Numerical Studies of Dynamo Action in a Turbulent Shear Flow. I.

Singh, Nishant K.; Jingade, Naveen

doi:10.1088/0004-637x/806/1/118

Cited by 16 publications

(39 citation statements)

References 34 publications

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“…Measurements of mean-field responses (using the test-field method discussed in § 4.7.2) in several independent numerical simulations of non-rotating, sheared, non-helical turbulence with , now seem to have confirmed that the contribution of the shear-current effect to has the wrong sign for a large-scale dynamo, both in the FOSA regime of low (as it should be) and for moderate up to (Brandenburg et al. 2008 a ; Squire & Bhattacharjee 2015 c ; Singh & Jingade 2015).…”

Section: The Diverse Challenging Complexity Of Large-scale Dynamosmentioning

confidence: 76%

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Dynamo theories

2019

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These lecture notes are based on a tutorial given in 2017 at a plasma physics winter school in Les Houches. Their aim is to provide a self-contained graduate-student level introduction to the theory and modelling of the dynamo effect in turbulent fluids and plasmas, blended with a review of current research in the field. The primary focus is on the physical and mathematical concepts underlying different (turbulent) branches of dynamo theory, with some astrophysical, geophysical and experimental contexts disseminated throughout the document. The text begins with an introduction to the rationale, observational and historical roots of the subject, and to the basic concepts of magnetohydrodynamics relevant to dynamo theory. The next two sections discuss the fundamental phenomenological and mathematical aspects of (linear and nonlinear) small- and large-scale magnetohydrodynamic (MHD) dynamos. These sections are complemented by an overview of a selection of current active research topics in the field, including the numerical modelling of the geo- and solar dynamos, shear dynamos driven by turbulence with zero net helicity and MHD-instability-driven dynamos such as the magnetorotational dynamo. The difficult problem of a unified, self-consistent statistical treatment of small- and large-scale dynamos at large magnetic Reynolds numbers is also discussed throughout the text. Finally, an excursion is made into the relatively new but increasingly popular realm of magnetic-field generation in weakly collisional plasmas. A short discussion of the outlook and challenges for the future of the field concludes the presentation.

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Section: The Diverse Challenging Complexity Of Large-scale Dynamosmentioning

confidence: 76%

“…2008 b ; Brandenburg et al. 2008 a ; Käpylä, Korpi & Brandenburg 2008; Hughes & Proctor 2009; Singh & Jingade 2015). In the simplest possible Cartesian case, a shearing-box extension of the Meneguzzi et al.…”

Section: The Diverse Challenging Complexity Of Large-scale Dynamosmentioning

confidence: 99%

Dynamo theories

2019

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“…The important difference in the present work is that the α fluctuations considered here are statistically stationary and homogeneous. The numerical simulations of Brandenburg et al (2008); Yousef et al (2008); Singh & Jingade (2015) demonstrated large-scale dynamo action in a shear flow with turbulence that is, on average, non-helical. This problem of the shear dynamo was taken up in a number of analytical works where the quantity α was assumed to be strictly zero, i.e., it vanishes point-wise both in space and time Sridhar & Subramanian 2009a,b;Sridhar & Singh 2010;Singh & Sridhar 2011).…”

Section: Introductionmentioning

confidence: 96%

Moffatt-drift-driven large-scale dynamo due to fluctuations with non-zero correlation times

