arXiv subjects

Nishant K. Singh

Publications and source records attributed to Nishant K. Singh.

At least 19 recordsLinked to original sources

arXiv2026

Turbulent Convection: Modal Equations and Energy Pathways

We present a framework for studying high Rayleigh number turbulent convection to better understand stellar and planetary convection zones. Utilizing the statistical symmetries of the fully developed turbulent state of Boussinesq convection, we identify relevant mean and fluctuating quantities. After validating these symmetry assumptions through numerical simulations, we formulate the governing equations. Vertical profiles of key physical quantities in the saturated turbulent state are explored in the simulations. To develop a modal theory, we use Fourier expansions, review linear theory, and use the Craya-Herring velocity decomposition. The modal equations we derive describe high Rayleigh-number turbulent convection dynamics self-consistently in terms of nonlinear interactions between three mode types: growing gravity modes, decaying gravity modes, and horizontal modes. Energy extracted by the growing modes from the superadiabatic background subsequently follows multiple pathways toward dissipation, enabled by the mode couplings. Among these, the traditionally dominant pathway is the turbulent cascade of the growing modes themselves. Reduced modal equations capture this pathway, precisely describing (i) mutual interactions between growing modes, and (ii) the excitation of decaying and horizontal modes, which are subordinate to the growing modes. Determining the relative efficiency of the pathways requires investigating their modal spectra using numerical simulations and kinetic models.

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arXiv2026

Effects of Dynamo-Generated Large-Scale Magnetic Fields on the Surface Gravity ($f$) Mode

By modelling the upper layers of the Sun in terms of a two-layer setup where a free-surface exists within the computational domain, we numerically study the interaction between the surface gravity, or the fundamental ($f$) mode, and the magnetic fields. Earlier such works were idealized in the sense that the static magnetic fields were imposed below the photosphere, i.e., the free-surface, to detect signatures of sub-surface magnetic fields and flows on the $f$-mode. In this work, we perform three-dimensional (3D) numerical simulations where the interior fluid below the photosphere is stirred helically at small scales, thus facilitating an $α^2$-dynamo. This allows us to investigate how these self-consistently generated large-scale magnetic fields influence the properties of the $f$-mode. We find that when the magnetic fields saturate near the equipartition values with the turbulent kinetic energy of the flow, the $f$-mode is significantly perturbed. Compared to the non-magnetic case, or the kinematic phase of the dynamo when fields are too weak, we note that the frequencies and the strengths of the $f$-mode are enhanced in presence of saturated magnetic fields, with these effects being larger at larger wavenumbers. This qualitatively confirms the earlier findings from observational and numerical works which reported the $f$-mode strengthening due to strong sub-surface magnetic fields.

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arXiv2025

The spectra of solar magnetic energy and helicity

Previous studies have used magnetic energy and helicity spectra, the latter computed using the two-scale method, to search for signatures of mean-field dynamos. In this study, we compare cotemporal HMI and SOLIS magnetograms to illustrate the instrument-dependence of even qualitative features of the energy and helicity spectra. Around the minimum between solar cycles 24 and 25, we find that the magnetic energy spectrum computed from HMI observations exhibits two distinct peaks. One of these peaks is only present near the cycle minimum, and corresponds to large-scale magnetic fields at high latitudes. Nevertheless, such magnetic fields are not present in contemporaneous synoptic vector magnetograms from SOLIS. Further, even when magnetograms from both the instruments are apodized, the helicity spectra calculated using the two-scale method disagree (on both the sign and the value of the fractional helicity). This suggests that currently available synoptic magnetograms are not reliable enough for such studies.

