arXiv subjects

Nishant K. Singh

Publications and source records attributed to Nishant K. Singh.

35 records · Page 2Linked to original sources

arXiv2018

Non-linear Galactic Dynamos and the Magnetic Rädler Effect

We show that the magnetic analogue of the Rädler effect of mean-field dynamo theory leads to a non-linear backreaction that quenches a large-scale galactic dynamo, and can result in saturation of the large-scale magnetic field at near-equipartition with turbulent kinetic energy density. In a rotating fluid containing small-scale magnetic fluctuations, anisotropic terms in the mean electromotive force are induced via the Coriolis effect and these terms lead to a reduction of the growth rate in a predominantly $αΩ$-type galactic dynamo (Chamandy & Singh 2017). By including the generation of small-scale magnetic fluctuations by turbulent tangling of the large-scale magnetic field, one obtains a negative feedback effect that quenches the dynamo and leads to the saturation of the large-scale field. This saturation mechanism is found to be competitive with the dynamical $α$-quenching mechanism for realistic galactic parameter values. Furthermore, in the context of the dynamical $α$-quenching model, a separate non-linear term is obtained which has the same form as the helicity flux term of Vishniac & Cho (2001), but which depends on the strength of small-scale magnetic fluctuations. We briefly discuss the observational implications of the magnetic Rädler effect for galaxies.

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arXiv2018

Bihelical spectrum of solar magnetic helicity and its evolution

Using a recently developed two-scale formalism to determine the magnetic helicity spectrum (Brandenburg et al. 2017), we analyze synoptic vector magnetograms built with data from the Vector Spectromagnetograph (VSM) instrument on the \emph{Synoptic Optical Long-term Investigations of the Sun} (SOLIS) telescope during January 2010-July 2016. In contrast to an earlier study using only three Carrington rotations, our analysis includes 74 synoptic Carrington rotation maps. We recover here bihelical spectra at different phases of solar cycle~24, where the net magnetic helicity in the majority of the data is consistent with a large-scale dynamo with helical turbulence operating in the Sun. More than $20\%$ of the analyzed maps, however, show violations of the expected sign rule.

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arXiv2017

Plane shearing waves of arbitrary form: exact solutions of the Navier-Stokes equations

We present exact solutions of the incompressible Navier-Stokes equations in a background linear shear flow. The method of construction is based on Kelvin's investigations into linearized disturbances in an unbounded Couette flow. We obtain explicit formulae for all three components of a Kelvin mode in terms of elementary functions. We then prove that Kelvin modes with parallel (though time-dependent) wave vectors can be superposed to construct the most general plane transverse shearing wave. An explicit solution is given, with any specified initial orientation, profile and polarization structure, with either unbounded or shear-periodic boundary conditions.

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arXiv2017

Enhancement of small-scale turbulent dynamo by large-scale shear

Small-scale dynamos are ubiquitous in a broad range of turbulent flows with large-scale shear, ranging from solar and galactic magnetism to accretion disks, cosmology and structure formation. Using high-resolution direct numerical simulations we show that in non-helically forced turbulence with zero mean magnetic field, large-scale shear supports small-scale dynamo action, i.e., the dynamo growth rate increases with shear and shear enhances or even produces turbulence, which, in turn, further increases the dynamo growth rate. When the production rates of turbulent kinetic energy due to shear and forcing are comparable, we find scalings for the growth rate $γ$ of the small-scale dynamo and the turbulent velocity $u_{\rm rms}$ with shear rate $S$ that are independent of the magnetic Prandtl number: $γ\propto |S|$ and $u_{\rm rms} \propto |S|^{2/3}$. For large fluid and magnetic Reynolds numbers, $γ$, normalized by its shear-free value, depends only on shear. Having compensated for shear-induced effects on turbulent velocity, we find that the normalized growth rate of the small-scale dynamo exhibits the scaling, $\widetildeγ\propto |S|^{2/3}$, arising solely from the induction equation for a given velocity field.

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arXiv2017

A new constraint on mean-field galactic dynamo theory

Appealing to an analytical result from mean-field theory, we show, using a generic galaxy model, that galactic dynamo action can be suppressed by small-scale magnetic fluctuations. This is caused by the magnetic analogue of the Rädler or $Ω\times J$ effect, where rotation-induced corrections to the mean-field turbulent transport result in what we interpret to be an effective reduction of the standard $α$ effect in the presence of small-scale magnetic fields.

