Showing papers on "Magnetic Prandtl number published in 2015"
TL;DR: The 3D MHD Anelastic Spherical Harmonic code was employed to capture convective and dynamo processes achieved in a global-scale stellar convection simulation for a model solar-mass star rotating at three times the solar rate as mentioned in this paper.
Abstract: The 3D MHD Anelastic Spherical Harmonic code, using slope-limited diffusion, is employed to capture convective and dynamo processes achieved in a global-scale stellar convection simulation for a model solar-mass star rotating at three times the solar rate. The dynamo-generated magnetic fields possesses many timescales, with a prominent polarity cycle occurring roughly every 6.2 years. The magnetic field forms large-scale toroidal wreaths, whose formation is tied to the low Rossby number of the convection in this simulation. The polarity reversals are linked to the weakened differential rotation and a resistive collapse of the large-scale magnetic field. An equatorial migration of the magnetic field is seen, which is due to the strong modulation of the differential rotation rather than a dynamo wave. A poleward migration of magnetic flux from the equator eventually leads to the reversal of the polarity of the high-latitude magnetic field. This simulation also enters an interval with reduced magnetic energy at low latitudes lasting roughly 16 years (about 2.5 polarity cycles), during which the polarity cycles are disrupted and after which the dynamo recovers its regular polarity cycles. An analysis of this grand minimum reveals that it likely arises through the interplay of symmetric and antisymmetric dynamo families. This intermittent dynamo state potentially results from the simulation’s relatively low magnetic Prandtl number. A mean-field-based analysis of this dynamo simulation demonstrates that it is of the α-Ω type. The timescales that appear to be relevant to the magnetic polarity reversal are also identified.
141 citations
TL;DR: In this article, the authors proposed a new formulation of the turbulent Prandtl number for diapycnal diffusivity, which is based on the original Osborn-Cox formulation.
Abstract: In order that it be correctly characterized, irreversible turbulent mixing in stratified fluids must distinguish between adiabatic ‘stirring’ and diabatic ‘mixing’. Such a distinction has been formalized through the definition of a diapycnal diffusivity, (Winters & D’Asaro, J. Fluid Mech., vol. 317, 1996, pp. 179–193) and an appropriate mixing efficiency, (Caulfield & Peltier, J. Fluid Mech., vol. 413, 2000, pp. 1–47). Equivalent attention has not been paid to the definitions of a corresponding momentum diffusivity and hence an appropriately defined turbulent Prandtl number . In this paper, the diascalar framework of Winters & D’Asaro (1996) is first reformulated to obtain an ‘Osborn-like’ formula in which the correct definition of irreversible mixing efficiency is shown to replace the flux Richardson number which Osborn (J. Phys. Oceanogr., vol. 10, 1980, pp. 83–89) assumed to characterize this efficiency. We advocate the use of this revised representation for diapycnal diffusivity since the proposed reformulation effectively removes the simplifying assumptions on which the original Osborn formula was based. We similarly propose correspondingly reasonable definitions for and by eliminating the reversible component of the momentum production term. To explore implications of the reformulations for both diapycnal and momentum diffusivity we employ an extensive series of direct numerical simulations (DNS) to investigate the properties of the shear-induced density-stratified turbulence that is engendered through the breaking of a freely evolving Kelvin–Helmholtz wave. The DNS results based on the proposed reformulation of are compared with available estimations due to the mixing length model, as well as both the Osborn–Cox and the Osborn models. Estimates based upon the Osborn–Cox formulation are shown to provide the closest approximation to the diapycnal diffusivity delivered by the exact representation. Through compilation of the complete set of DNS results we explore the characteristic dependence of on the buoyancy Reynolds number as originally investigated by Shih et al. (J. Fluid Mech., vol. 525, 2005, pp. 193–214) in their idealized study of homogeneous stratified and sheared turbulence, and show that the validity of their results is only further reinforced through analysis of the turbulence produced in the more geophysically relevant Kelvin–Helmholtz wave life-cycle ansatz. In contrast to the results described by Shih et al. (2005) however, we show that, besides , a vertically averaged measure of the gradient Richardson number may equivalently characterize the turbulent mixing at high . Based on the dominant driving processes involved in irreversible mixing, we categorize the intermediate (i.e. ) and high (i.e. ) range of as ‘buoyancy-dominated’ and ‘shear-dominated’ mixing regimes, which together define a transition value of . Mixing efficiency varies non-monotonically with both and , with its maximum (on the order of 0.2–0.3) occurring in the ‘buoyancy-dominated’ regime. Unlike which is very sensitive to the correct choice of (i.e. ), we show that is almost insensitive to the choice of (i.e. ) so long as is not close to unity, which implies for the entire range of . The turbulent Prandtl number is consequently shown to decrease monotonically with and may be (to first order) simply approximated by itself. Assuming , or (as is common in large-scale numerical models of the ocean general circulation), is also suggested to be a questionable assumption.