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arXiv2025

Rotational effects on the small-scale dynamo

Using direct numerical simulations of forced rotating turbulence, we study the effect of rotation on the growth rate and the saturation level of the small-scale dynamo. For slow rotation rates, increasing the rotation rate reduces both the growth rate and the saturation level. Once the rotation rate crosses a threshold, large-scale vortices are formed which enhance the growth rate and the saturation level. Below this threshold, the suppression of the small-scale dynamo with increasing rotation is explained by the fact that at scales close to, but smaller than, the forcing scale, rotating turbulence is one-dimensionalized, with the velocity component along the rotation axis being larger than the other two components. This is due to the rotational destabilization of vortices produced by the forcing function. While the rotational effect on the growth rate becomes small at high Re, the ratio of the steady-state magnetic to kinetic energies remains suppressed by up to 35% as compared to the non-rotating case.

physics.flu-dyn↗

arXiv2025

Turbulent transport in a non-Markovian velocity field

The commonly used quasilinear approximation allows one to calculate the turbulent transport coefficients for the mean of a passive scalar or a magnetic field in a given velocity field. Formally, the quasilinear approximation is exact when the correlation time of the velocity field is zero. We calculate the lowest-order corrections to the transport coefficients due to the correlation time being nonzero. For this, we use the Furutsu-Novikov theorem, which allows one to express the turbulent transport coefficients in a Gaussian random velocity field as a series in the correlation time. We find that the turbulent diffusivities of both the mean passive scalar and the mean magnetic field are suppressed. Nevertheless, contradicting a previous study, we show that the turbulent diffusivity of the mean magnetic field is smaller than that of the mean passive scalar. We also find corrections to the $α$ effect.

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arXiv2024

Reversals of toroidal magnetic field in local shearing box simulations of accretion disc with a hot corona

Presence of a hot corona above the accretion disc can have important consequences for the evolution of magnetic fields and the Shakura-Sunyaev (SS) viscosity parameter $α$ in such a strongly coupled system. In this work, we have performed three-dimensional magnetohydrodynamical shearing-box numerical simulations of accretion disc with a hot corona above the cool disc. Such a two-layer, piece-wise isothermal system is vertically stratified under linear gravity and initial conditions here include a strong azimuthal magnetic field with a ratio between the thermal and magnetic pressures being of order unity in the disc region. Instabilities in this magnetized system lead to the generation of turbulence, which, in turn, governs the further evolution of magnetic fields in a self-sustaining manner. Remarkably, the mean toroidal magnetic field undergoes a complete reversal in time by changing its sign, and it is predominantly confined within the disc. This is a rather unique class of evolution of the magnetic field which has not been reported earlier. Solutions of mean magnetic fields here are thus qualitatively different from the vertically migrating dynamo waves that are commonly seen in previous works which model a single layer of an isothermal gas. Effective $α$ is found to have values between 0.01 and 0.03. We have also made a comparison between models with Smagorinsky and explicit schemes for the kinematic viscosity ($ν$). In some cases with an explicit $ν$ we find a burst-like temporal behavior in $α$.

astro-ph.HE↗

arXiv2022

The small-scale dynamo in a multiphase supernova-driven medium

Magnetic fields grow quickly, even at early cosmological times, suggesting the action of a small-scale dynamo (SSD) in the interstellar medium (ISM) of galaxies. Many studies have focused on idealized, isotropic, homogeneous, turbulent driving of the SSD. Here we analyze more realistic simulations of supernova-driven turbulence to understand how it drives an SSD. We find that SSD growth rates are intermittently variable as a result of the evolving multiphase ISM structure. Rapid growth in the magnetic field typically occurs in hot gas, with the highest overall growth rates occurring when the fractional volume of hot gas is large. SSD growth rates correlate most strongly with vorticity and fluid Reynolds number, which also both correlate strongly with gas temperature. Rotational energy exceeds irrotational energy in all phases, but particularly in the hot phase while SSD growth is most rapid. Supernova (SN) rate does not significantly affect the ISM average kinetic energy density. Rather, higher temperatures associated with high SN rates tend to increase SSD growth rates. SSD saturates with total magnetic energy density around 5% of equipartition to kinetic energy density, increasing slightly with magnetic Prandtl number. While magnetic energy density in the hot gas can exceed that of the other phases when SSD grows most rapidly, it saturates below 5% of equipartition with kinetic energy in the hot gas, while in the cold gas it attains 100%. Fast, intermittent growth of the magnetic field appears to be a characteristic behavior of SN-driven, multiphase turbulence.

astro-ph.GA↗

arXiv2022

Understanding spectral states of sub-Keplerian accretion discs around compact objects as transitions between steady states