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arXiv2017

Two-scale analysis of solar magnetic helicity

We develop a two-scale formalism to determine global magnetic helicity spectra in systems where the local magnetic helicity has opposite signs on both sides of the equator, giving rise to cancelation with conventional methods. We verify this approach using first a synthetic one-dimensional magnetic field and then two-dimensional slices from a three-dimensional alpha effect-type dynamo-generated magnetic field with forced turbulence of opposite helicity above and below the midplane of the domain. We then apply this formalism to global solar synoptic vector magnetograms. To improve the statistics, data from three consecutive Carrington rotations (2161--2163) are combined into a single map. We find that the spectral magnetic helicity representative of the northern hemisphere is negative at all wavenumbers and peaks at ~ 0.06 Mm^{-1} (scales around 100 Mm). There is no evidence of bihelical magnetic fields that are found in three-dimensional turbulence simulations of helicity-driven alpha effect-type dynamos.

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arXiv2016

High-wavenumber solar $f$-mode strengthening prior to active region formation

We report a systematic strengthening of the local solar surface or fundamental $f$-mode $1$-$2$ days prior to the emergence of an active region (AR) in the same (corotating) location. Except for a possibly related increase in the kurtosis of the magnetic field, no indication can be seen in the magnetograms at that time. Our study is motivated by earlier numerical findings of Singh et al. (2014) which showed that, in the presence of a nonuniform magnetic field that is concentrated a few scale heights below the surface, the $f$-mode fans out in the diagnostic $kω$ diagram at high wavenumbers. Here we explore this possibility using data from the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory and show for six isolated ARs, 11130, 11158, 11242, 11105, 11072, and 11768, that at large latitudinal wavenumbers (corresponding to horizontal scales of around 3000 km), the $f$-mode displays strengthening about two days prior to AR formation and thus provides a new precursor for AR formation. Furthermore, we study two ARs, 12051 and 11678, apart from a magnetically quiet patch lying next to AR~12529, to demonstrate the challenges in extracting such a precursor signal when a newly forming AR emerges in a patch that lies in close proximity of one or several already existing ARs which are expected to pollute neighboring patches. We then discuss plausible procedures for extracting precursor signals from regions with crowded environments. The idea that the $f$-mode is perturbed days before any visible magnetic activity occurs at the surface can be important in constraining dynamo models aimed at understanding the global magnetic activity of the Sun.

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arXiv2016

Moffatt drift driven large scale dynamo due to $α$ fluctuations with nonzero correlation times

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 $τ_α\neq 0$, 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; (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. Thus we show that a finite Moffatt drift can always facilitate large-scale dynamo action if sufficiently strong, even in case of weak $α$ fluctuations, and the maximum growth occurs at intermediate wavenumbers.

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arXiv2015

Dynamics of stellar wind in a Roche potential: implications for (i) outflows & periodicities relevant to astronomical masers, and (ii) generation of baroclinicity

We study the dynamics of stellar wind from one of the bodies in the binary system, where the other body interacts only gravitationally. We focus on following three issues: (i) we explore the origin of observed periodic variations in maser intensity; (ii) we address the nature of bipolar molecular outflows; and (iii) we show generation of baroclinicity in the same model setup. From direct numerical simulations and further numerical modelling, we find that the maser intensity along a given line of sight varies periodically due to periodic modulation of material density. This modulation period is of the order of the binary period. Another feature of this model is that the velocity structure of the flow remains unchanged with time in late stages of wind evolution. Therefore the location of the masing spot along the chosen sightline stays at the same spatial location, thus naturally explaining the observational fact. This also gives an appearance of bipolar nature in the standard position-velocity diagram, as has been observed in a number of molecular outflows. Remarkably, we also find the generation of baroclinicity in the flow around binary system, offering another site where the seed magnetic fields could possibly be generated due to the Biermann battery mechanisms, within galaxies.