109 citations
TL;DR: In this article, 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.
Abstract: 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.
85 citations
TL;DR: It is found that homogenous turbulence is unstable to a large-scale dynamo instability, which saturates to an inhomogenous equilibrium with a strong dependence on the magnetic Prandtl number (Pm) in the quasilinear model.
Abstract: Turbulence and dynamo induced by the magnetorotational instability (MRI) are analyzed using quasilinear statistical simulation methods. It is found that homogenous turbulence is unstable to a large-scale dynamo instability, which saturates to an inhomogenous equilibrium with a strong dependence on the magnetic Prandtl number (Pm). Despite its enormously reduced nonlinearity, the dependence of the angular momentum transport on Pm in the quasilinear model is qualitatively similar to that of nonlinear MRI turbulence. This demonstrates the importance of the large-scale dynamo and suggests how dramatically simplified models may be used to gain insight into the astrophysically relevant regimes of very low or high Pm.
50 citations
TL;DR: In this article, the authors investigated the properties of the turbulent state in the small magnetic Prandtl number limit and showed that angular momentum transport in accretion discs is due to magnetohydrodynamic turbulence mediated by the magnetorotational instability.
Abstract: Context. Angular momentum transport in accretion discs is often believed to be due to magnetohydrodynamic turbulence mediated by the magnetorotational instability (MRI). Despite an abundant literature on the MRI, the parameters governing the saturation amplitude of the turbulence are poorly understood and the existence of an asymptotic behaviour in the Ohmic diffusion regime has not been clearly established.Aims. We investigate the properties of the turbulent state in the small magnetic Prandtl number limit. Since this is extremely computationally expensive, we also study the relevance and range of applicability of the most common subgrid scale models for this problem. Methods. Unstratified shearing box simulations are performed both in the compressible and incompressible limits, with a resolution up to 800 cells per disc scale height. This is the highest resolution ever attained for a simulation of MRI turbulence. Different magnetic field geometry and a wide range of dimensionless dissipative coefficients are considered. We also systematically investigate the relevance of using large eddy simulations (LES) in place of direct numerical simulations. Results. In the presence of a mean magnetic field threading the domain, angular momentum transport converges to a finite value in the small Pm limit. When the mean vertical field amplitude is such that β (the ratio between the thermal and magnetic pressure) equals 103 , we find α ~ 3.2 × 10-2 when Pm approaches zero. In the case of a mean toroidal field for which β = 100, we find α ~ 1.8 × 10-2 in the same limit. Implicit LES and the Chollet-Lesieur closure model both reproduce these results for the α parameter and the power spectra. A reduction in computational cost by a factor of at least 16 (and up to 256) is achieved when using such methods. Conclusions. MRI turbulence operates efficiently in the small Pm limit provided there is a mean magnetic field. Implicit LES offers a practical and efficient means of investigation of this regime but should be used with care, particularly in the case of a vertical field. The Chollet-Lesieur closure model is perfectly suited for simulations done with a spectral code.
46 citations
TL;DR: In this paper, the role of both linear and nonlinear dissipative effects in the excitation and sustainment of the magnetorotational (MRI) dynamo at moderate magnetic Reynolds number (Rm) was investigated.
