اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThe nature of mean-field generation in three classes of optimal dynamos
443
0
0.0
(
0
)
تأليف
Axel Brandenburg
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In recent years, several optimal dynamos have been discovered. They minimize the magnetic energy dissipation or, equivalently, maximize the growth rate at a fixed magnetic Reynolds number. In the optimal dynamo of Willis (2012, Phys. Rev. Lett. 109, 251101), we find mean-field dynamo action for planar averages. One component of the magnetic field grows exponentially while the other decays in an oscillatory fashion near onset. This behavior is different from that of an alpha^2 dynamo, where the two non-vanishing components of the planar averages are coupled and have the same growth rate. For the Willis dynamo, we find that the mean field is excited by a negative turbulent magnetic diffusivity, which has a non-uniform spatial profile near onset. The temporal oscillations in the decaying component are caused by the corresponding component of the diffusivity tensor being complex when the mean field is decaying and, in this way, time-dependent. The growing mean field can be modeled by a negative magnetic diffusivity combined with a positive magnetic hyperdiffusivity. In two other classes of optimal dynamos of Chen et al. (2015, J. Fluid Mech. 783, 23), we find, to some extent, similar mean-field dynamo actions. When the magnetic boundary conditions are mixed, the two components of the planar averaged field grow at different rates when the dynamo is 15% supercritical. When the mean magnetic field satisfies homogeneous boundary conditions (where the magnetic field is tangential to the boundary), mean-field dynamo action is found for one-dimensional averages, but not for planar averages. Despite having different spatial profiles, both dynamos show negative turbulent magnetic diffusivities. Our finding suggests negative turbulent magnetic diffusivities may support a broader class of dynamos than previously thought, including these three optimal dynamos.
قيم البحث
اقرأ أيضاً
The relative importance of the helicity and cross-helicity electromotive dynamo effects for self-sustained magnetic field generation by chaotic thermal convection in rotating spherical shells is investigated as a function of shell thickness. Two dist
inct branches of dynamo solutions are found to coexist in direct numerical simulations for shell aspect ratios between 0.25 and 0.6 - a mean-field dipolar regime and a fluctuating dipolar regime. The properties characterising the coexisting dynamo attractors are compared and contrasted, including differences in temporal behavior and spatial structures of both the magnetic field and rotating thermal convection. The helicity $alpha$-effect and the cross-helicity $gamma$-effect are found to be comparable in intensity within the fluctuating dipolar dynamo regime, where their ratio does not vary significantly with the shell thickness. In contrast, within the mean-field dipolar dynamo regime the helicity $alpha$-effect dominates by approximately two orders of magnitude and becomes stronger with decreasing shell thickness.
A mean-field theory of differential rotation in a density stratified turbulent convection has been developed. This theory is based on a combined effect of the turbulent heat flux and anisotropy of turbulent convection on the Reynolds stress. A couple
d system of dynamical budget equations consisting in the equations for the Reynolds stress, the entropy fluctuations and the turbulent heat flux has been solved. To close the system of these equations, the spectral tau approach which is valid for large Reynolds and Peclet numbers, has been applied. The adopted model of the background turbulent convection takes into account an increase of the turbulence anisotropy and a decrease of the turbulent correlation time with the rotation rate. This theory yields the radial profile of the differential rotation which is in agreement with that for the solar differential rotation.
Stellar radiative zones are typically assumed to be motionless in standard models of stellar structure but there is sound theoretical and observational evidence that this cannot be the case. We investigate by direct numerical simulations a three-dime
nsional and time-dependent model of stellar radiation zones consisting of an electrically-conductive and stably-stratified anelastic fluid confined to a rotating spherical shell and driven by a baroclinic torque. As the baroclinic driving is gradually increased a sequence of transitions from an axisymmetric and equatorially-symmetric time-independent flow to flows with a strong poloidal component and lesser symmetry are found. It is shown that all flow regimes characterised with significant non-axisymmetric components are capable of generating self-sustained magnetic field. As the value of the Prandtl number is decreased and the value of the Ekman number is decreased flows become strongly time-dependent with progressively complex spatial structure and dynamos can be generated at lower values of the magnetic Prandtl number.
Small-scale dynamos are expected to operate in all astrophysical fluids that are turbulent and electrically conducting, for example the interstellar medium, stellar interiors, and accretion disks, where they may also be affected by or competing with
large-scale dynamos. However, the possibility of small-scale dynamos being excited at small and intermediate ratios of viscosity to magnetic diffusivity (the magnetic Prandtl number) has been debated, and the possibility of them depending on the large-scale forcing wavenumber has been raised. Here we show, using four values of the forcing wavenumber, that the small-scale dynamo does not depend on the scale-separation between the size of the simulation domain and the integral scale of the turbulence, i.e., the forcing scale. Moreover, the spectral bottleneck in turbulence, which has been implied as being responsible for raising the excitation conditions of small-scale dynamos, is found to be invariant under changing the forcing wavenumber. However, when forcing at the lowest few wavenumbers, the effective forcing wavenumber that enters in the definition of the magnetic Reynolds number is found to be about twice the minimum wavenumber of the domain. Our work is relevant to future studies of small-scale dynamos, of which several applications are being discussed.
We discuss a mean-field theory of generation of large-scale vorticity in a rotating density stratified developed turbulence with inhomogeneous kinetic helicity. We show that the large-scale nonuniform flow is produced due to ether a combined action o
f a density stratified rotating turbulence and uniform kinetic helicity or a combined effect of a rotating incompressible turbulence and inhomogeneous kinetic helicity. These effects result in the formation of a large-scale shear, and in turn its interaction with the small-scale turbulence causes an excitation of the large-scale instability (known as a vorticity dynamo) due to a combined effect of the large-scale shear and Reynolds stress-induced generation of the mean vorticity. The latter is due to the effect of large-scale shear on the Reynolds stress. A fast rotation suppresses this large-scale instability.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