We present here a simple hydrodynamic model based on a sequence of steady states of the inner sub-Keplerian accretion disc to model its spectral states. Correlations between different hydrodynamic steady states are studied with a goal to understand the origin of, e.g., the aperiodic variabilities. The plausible source of corona/outflow close to the central compact object is shown to be a consequence of steady state transition in the underlying accretion flow. We envisage that this phenomenological model can give insight on the influence of environment on the inner sub-Keplerian accretion disc.

astro-ph.HE↗

arXiv2022

Turbulent Prandtl number from isotropically forced turbulence

Turbulent motions enhance the diffusion of large-scale flows and temperature gradients. Such diffusion is often parameterized by coefficients of turbulent viscosity ($ν_{\rm t}$) and turbulent thermal diffusivity ($χ_{\rm t}$) that are analogous to their microscopic counterparts. We compute the turbulent diffusion coefficients by imposing large-scale velocity and temperature gradients on a turbulent flow and measuring the response of the system. We also confirm our results using experiments where the imposed gradients are allowed to decay. To achieve this, we use weakly compressible three-dimensional hydrodynamic simulations of isotropically forced homogeneous turbulence. We find that the turbulent viscosity and thermal diffusion, as well as their ratio the turbulent Prandtl number, ${\rm Pr}_{\rm t} = ν_{\rm t}/χ_{\rm t}$, approach asymptotic values at sufficiently high Reynolds and Peclét numbers. We also do not find a significant dependence of ${\rm Pr}_{\rm t}$ on the microscopic Prandtl number ${\rm Pr} = ν/χ$. These findings are in stark contrast to results from the $k-ε$ model which suggests that ${\rm Pr}_{\rm t}$ increases monotonically with decreasing ${\rm Pr}$. The current results are relevant for the ongoing debate of, for example, the nature of the turbulent flows in the very low ${\rm Pr}$ regimes of stellar convection zones.

physics.flu-dyn↗

arXiv2022

Shell model for stratified convection: implications for the solar convective conundrum

We extend the notion of a shell model to stratified systems, and propose one that represents stratified, nonmagnetic, nonrotating convection at low Mach number. Motivated by profiles of background stratification that support convection in stars such as the Sun, we study numerical solutions corresponding to a highly unstable layer above a mildly unstable layer. We find that at low Prandtl number, convective amplitudes decrease with depth in the lower layer. This suggests that the suppression of convection in the deeper layers of the Sun's convection zone (the convective conundrum) can be addressed without necessarily appealing to rotation or magnetic fields.

astro-ph.SR↗

arXiv2021

Mean field dynamo action in shearing flows. II: fluctuating kinetic helicity with zero mean

Here we explore the role of temporal fluctuations in kinetic helicity on the generation of large-scale magnetic fields in presence of a background linear shear flow. Key techniques involved here are same as in our earlier work \citep[][hereafter paper~I]{JS20}, where we have used the renovating flow based model with shearing waves. Both, the velocity and the helicity fields, are treated as stochastic variables with finite correlation times, $τ$ and $τ_h$, respectively. Growing solutions are obtained when $τ_h > τ$, even when this time-scale separation, characterised by $m=τ_h/τ$, remains below the threshold for causing the turbulent diffusion to turn negative. In regimes when turbulent diffusion remains positive, and $τ$ is on the order of eddy turnover time $T$, the axisymmetric modes display non-monotonic behaviour with shear rate $S$: both, the growth rate $γ$ and the wavenumber $k_\ast$ corresponding to the fastest growing mode, first increase, reach a maximum and then decrease with $|S|$, with $k_\ast$ being always smaller than eddy-wavenumber, thus boosting growth of magnetic fields at large length scales. The cycle period $P_{\rm cyc}$ of growing dynamo wave is inversely proportional to $|S|$ at small shear, exactly as in the fixed kinetic helicity case of paper~I. This dependence becomes shallower at larger shear. Interestingly enough, various curves corresponding to different choices of $m$ collapse on top of each other in a plot of $m P_{\rm cyc}$ with $|S|$.