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arXiv2015

Properties of $p$- and $f$-modes in hydromagnetic turbulence

With the ultimate aim of using the fundamental or $f$-mode to study helioseismic aspects of turbulence-generated magnetic flux concentrations, we use randomly forced hydromagnetic simulations of a piecewise isothermal layer in two dimensions with reflecting boundaries at top and bottom. We compute numerically diagnostic wavenumber-frequency diagrams of the vertical velocity at the interface between the denser gas below and the less dense gas above. For an Alfvén-to-sound speed ratio of about 0.1, a 5% frequency increase of the $f$-mode can be measured when $k_xH_{\rm p}=3$-$4$, where $k_x$ is the horizontal wavenumber and $H_{\rm p}$ is the pressure scale height at the surface. Since the solar radius is about 2000 times larger than $H_{\rm p}$, the corresponding spherical harmonic degree would be 6000-8000. For weaker fields, a $k_x$-dependent frequency decrease by the turbulent motions becomes dominant. For vertical magnetic fields, the frequency is enhanced for $k_xH_{\rm p}\approx4$, but decreased relative to its nonmagnetic value for $k_xH_{\rm p}\approx9$.

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arXiv2015

Numerical studies of dynamo action in a turbulent shear flow - I

We perform numerical experiments to study the shear dynamo problem where we look for the growth of large--scale magnetic field due to non--helical stirring at small scales in a background linear shear flow, in previously unexplored parameter regimes. We demonstrate the large--scale dynamo action in the limit when the fluid Reynolds number (${\rm Re}$) is below unity whereas the magnetic Reynolds number (${\rm Rm}$) is above unity; the exponential growth rate scales linearly with shear, which is consistent with earlier numerical works. The limit of low ${\rm Re}$ is particularly interesting, as seeing the dynamo action in this limit would provide enough motivation for further theoretical investigations, which may focus the attention to this analytically more tractable limit of ${\rm Re} < 1$ as compared to more formidable limit of ${\rm Re} > 1$. We also perform simulations in the regimes when, (i) both (${\rm Re}$, ${\rm Rm}$) $< 1$; (ii) ${\rm Re} > 1$ & ${\rm Rm} < 1$, and compute all components of the turbulent transport coefficients ($α_{ij}$ and $η_{ij}$) using the test--field method. A reasonably good agreement is seen between our results and the results of earlier analytical works (Sridhar & Singh 2010; Singh & Sridhar 2011) in the similar parameter regimes.

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arXiv2014

Large-scale dynamo action due to $α$ fluctuations in a linear shear flow

We present a model of large-scale dynamo action in a shear flow that has stochastic, zero-mean fluctuations of the $α$ parameter. This is based on a minimal extension of the Kraichnan-Moffatt model, to include a background linear shear and Galilean-invariant $α$-statistics. Using the first order smoothing approximation we derive a linear integro-differential equation for the large-scale magnetic field, which is non perturbative in the shearing rate $S\,$, and the $α$-correlation time $τ_α\,$. The white-noise case, $τ_α= 0\,$, is solved exactly, and it is concluded that the necessary condition for dynamo action is identical to the Kraichnan-Moffatt model without shear; this is because white-noise does not allow for memory effects, whereas shear needs time to act. To explore memory effects we reduce the integro-differential equation to a partial differential equation, valid for slowly varying fields when $τ_α$ is small but non zero. Seeking exponential modal solutions, we solve the modal dispersion relation and obtain an explicit expression for the growth rate as a function of the six independent parameters of the problem. A non zero $τ_α$ gives rise to new physical scales, and dynamo action is completely different from the white-noise case; e.g. even weak $α$ fluctuations can give rise to a dynamo. We argue that, at any wavenumber, both Moffatt drift and Shear always contribute to increasing the growth rate. Two examples are presented: (a) a Moffatt drift dynamo in the absence of shear; (b) a Shear dynamo in the absence of Moffatt drift.

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arXiv2014

Fanning out of the $f$-mode in presence of nonuniform magnetic fields

We show that in the presence of a harmonically varying magnetic field the fundamental or $f$-mode in a stratified layer is altered in such a way that it fans out in the diagnostic $kω$ diagram, but with mode power also within the fan. In our simulations, the surface is defined by a temperature and density jump in a piecewise isothermal layer. Unlike our previous work (Singh et al. 2014) where a uniform magnetic field was considered, we employ here a nonuniform magnetic field together with hydromagnetic turbulence at length scales much smaller than those of the magnetic fields. The expansion of the $f$-mode is stronger for fields confined to the layer below the surface. In some of those cases, the $kω$ diagram also reveals a new class of low frequency vertical stripes at multiples of twice the horizontal wavenumber of the background magnetic field. We argue that the study of the $f$-mode expansion might be a new and sensitive tool to determining subsurface magnetic fields with longitudinal periodicity.

