اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدScaling and intermittency in incoherent alpha-shear dynamo
139
0
0.0
(
0
)
تأليف
Dhrubaditya Mitra
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We consider mean-field dynamo models with fluctuating alpha effect, both with and without shear. The alpha effect is chosen to be Gaussian white noise with zero mean and given covariance. We show analytically that the mean magnetic field does not grow, but, in an infinitely large domain, the mean-squared magnetic field shows exponential growth of the fastest growing mode at a rate proportional to the shear rate, which agrees with earlier numerical results of Yousef et al (2008) and recent analytical treatment by Heinemann et al (2011) who use a method different from ours. In the absence of shear, an incoherent alpha^2 dynamo may also be possible. We further show by explicit calculation of the growth rate of third and fourth order moments of the magnetic field that the probability density function of the mean magnetic field generated by this dynamo is non-Gaussian.
قيم البحث
اقرأ أيضاً
In this paper we discuss the dynamical features of intermittent fluctuations in homogeneous shear flow turbulence. In this flow the energy cascade is strongly modified by the production of turbulent kinetic energy related to the presence of vortical
structures induced by the shear. By using direct numerical simulations, we show that the refined Kolmogorov similarity is broken and a new form of similarity is observed, in agreement to previous results obtained in turbulent boundary layers. As a consequence, the intermittency of velocity fluctuations increases with respect to homogeneous and isotropic turbulence. We find here that the statistical properties of the energy dissipation are practically unchanged with respect to homogeneous isotropic conditions, while the increased intermittency is entirely captured in terms of the new similarity law.
The Refined Kolmogorov Similarity Hypothesis is a valuable tool for the description of intermittency in isotropic conditions. For flows in presence of a substantial mean shear, the nature of intermittency changes since the process of energy transfer
is affected by the turbulent kinetic energy production associated with the Reynolds stresses. In these conditions a new form of refined similarity law has been found able to describe the increased level of intermittency which characterizes shear dominated flows. Ideally a length scale associated with the mean shear separates the two ranges, i.e. the classical Kolmogorov-like inertial range, below, and the shear dominated range, above. However, the data analyzed in previous papers correspond to conditions where the two scaling regimes can only be observed individually. In the present letter we give evidence of the coexistence of the two regimes and support the conjecture that the statistical properties of the dissipation field are practically insensible to the mean shear. This allows for a theoretical prediction of the scaling exponents of structure functions in the shear dominated range based on the known intermittency corrections for isotropic flows. The prediction is found to closely match the available numerical and experimental data.
A quasi-linear theory is presented for how randomly forced, barotropic velocity fluctuations cause an exponentially-growing, large-scale (mean) magnetic dynamo in the presence of a uniform shear flow, $vec{U} = S x vec{e}_y$. It is a kinematic theory
for the growth of the mean magnetic energy from a small initial seed, neglecting the saturation effects of the Lorentz force. The quasi-linear approximation is most broadly justifiable by its correspondence with computational solutions of nonlinear magneto-hydrodynamics, and it is rigorously derived in the limit of large resistivity, $eta rightarrow infty$. Dynamo action occurs even without mean helicity in the forcing or flow, but random helicity variance is then essential. In a sufficiently large domain and with small wavenumber $k_z$ in the direction perpendicular to the mean shearing plane, a positive exponential growth rate $gamma$ can occur for arbitrary values of $eta$, the viscosity $ u$, and the random-forcing correlation time $t_f$ and phase angle $theta_f$ in the shearing plane. The value of $gamma$ is independent of the domain size. The shear dynamo is fast, with finite $gamma > 0$ in the limit of $eta rightarrow 0$. Averaged over the random forcing ensemble, the mean magnetic field grows more slowly, if at all, compared to the r.m.s. field (or magnetic energy). In the limit of small Reynolds numbers ($eta, u rightarrow infty$), the dynamo behavior is related to the well-known alpha--omega {it ansatz} when the forcing is steady ($t_f rightarrow infty$) and to the incoherent alpha--omega {it ansatz} when the forcing is purely fluctuating.
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 th
at 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.
Via amplification by turbulent dynamo, magnetic fields can be potentially important for the formation of the first stars. To examine the dynamo behavior during the gravitational collapse of primordial gas, we extend the theory of nonlinear turbulent
dynamo to include the effect of gravitational compression. The relative importance between dynamo and compression varies during contraction, with the transition from dynamo- to compression-dominated amplification of magnetic fields with the increase of density. In the nonlinear stage of magnetic field amplification with the scale-by-scale energy equipartition between turbulence and magnetic fields, reconnection diffusion of magnetic fields in ideal magnetohydrodynamic (MHD) turbulence becomes important. It causes the violation of flux-freezing condition and accounts for (a) the small growth rate of nonlinear dynamo, (b) the weak dependence of magnetic energy on density during contraction, (c) the saturated magnetic energy, and (d) the large correlation length of magnetic fields. The resulting magnetic field structure and the scaling of magnetic field strength with density are radically different from the expectations of flux-freezing.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
