical forecasts, several cross-comparison numerical simulations were performed to analyze the relative role of the coupler/coupling models and to compare two ways of process-scale uncertainties mitigation: optimizing the forecast range and performing ensemble forecast through the perturbation of the lateral boundary conditions. The results underline, for this case, the importance of physical parametrization package on the first place and secondary, the importance of the model horizontal resolution. The resolution increase is beneficial only in the local process representation; on larger scale it may either improve or decrease the accuracy effect, depending on the specified nudging between large-scale and small-scale information. The event capture is likely to be favored by two elements: a more appropriate time-scale of the event's physics and the quality of the transmitted large-scale information. Concerning the time scale, the statistics on skill as a function of forecast range are shown to be a useful tool in order to increase the accuracy of the numerical simulations. Ensembles forecasting versus resolution increase experiments indicate, for such atypical events, an interesting supply in the forecast accuracy through the ensemble method when applied to correct the minimum skill of the deterministic forecast.

Inertia–gravity waves in a liquid-filled, differentially heated, rotating annulus

2015 ◽  
Vol 782 ◽  
pp. 144-177 ◽  
Author(s):  
Anthony Randriamampianina ◽  
Emilia Crespo del Arco
Keyword(s):  
Prandtl Number ◽  
Gravity Waves ◽  
Large Scale ◽  
Baroclinic Instability ◽  
Zonal Flow ◽  
Small Scale ◽  
Mean Flow ◽  
Baroclinic Waves ◽  
Fluid Properties ◽  
Spatio Temporal

Direct numerical simulations based on high-resolution pseudospectral methods are carried out for detailed investigation into the instabilities arising in a differentially heated, rotating annulus, the baroclinic cavity. Following previous works using air (Randriamampianina et al., J. Fluid Mech., vol. 561, 2006, pp. 359–389), a liquid defined by Prandtl number $Pr=16$ is considered in order to better understand, via the Prandtl number, the effects of fluid properties on the onset of gravity waves. The computations are particularly aimed at identifying and characterizing the spontaneously emitted small-scale fluctuations occurring simultaneously with the baroclinic waves. These features have been observed as soon as the baroclinic instability sets in. A three-term decomposition is introduced to isolate the fluctuation field from the large-scale baroclinic waves and the time-averaged mean flow. Even though these fluctuations are found to propagate as packets, they remain attached to the background baroclinic waves, locally triggering spatio-temporal chaos, a behaviour not observed with the air-filled cavity. The properties of these features are analysed and discussed in the context of linear theory. Based on the Richardson number criterion, the characteristics of the generation mechanism are consistent with a localized instability of the shear zonal flow, invoking resonant over-reflection.

The growth of meteorological disturbances

1949 ◽  
Vol 45 (1) ◽  
pp. 92-98 ◽  
Author(s):  
H. Bondi
Keyword(s):  
Heat Conduction ◽  
Temperature Gradient ◽  
Lower Limit ◽  
Time Scale ◽  
Large Scale ◽  
Ideal Gas ◽  
Small Scale ◽  
Sharp Distinction ◽  
The Subject ◽  
The Stability

1. Introduction. A considerable amount of attention has been paid to the problem of determining the conditions which decide whether a liquid heated from below is stable or unstable. The motion consequent upon the disturbance of an unstable ideal gas does not, however, seem to have been treated so far, and this problem forms the subject of the present paper. Heat conduction and viscosity are at first neglected, and we are therefore dealing with the small motions of a gas slightly disturbed from a position of equilibrium under the influence of gravity. The condition for the stability of such a gas is well known, namely, the temperature gradient must be less than the adiabatic gradient. Furthermore, it is known that there is a sharp distinction between slow large-scale (meteorological) and rapidly varying small-scale (acoustical) phenomena. The present paper confirms these points and derives the time scale of meteorological phenomena. Heat conduction and viscosity are then shown to set a lower limit to the dimensions of such disturbances, while the effect of the earth's rotation is shown to be negligible.

scholarly journals A shell model for turbulent dynamos

2010 ◽  
Vol 6 (S274) ◽  
pp. 159-161
Author(s):  
G. Nigro ◽  
D. Perrone ◽  
P. Veltri
Keyword(s):  
Shell Model ◽  
Large Scale ◽  
Nonlinear Behavior ◽  
Magnetic Polarity ◽  
Dynamo Model ◽  
Small Scale ◽  
Natural Systems ◽  
Large Scale Magnetic Field ◽  
Time Correlations ◽  
Long Time

AbstractA self-consistent nonlinear dynamo model is presented. The nonlinear behavior of the plasma at small scale is described by using a MHD shell model for fields fluctuations; this allow us to study the dynamo problem in a large parameter regime which characterizes the dynamo phenomenon in many natural systems and which is beyond the power of supercomputers at today. The model is able to reproduce dynamical situations in which the system can undergo transactions to different dynamo regimes. In one of these the large-scale magnetic field jumps between two states reproducing the magnetic polarity reversals. From the analysis of long time series of reversals we infer results about the statistics of persistence times, revealing the presence of hidden long-time correlations in the chaotic dynamo process.

scholarly journals Current helicity constraints in solar dynamo models

2012 ◽  
Vol 8 (S294) ◽  
pp. 313-318
Author(s):  
D. Sokoloff ◽  
H. Zhang ◽  
D. Moss ◽  
N. Kleeorin ◽  
K. Kuzanyan ◽  
...  
Keyword(s):  
Large Scale ◽  
Numerical Models ◽  
Mean Field ◽  
Active Regions ◽  
Solar Dynamo ◽  
Magnetic Helicity ◽  
Dynamo Model ◽  
Small Scale ◽  
Mean Field Dynamo ◽  
Current Helicity

AbstractWe investigate to what extent the current helicity distribution observed in solar active regions is compatible with solar dynamo models. We use an advanced 2D mean-field dynamo model with dynamo action largely concentrated near the bottom of the convective zone, and dynamo saturation based on the evolution of the magnetic helicity and algebraic quenching. For comparison, we also studied a more basic 2D mean-field dynamo model with simple algebraic alpha quenching only. Using these numerical models we obtain butterfly diagrams for both the small-scale current helicity and the large-scale magnetic helicity, and compare them with the butterfly diagram for the current helicity in active regions obtained from observations. This comparison shows that the current helicity of active regions, as estimated by −A·B evaluated at the depth from which the active region arises, resembles the observational data much better than the small-scale current helicity calculated directly from the helicity evolution equation. Here B and A are respectively the dynamo generated mean magnetic field and its vector potential.

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