Abstract: The magnetorotational (MRI) dynamo has long been considered one of the possible drivers of turbulent angular momentum transport in astrophysical accretion disks. However, various numerical results suggest that this dynamo may be difficult to excite in the astrophysically relevant regime of magnetic Prandtl number (Pm) significantly smaller than unity, for reasons currently not well understood. The aim of this article is to present the first results of an ongoing numerical investigation of the role of both linear and nonlinear dissipative effects in this problem. Combining a parametric exploration and an energy analysis of incompressible nonlinear MRI dynamo cycles representative of the transitional dynamics in large aspect ratio shearing boxes, we find that turbulent magnetic diffusion makes the excitation and sustainment of this dynamo at moderate magnetic Reynolds number (Rm) increasingly difficult for decreasing Pm. This results in an increase in the critical Rm of the dynamo for increasing kinematic Reynolds number (Re), in agreement with earlier numerical results. Given its very generic nature, we argue that turbulent magnetic diffusion could be an important determinant of MRI dynamo excitation in disks, and may also limit the efficiency of angular momentum transport by MRI turbulence in low Pm regimes.
36 citations
TL;DR: In this paper, the velocity and temperature distributions have been evaluated numerically by shooting approach and the solution depends on various interesting parameters including local Deborah number De, magnetic field parameter M, Prandtl number Pr and Biot number Bi.
Abstract: In this paper we address the flow of Maxwell fluid due to constantly moving flat radiative surface with convective condition. The flow is under the influence of non-uniform transverse magnetic field. The velocity and temperature distributions have been evaluated numerically by shooting approach. The solution depends on various interesting parameters including local Deborah number De, magnetic field parameter M, Prandtl number Pr and Biot number Bi. We found that variation in velocity with an increase in local Deborah number De is non-monotonic. However temperature is a decreasing function of local Deborah number De.
32 citations
TL;DR: In this paper, a theoretical analysis is performed to study induced magnetic field effects on free convection flow past a vertical plate, and the coupled nonlinear partial differential equations are solved by Perturbation technique and the effects of various physical parameters on velocity, temperature, and induced magnetic fields are studied through graphs and tables.
29 citations
TL;DR: In this paper, it was shown that there exists a critical value of the magnetic Prandtl number between unity and 10 in the outer disk above which the cosmic battery mechanism is suppressed.
Abstract: The aberrated radiation pressure at the inner edge of the accretion disk around an astrophysical black hole imparts a relative azimuthal velocity on the electrons with respect to the ions which gives rise to a ring electric current that generates large-scale poloidal magnetic field loops. This is the Cosmic Battery established by Contopoulos and Kazanas in 1998. In the present work we perform realistic numerical simulations of this important astrophysical mechanism in advection-dominated accretion flows, ADAFs. We confirm the original prediction that the inner parts of the loops are continuously advected toward the central black hole and contribute to the growth of the large-scale magnetic field, whereas the outer parts of the loops are continuously diffusing outward through the turbulent accretion flow. This process of inward advection of the axial field and outward diffusion of the return field proceeds all the way to equipartition, thus generating astrophysically significant magnetic fields on astrophysically relevant timescales. We confirm that there exists a critical value of the magnetic Prandtl number between unity and 10 in the outer disk above which the Cosmic Battery mechanism is suppressed.
25 citations
TL;DR: In this paper, the dynamo hysteresis predicted by Kitchatinov & Olemskoy with direct numerical simulations was investigated by performing 3D simulations of large-scale dynamos in a shearing box with helically forced turbulence.
Abstract: Nonlinear mean-field models of the solar dynamo show long-term variability, which may be relevant to different states of activity inferred from long-term radiocarbon data. This paper is aimed at probing the dynamo hysteresis predicted by the recent mean-field models of Kitchatinov & Olemskoy with direct numerical simulations. We perform three-dimensional (3D) simulations of large-scale dynamos in a shearing box with helically forced turbulence. As an initial condition, we either take a weak random magnetic field or we start from a snapshot of an earlier simulation. Two quasi-stable states are found to coexist in a certain range of parameters close to the onset of the large-scale dynamo. The simulations converge to one of these states depending on the initial conditions. When either the fractional helicity or the magnetic Prandtl number is increased between successive runs above the critical value for onset of the dynamo, the field strength jumps to a finite value. However, when the fractional helicity or the magnetic Prandtl number is then decreased again, the field strength stays at a similar value (strong field branch) even below the original onset. We also observe intermittent decaying phases away from the strong field branch close to the point where large-scale dynamo action is just possible. The dynamo hysteresis seen previously in mean-field models is thus reproduced by 3D simulations. Its possible relation to distinct modes of solar activity such as grand minima is discussed.