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arXiv2014

Time variability of viscosity parameter in differentially rotating discs

We propose a mechanism to produce fluctuations in the viscosity parameter ($α$) in differetially rotating discs. We carried out a nonlinear analysis of a general accretion flow, where any perturbation on the background $α$ was treated as a passive/slave variable in the sense of dynamical system theory. We demonstrate a complete physical picture of growth, saturation and final degradation of the perturbation as a result of the nonlinear nature of coupled system of equations. The strong dependence of this fluctuation on the radial location in the accretion disc and the base angular momentum distribution is demonstrated. The growth of fluctuations is shown to have a time scale comparable to the radial drift time and hence the physical significance is discussed. The fluctuation is found to be a power law in time in the growing phase and we briefly discuss its statistical significance.

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arXiv2012

Binary systems: implications for outflows & periodicities relevant to masers

Bipolar molecular outflows have been observed and studied extensively in the past, but some recent observations of periodic variations in maser intensity pose new challenges. Even quasi-periodic maser flares have been observed and reported in the literature. Motivated by these data, we have tried to study situations in binary systems with specific attention to the two observed features, i.e., the bipolar flows and the variabilities in the maser intensity. We have studied the evolution of spherically symmetric wind from one of the bodies in the binary system, in the plane of the binary. Our approach includes the analytical study of rotating flows with numerical computation of streamlines of fluid particles using PLUTO code. We present the results of our findings assuming simple configurations, and discuss the implications.

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arXiv2011

Transport coefficients for the shear dynamo problem at small Reynolds numbers

We build on the formulation developed in Sridhar & Singh (JFM, 664, 265, 2010), and present a theory of the \emph{shear dynamo problem} for small magnetic and fluid Reynolds numbers, but for arbitrary values of the shear parameter. Specializing to the case of a mean magnetic field that is slowly varying in time, explicit expressions for the transport coefficients, $α_{il}$ and $η_{iml}$, are derived. We prove that, when the velocity field is non helical, the transport coefficient $α_{il}$ vanishes. We then consider forced, stochastic dynamics for the incompressible velocity field at low Reynolds number. An exact, explicit solution for the velocity field is derived, and the velocity spectrum tensor is calculated in terms of the Galilean--invariant forcing statistics. We consider forcing statistics that is non helical, isotropic and delta-correlated-in-time, and specialize to the case when the mean-field is a function only of the spatial coordinate $X_3$ and time $τ\,$; this reduction is necessary for comparison with the numerical experiments of Brandenburg, R{ä}dler, Rheinhardt & Käpylä (ApJ, 676, 740, 2008). Explicit expressions are derived for all four components of the magnetic diffusivity tensor, $η_{ij}(τ)\,$. These are used to prove that the shear-current effect cannot be responsible for dynamo action at small $\re$ and $\rem$, but for all values of the shear parameter.

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arXiv2010

The shear dynamo problem for small magnetic Reynolds numbers

We study large-scale dynamo action due to turbulence in the presence of a linear shear flow, in the low conductivity limit. Our treatment is nonperturbative in the shear strength and makes systematic use of both the shearing coordinate transformation and the Galilean invariance of the linear shear flow. The velocity fluctuations are assumed to have low magnetic Reynolds number (Rm) but could have arbitrary fluid Reynolds number. The magnetic fluctuations are determined to lowest order in Rm by explicit calculation of the resistive Green's function for the linear shear flow. The mean electromotive force is calculated and an integro-differential equation is derived for the time evolution of the mean magnetic field. In this equation, velocity fluctuations contribute to two different kinds of terms, the C and D terms, in which first and second spatial derivatives of the mean magnetic field, respectively, appear inside the spacetime integrals. The contribution of the D terms is such that the time evolution of the cross-shear components of the mean field do not depend on any other components excepting themselves. Therefore, to lowest order in Rm but to all orders in the shear strength, the D terms cannot give rise to a shear-current assisted dynamo effect. Casting the integro-differential equation in Fourier space, we show that the normal modes of the theory are a set of shearing waves, labelled by their sheared wavevectors. The integral kernels are expressed in terms of the velocity spectrum tensor, which is the fundamental quantity that needs to be specified to complete the integro-differential equation description of the time evolution of the mean magnetic field.

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