Singh

2016

J. Fluid Mech.

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We present a theory of large-scale dynamo action in a turbulent flow that has stochastic, zero-mean fluctuations of the α parameter. Particularly interesting is the possibility of the growth of the mean magnetic field due to Moffatt drift, which is expected to be finite in a statistically anisotropic turbulence. We extend the Kraichnan-Moffatt model to explore effects of finite memory of α fluctuations, in a spirit similar to that of Sridhar & Singh (2014), hereafter SS14. Using the first-order smoothing approximation, we derive a linear integro-differential equation governing the dynamics of the large-scale magnetic field, which is non-perturbative in the α-correlation time τ α . We recover earlier results in the exactly solvable white-noise (WN) limit where the Moffatt drift does not contribute to the dynamo growth/decay. To study finite memory effects, we reduce the integro-differential equation to a partial differential equation by assuming that the τ α be small but nonzero and the large-scale magnetic field is slowly varying. We derive the dispersion relation and provide explicit expression for the growth rate as a function of four independent parameters. When τ α = 0, we find that: (i) in the absence of the Moffatt drift, but with finite Kraichnan diffusivity, only strong α-fluctuations can enable a mean-field dynamo (this is qualitatively similar to the WN case); (ii) in the general case when also the Moffatt drift is nonzero, both, weak or strong α fluctuations, can lead to a large-scale dynamo; and (iii) there always exists a wavenumber (k) cutoff at some large k beyond which the growth rate turns negative, irrespective of weak or strong α fluctuations. Thus we show that a finite Moffatt drift can always facilitate largescale dynamo action if sufficiently strong, even in case of weak α fluctuations, and the maximum growth occurs at intermediate wavenumbers.

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“…2008; Yousef et al. 2008 a , b ; Singh & Jingade 2015) where large-scale magnetic fields were generated due to non-helically forced turbulence in shear flows, and failure to understand these in terms of simple ideas involving a shear–current effect (Kleeorin & Rogachevskii 2008; Rogachevskii & Kleeorin 2008; Sridhar & Subramanian 2009 a , b ; Sridhar & Singh 2010; Singh & Sridhar 2011; Kolekar, Subramanian & Sridhar 2012), brought the focus to a stochastic which could potentially lead to the dynamo action generically in shearing systems (Heinemann, McWilliams & Schekochihin 2011; McWilliams 2012; Mitra & Brandenburg 2012; Proctor 2012; Richardson & Proctor 2012; Sridhar & Singh 2014). There is still a need to verify the model predictions for the growth of the first moment of the mean magnetic field in such systems by performing more simulations.…”

Section: Introductionmentioning

confidence: 99%

Generation of large-scale magnetic fields due to fluctuating in shearing systems

2018

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We explore the growth of large-scale magnetic fields in a shear flow, due to helicity fluctuations with a finite correlation time, through a study of the Kraichnan–Moffatt model of zero-mean stochastic fluctuations of the $\unicode[STIX]{x1D6FC}$ parameter of dynamo theory. We derive a linear integro-differential equation for the evolution of the large-scale magnetic field, using the first-order smoothing approximation and the Galilean invariance of the $\unicode[STIX]{x1D6FC}$-statistics. This enables construction of a model that is non-perturbative in the shearing rate $S$ and the $\unicode[STIX]{x1D6FC}$-correlation time $\unicode[STIX]{x1D70F}_{\unicode[STIX]{x1D6FC}}$. After a brief review of the salient features of the exactly solvable white-noise limit, we consider the case of small but non-zero $\unicode[STIX]{x1D70F}_{\unicode[STIX]{x1D6FC}}$. When the large-scale magnetic field varies slowly, the evolution is governed by a partial differential equation. We present modal solutions and conditions for the exponential growth rate of the large-scale magnetic field, whose drivers are the Kraichnan diffusivity, Moffatt drift, shear and a non-zero correlation time. Of particular interest is dynamo action when the $\unicode[STIX]{x1D6FC}$-fluctuations are weak; i.e. when the Kraichnan diffusivity is positive. We show that in the absence of Moffatt drift, shear does not give rise to growing solutions. But shear and Moffatt drift acting together can drive large-scale dynamo action with growth rate $\unicode[STIX]{x1D6FE}\propto |S|$.

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Numerical Studies of Dynamo Action in a Turbulent Shear Flow. I.

Cited by 16 publications

References 34 publications

Dynamo theories

Dynamo theories

Moffatt-drift-driven large-scale dynamo due to fluctuations with non-zero correlation times

Generation of large-scale magnetic fields due to fluctuating in shearing systems

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