23 citations
TL;DR: In this article, it was shown that the inner parts of the loops are continuously advected toward the central black hole and contribute to the growth of the large scale magnetic field, whereas the outer parts are continuously diffusing outward through the turbulent accretion flow.
Abstract: The aberrated radiation pressure at the inner edge of the accretion disk around an astrophysical black hole imparts a relative azimuthal velocity on the electrons with respect to the ions which gives rise to a ring electric current that generates large scale poloidal magnetic field loops. This is the Cosmic Battery established by Contopoulos and Kazanas in 1998. In the present work we perform realistic numerical simulations of this important astrophysical mechanism in advection-dominated accretion flows-ADAF. We confirm the original prediction that the inner parts of the loops are continuously advected toward the central black hole and contribute to the growth of the large scale magnetic field, whereas the outer parts of the loops are continuously diffusing outward through the turbulent accretion flow. This process of inward advection of the axial field and outward diffusion of the return field proceeds all the way to equipartition, thus generating astrophysically significant magnetic fields on astrophysically relevant timescales. We confirm that there exists a critical value of the magnetic Prandtl number between unity and 10 in the outer disk above which the Cosmic Battery mechanism is suppressed.
TL;DR: In this article, a large set of numerical simulations of MHD turbulence induced by the magnetorotational instability is presented, and the saturation level is more sensitive to the numerical magnetic Prandtl number than the pressure.
Abstract: A large set of numerical simulations of MHD turbulence induced by the magnetorotational instability is presented. Revisiting the previous survey conducted by Sano et al., we investigate the gas pressure dependence of the saturation level. In ideal MHD simulations, the gas pressure dependence is found to be very sensitive to the choice of numerical scheme. This is because the numerical magnetic Prandtl number varies according to the scheme as well as the pressure, which considerably affects the results. The saturation level is more sensitive to the numerical magnetic Prandtl number than the pressure. In MHD simulations with explicit viscosity and resistivity, the saturation level increases with the physical magnetic Prandtl number, and it is almost independent of the gas pressure when the magnetic Prandtl number is constant. This is indicative of the incompressible turbulence saturated by the secondary tearing instability.
TL;DR: In this article, the authors investigate numerical dynamo simulations in a rotating spherical shell including a stably stratified region below the outer boundary to discuss dynamo solution behaviors and some implications for the dynamics of Earth's core.
TL;DR: In this article, the formation process of bipolar magnetic flux in a two-layer model is analyzed in terms of negative effective magnetic pressure instability (NEMPI), which is a possible mechanism to explain the origin of sunspots.
Abstract: This work presents an extensive study of the previously discovered formation of bipolar flux concentrations in a two-layer model. We interpret the formation process in terms of negative effective magnetic pressure instability (NEMPI), which is a possible mechanism to explain the origin of sunspots. In our simulations, we use a Cartesian domain of isothermal stratified gas that is divided into two layers. In the lower layer, turbulence is forced with transverse nonhelical random waves, whereas in the upper layer no flow is induced. A weak uniform magnetic field is imposed in the entire domain at all times. In this study we vary the stratification by changing the gravitational acceleration, magnetic Reynolds number, strength of the imposed magnetic field, and size of the domain to investigate their influence on the formation process. Bipolar magnetic structure formation takes place over a large range of parameters. The magnetic structures become more intense for higher stratification until the density contrast becomes around $100$ across the turbulent layer. For the Reynolds numbers considered, magnetic flux concentrations are generated at magnetic Prandtl number between 0.1 and 1. The magnetic field in bipolar regions increases with higher imposed field strength until the field becomes comparable to the equipartition field strength of the turbulence. A larger horizontal extent enables the flux concentrations to become stronger and more coherent. The size of the bipolar structures turns out to be independent of the domain size. In the case of bipolar region formation, we find an exponential growth of the large-scale magnetic field, which is indicative of a hydromagnetic instability. Additionally, the flux concentrations are correlated with strong large-scale downward and converging flows. These findings imply that NEMPI is responsible for magnetic flux concentrations.
TL;DR: In this article, the authors performed numerical simulation of dynamo with magnetic Prandtl number Pm = 0.2 on 10243 grid, and computed the energy fluxes and the shell-to-shell energy transfers.
Abstract: We perform numerical simulation of dynamo with magnetic Prandtl number Pm = 0.2 on 10243 grid, and compute the energy fluxes and the shell-to-shell energy transfers. These computations indicate that the magnetic energy growth takes place mainly due to the energy transfers from large-scale velocity field to large-scale magnetic field and that the magnetic energy flux is forward. The steady-state magnetic energy is much smaller than the kinetic energy, rather than equipartition; this is because the magnetic Reynolds number is near the dynamo transition regime. We also contrast our results with those for dynamo with Pm = 20 and decaying dynamo.
TL;DR: In this article, the authors revisited the question of possible small-scale dynamo action in the surface layers of the Sun with realistic 3D MHD simulations and found that dynamo activity is a sensitive function of the magnetic Prandtl number Pm = = ; it disappears below a critical value Pc which is a function of numerical resolution.
Abstract: The question of possible small-scale dynamo action in the surface layers of the Sun is revisited with realistic 3D MHD simulations. As in other MHD problems, dynamo action is found to be a sensitive function of the magnetic Prandtl number Pm = = ; it disappears below a critical value Pc which is a function of the numerical resolution. At a grid spacing of 3.5 km, Pc based on the hyperdi usivities implemented in the code (STAGGER) is 1, increasing with increasing grid spacing. As in other settings, it remains uncertain whether small scale dynamo action is present in the astrophysical limit where Pm 1 and magnetic Reynolds number Rm 1. The question is discussed in the context of the strong e ect that external stray fields are observed to have in generating and maintaining dynamo action in other numerical and laboratory systems, and in connection with the type-II hypertransient behavior of dynamo action observed in the absence of such external fields.
TL;DR: In this article, the authors examined the effect of induced magnetic field and convective boundary condition on stagnation point flow and heat transfer due to nanofluid over a stretching sheet and found that the skin friction coefficient, the local Nusselt number, and Sherwood number decrease with an increase in B and M parameters.
Abstract: This study examines the effect of induced magnetic field and convective boundary condition on MHD stagnation point flow and heat transfer due to nanofluid over a stretching sheet. It takes into account the effect of Brownian motion and thermophoresis parameters. The nonlinear governing equations and their associated boundary conditions are reduced into dimensionless form by similarity variables. The resulting systems of equations are then solved numerically using fourth-order Runge–Kutta method along with shooting technique. The solution for the problem depends on parameters: magnetic M, velocity ratio B, Biot number Bi, Prandtl number Pr, Lewis number Le, Brownian motion Nb, thermophoresis Nt, and reciprocal of magnetic Prandtl number A. Numerical results of the study are obtained for velocity, temperature, induced magnetic field, and concentration profiles as well as skin friction coefficient, the local Nusselt number, and Sherwood number. It is found that the skin friction coefficient, the local Nusselt number, and Sherwood number decrease with an increase in B and M parameters. However, the local Nusselt number $-$ $\theta ^{\prime }(0)$ increases with an increase in Bi, and local Sherwood number $-$ $\phi ^{\prime }(0)$ decreases with an increase in convective parameter Bi. The study indicated that the flow velocity and the skin friction coefficient on stretching sheet are strongly influenced by velocity ratio ( $B ) and magnetic parameters. It is also observed that the skin friction coefficient $-$ $f^{\prime \prime }(0)$ is an increasing function of magnetic parameter and a decreasing function of velocity ratio parameter B. The study also shows that the local heat transfer rate $-$ $\theta ^{\prime }(0)$ is an increasing function of the convective parameter Bi, but it is a decreasing function of magnetic parameter M, velocity ratio parameter B, and thermophoresis parameter Nt. The obtained results are displayed both in graphical and tabular form to show the effect of the governing parameters on the dimensionless velocity, induced magnetic field, temperature and concentration. The numerical results are compared and found to be in good agreement with the previously published results on special cases of the problem.
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TL;DR: In this article, the Navier Stokes flows can be decomposed into Euler and Prandtl flows in the inviscid limit, and several embedding theorems are derived to capture the interaction between the scaling and the geometry of the domain.
Abstract: This paper concerns the validity of the Prandtl boundary layer theory for steady, incompressible Navier-Stokes flows over a rotating disk. We prove that the Navier Stokes flows can be decomposed into Euler and Prandtl flows in the inviscid limit. In so doing, we develop a new set of function spaces and prove several embedding theorems which capture the interaction between the Prandtl scaling and the geometry of our domain.
TL;DR: In this paper, the authors propose a new representation of the magnetic reconnection process, which highlights the parameter regions of a given system in which the magnetar reconnection processes are expected to be distinguished by a specific evolution.
Abstract: Recent progress in the understanding of how externally driven magnetic reconnection evolves is organized in terms of parameter space diagrams. These diagrams are constructed using four pivotal dimensionless parameters: the Lundquist number , the magnetic Prandtl number , the amplitude of the boundary perturbation , and the perturbation wave number . This new representation highlights the parameter regions of a given system in which the magnetic reconnection process is expected to be distinguished by a specific evolution. Contrary to previously proposed phase diagrams, the diagrams introduced here take into account the dynamical evolution of the reconnection process and are able to predict slow or fast reconnection regimes for the same values of and , depending on the parameters that characterize the external drive, which have not been considered until now. These features are crucial to understanding the onset and evolution of magnetic reconnection in diverse physical systems.
TL;DR: In this article, a large set of numerical simulations of magnetohydrodynamic (MHD) turbulence induced by the magnetorotational instability (MRI) is presented, and the saturation level is more sensitive to the numerical magnetic Prandtl number than the pressure.
Abstract: A large set of numerical simulations of magnetohydrodynamic (MHD) turbulence induced by the magnetorotational instability (MRI) is presented. Revisiting the previous survey conducted by Sano et al. (2004), we investigate the gas pressure dependence of the saturation level. In ideal MHD simulations, the gas pressure dependence is found to be very sensitive to the choice of a numerical scheme. This is because the numerical magnetic Prandtl number varies according to the scheme as well as the pressure, which considerably affects the results. The saturation level is more sensitive to the numerical magnetic Prandtl number than the pressure. In MHD simulations with explicit viscosity and resistivity, the saturation level increases with the physical magnetic Prandtl number, and it is almost independent of the gas pressure when the magnetic Prandtl number is constant. This is indicative of the incompressible turbulence saturated by the secondary tearing instability.
TL;DR: Chian et al. as mentioned in this paper studied the development of coherent structures in local simulations of the magnetorotational instability in accretion discs in regimes of on-off intermittency, and showed that the large-scale coherent structures are characterized by a high degree of amplitude-phase synchronization.
Abstract: We study the development of coherent structures in local simulations of the magnetorotational instability in accretion discs in regimes of on-off intermittency. In a previous paper [Chian et al., Phys. Rev. Lett. 104, 254102 (2010)], we have shown that the laminar and bursty states due to the on-off spatiotemporal intermittency in a one-dimensional model of nonlinear waves correspond, respectively, to nonattracting coherent structures with higher and lower degrees of amplitude-phase synchronization. In this paper we extend these results to a three-dimensional model of magnetized Keplerian shear flows. Keeping the kinetic Reynolds number and the magnetic Prandtl number fixed, we investigate two different intermittent regimes by varying the plasma beta parameter. The first regime is characterized by turbulent patterns interrupted by the recurrent emergence of a large-scale coherent structure known as two-channel flow, where the state of the system can be described by a single Fourier mode. The second regime is dominated by the turbulence with sporadic emergence of coherent structures with shapes that are reminiscent of a perturbed channel flow. By computing the Fourier power and phase spectral entropies in three-dimensions, we show that the large-scale coherent structures are characterized by a high degree of amplitude-phase synchronization.
TL;DR: In this article, a numerical study on steady laminar magnetohydrodynamics (MHD) mixed convection flow of an electrically conducting fluid in a vertical square duct under the action of transverse magnetic field has been investigated.
Abstract: A numerical study on steady laminar magnetohydrodynamics (MHD) mixed convection flow of an electrically conducting fluid in a vertical square duct under the action of transverse magnetic field has been investigated. The walls of the duct are electrically non-conducting. In this study both forced and free convection flows are considered. The viscous dissipation and Joule heat are also considered in the energy equation and moreover the walls of the duct are kept at constant temperature. The governing equations of momentum, induction and energy are first transformed into dimensionless equations by using dimensionless quantities, then these are solved employing finite difference method for velocity, induced magnetic field and temperature distribution. The computed results for velocity, induced magnetic field and temperature distribution are presented graphically for different dimensionless parameters Hartmann number , Prandtl number , Grashof number and magnetic Reynolds number .
TL;DR: In this article, the authors investigate the singularities developed by a hydromagnetic shell model during the magnetohydrodynamic turbulent cascade and show that when the viscosity is equal to the magnetic diffusivity (unit magnetic Prandtl number), singularities appear in a finite time.
Abstract: Conventional surveys on the existence of singularities in fluid systems for vanishing dissipation have hitherto tried to infer some insight by searching for spatial features developing in asymptotic regimes. This approach has not yet produced a conclusive answer. One of the difficulties preventing us from getting a definitive answer is the limitations of direct numerical simulations which do not yet have a high enough resolution so far as to properly describe spatial fine structures in asymptotic regimes. In this paper, instead of searching for spatial details, we suggest seeking a principle, that would be able to discriminate between singular or not-singular behavior, among the integral and purely dynamical properties of a fluid system. We investigate the singularities developed by a hydromagnetic shell model during the magnetohydrodynamic turbulent cascade. Our results show that when the viscosity is equal to the magnetic diffusivity (unit magnetic Prandtl number) singularities appear in a finite time. A complex behavior is observed at extreme magnetic Prandtl numbers. In particular, the singularities persist in the limit of vanishing viscosity, while a complete regularization is observed in the limit of vanishing diffusivity. This dynamics is related to differences between the magnetic and the kinetic energy cascades towards small scales. Finally a comparison between the three-dimensional and the two-dimensional cases leads to conjecture that the existence of singularities may be related to the conservation of different ideal invariants.
TL;DR: In this paper, the authors propose a new representation of the parameters regions of a given system in which the magnetic reconnection process is expected to be distinguished by a specific evolution, which can be used to predict slow or fast reconnection regimes.
Abstract: Recent progress in the understanding of how externally driven magnetic reconnection evolves is organized in terms of parameter space diagrams. These diagrams are constructed using four pivotal dimensionless parameters: the Lundquist number $S$, the magnetic Prandtl number $P_m$, the amplitude of the boundary perturbation $\hat \Psi_0$, and the perturbation wave number $\hat k$. This new representation highlights the parameters regions of a given system in which the magnetic reconnection process is expected to be distinguished by a specific evolution. Contrary to previously proposed phase diagrams, the diagrams introduced here take into account the dynamical evolution of the reconnection process and are able to predict slow or fast reconnection regimes for the same values of $S$ and $P_m$, depending on the parameters that characterize the external drive, never considered so far. These features are important to understand the onset and evolution of magnetic reconnection in diverse physical systems
TL;DR: In this article, the high-Prandtl number passive scalar transport of the turbulent channel flow imposed a wall-normal magnetic field is investigated through the large-scale direct numerical simulation (DNS).
01 Aug 2015
TL;DR: The 3D MHD Anelastic Spherical Harmonic code was employed to capture convective and dynamo processes achieved in a global-scale stellar convection simulation for a model solar-mass star rotating at three times the solar rate as discussed by the authors.
Abstract: The 3D MHD Anelastic Spherical Harmonic code, using slope-limited diffusion, is employed to capture convective and dynamo processes achieved in a global-scale stellar convection simulation for a model solar-mass star rotating at three times the solar rate. The dynamo-generated magnetic fields possesses many timescales, with a prominent polarity cycle occurring roughly every 6.2 years. The magnetic field forms large-scale toroidal wreaths, whose formation is tied to the low Rossby number of the convection in this simulation. The polarity reversals are linked to the weakened differential rotation and a resistive collapse of the large-scale magnetic field. An equatorial migration of the magnetic field is seen, which is due to the strong modulation of the differential rotation rather than a dynamo wave. A poleward migration of magnetic flux from the equator eventually leads to the reversal of the polarity of the high-latitude magnetic field. This simulation also enters an interval with reduced magnetic energy at low latitudes lasting roughly 16 years (about 2.5 polarity cycles), during which the polarity cycles are disrupted and after which the dynamo recovers its regular polarity cycles. An analysis of this grand minimum reveals that it likely arises through the interplay of symmetric and antisymmetric dynamo families. This intermittent dynamo state potentially results from the simulation’s relatively low magnetic Prandtl number. A mean-field-based analysis of this dynamo simulation demonstrates that it is of the α-Ω type. The timescales that appear to be relevant to the magnetic polarity reversal are also identified.
TL;DR: In this paper, the authors investigated the properties of the turbulent state in the small magnetic Prandtl number limit and showed that angular momentum transport in accretion discs is due to magnetohydrodynamic turbulence mediated by magnetorotational instability.
Abstract: Angular momentum transport in accretion discs is often believed to be due to magnetohydrodynamic turbulence mediated by the magnetorotational instability. Despite an abundant literature on the MRI, the parameters governing the saturation amplitude of the turbulence are poorly understood and the existence of an asymptotic behavior in the Ohmic diffusion regime is not clearly established. We investigate the properties of the turbulent state in the small magnetic Prandtl number limit. Since this is extremely computationally expensive, we also study the relevance and range of applicability of the most common subgrid scale models for this problem. Unstratified shearing boxes simulations are performed both in the compressible and incompressible limits, with a resolution up to 800 cells per disc scale height. The latter constitutes the largest resolution ever attained for a simulation of MRI turbulence. In the presence of a mean magnetic field threading the domain, angular momentum transport converges to a finite value in the small Pm limit. When the mean vertical field amplitude is such that {\beta}, the ratio between the thermal and magnetic pressure, equals 1000, we find {\alpha}~0.032 when Pm approaches zero. In the case of a mean toroidal field for which {\beta}=100, we find {\alpha}~0.018 in the same limit. Both implicit LES and Chollet-Lesieur closure model reproduces these results for the {\alpha} parameter and the power spectra. A reduction in computational cost of a factor at least 16 (and up to 256) is achieved when using such methods. MRI turbulence operates efficiently in the small Pm limit provided there is a mean magnetic field. Implicit LES offers a practical and efficient mean of investigation of this regime but should be used with care, particularly in the case of a vertical field. Chollet-Lesieur closure model is perfectly suited for simulations done with a spectral code.
TL;DR: Numerical linear stability analysis of a cylindrical Taylor-Couette flow of liquid metal carrying axial electric current in a generally helical external magnetic field shows that the electric current passing through the liquid can extend the range of helical magnetorotational instability indefinitely by transforming it into a purely electromagnetic instability.
Abstract: This paper presents numerical linear stability analysis of a cylindrical Taylor-Couette flow of liquid metal carrying axial electric current in a generally helical external magnetic field. Axially symmetric disturbances are considered in the inductionless approximation corresponding to zero magnetic Prandtl number. Axial symmetry allows us to reveal an entirely new electromagnetic instability. First, we show that the electric current passing through the liquid can extend the range of helical magnetorotational instability (HMRI) indefinitely by transforming it into a purely electromagnetic instability. Two different electromagnetic instability mechanisms are identified. The first is an internal pinch-type instability, which is due to the interaction of the electric current with its own magnetic field. Axisymmetric mode of this instability requires a free-space component of the azimuthal magnetic field. When the azimuthal component of the magnetic field is purely rotational and the axial component is nonzero, a new kind of electromagnetic instability emerges. The latter, driven by the interaction of electric current with a weak collinear magnetic field in a quiescent fluid, gives rise to a steady meridional circulation coupled with azimuthal rotation.
TL;DR: In this paper, 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.
Abstract: 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 timescales that respectively characterize the convective timescale, the large-scale magnetic evolution timescale, and the large-scale thermal evolution timescale. 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-scales. 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 solid 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 and Soward [Phys. Rev. Lett., \textbf{29}, p.837, 1972]. These models may be useful for understanding the dynamics of convection-driven dynamos in regimes that are only just becoming accessible to direct numerical simulations.
TL;DR: In this paper, the authors describe a vertical hot plate moving with acceleration and with variation wall temperature, where the temperature and velocity are given by the governing equations, and the results show that the velocity profiles are significantly influenced by Prandtl and Grashoft number.
Abstract: This work describes a vertical hot plate moves with acceleration and with variation wall temperature. The temperatures of the plate decrease with the increase of velocity of the plate. The temperature and velocity are given by the governing equations. The dimensionless equations of the problem have been solved numerically by the finite difference method. The temperature and the velocity profiles against several parameters like Prandtl Number, Grashoft number and time are presented. The results show that the temperature and velocity profiles are significantly influenced by Prandtl and Grashoft number.