physics.flu-dyn↗

arXiv2021

Small-Scale Dynamo in Supernova-Driven Interstellar Turbulence

Magnetic fields grow quickly even at early cosmological times, suggesting the action of a small-scale dynamo (SSD) in the interstellar medium of galaxies. Many studies have focused on idealized turbulent driving of the SSD. Here we simulate more realistic supernova-driven turbulence to determine whether it can drive an SSD. Magnetic field growth occurring in our models appears inconsistent with simple tangling of magnetic fields, but consistent with SSD action, reproducing and confirming models by Balsara et al. (2004) that did not include physical resistivity $η$. We vary $η$, as well as the numerical resolution and supernova rate, $\dotσ$, to delineate the regime in which an SSD occurs. For a given $\dotσ$ we find convergence for SSD growth rate with resolution of a parsec. For $\dotσ\simeq\dotσ_{\rm sn}$, with $\dotσ_{\rm sn}$ the solar neighbourhood rate, the critical resistivity below which an SSD occurs is $0.005>η_{\rm crit}>0.001\,\rm kpc^{-1}\,\rm km s^{-1}$, and this increases with the supernova rate. Across the modelled range of 0.5--4 pc resolution we find that for $η<η_{\rm crit}$, the SSD saturates at about 5% of kinetic energy equipartition, independent of growth rate. In the range $0.2\dotσ_{\rm sn}\leq \dotσ\leq8\dotσ_{\rm sn}$ growth rate increases with $\dotσ$. SSDs in the supernova-driven interstellar medium commonly exhibit erratic growth.

astro-ph.GA↗

arXiv2021

On the existence of shear-current effects in magnetized burgulence

The possibility of explaining shear flow dynamos by a magnetic shear-current (MSC) effect is examined via numerical simulations. Our primary diagnostics is the determination of the turbulent magnetic diffusivity tensor $\boldsymbolη$. In our setup, a negative sign of its component $η_{yx}$ is necessary for coherent dynamo action by the SC effect. To be able to measure turbulent transport coefficients from systems with magnetic background turbulence, we present an extension of the test-field method (TFM), applicable to our setup where the pressure gradient is dropped from the momentum equation: the nonlinear TFM (NLTFM). Our momentum equation is related to Burgers' equation and the resulting flows are referred to as magnetized burgulence. We use both stochastic kinetic and magnetic forcings to mimic cases without and with simultaneous small-scale dynamo action (SSD). When we force only kinetically, negative $η_{yx}$ are obtained with exponential growth in both the radial and azimuthal mean magnetic field components. Using isotropic magnetic forcing, the field growth is no longer exponential, while NLTFM yields positive $η_{yx}$. By employing an alternative forcing from which wavevectors having small components are removed, the exponential growth is recovered, but the NLTFM results do not change significantly. Analyzing the dynamo excitation conditions for the coherent SC and incoherent $α$ and SC effects shows that the incoherent effects are the main drivers of the dynamo in the majority of cases. We find no evidence for MSC-effect-driven dynamos in our simulations.

physics.flu-dyn↗

arXiv2020

Mean field dynamo action in shear flows. I: fixed kinetic helicity

We study mean-field dynamo action in a background linear shear flow by employing pulsed renewing flows with fixed kinetic helicity and nonzero correlation time ($τ$). We use plane shearing waves in terms of time-dependent exact solutions to the Navier-Stokes equation as derived by Singh \& Sridhar (2017). This allows us to self-consistently include the anisotropic effects of shear on the stochastic flow. We determine the average response tensor governing the evolution of mean magnetic field, and study the properties of its eigenvalues which yield the growth rate ($γ$) and the cycle period ($P_{\rm cyc}$) of the mean magnetic field. Non-axisymmetric modes of the mean magnetic field decay as $t \to \infty$ and hence are deemed unimportant for mean-field dynamo. Both, $γ$ and the wavenumber corresponding to the fastest growing axisymmetric mode vary non-monotonically with shear rate $S$ when $τ$ is comparable to the eddy turnover time $T$, in which case, we also find quenching of dynamo when shear becomes too strong. When $τ/T\sim{\cal O}(1)$, the cycle period ($P_{\rm cyc}$) of growing dynamo wave scales with shear as $P_{\rm cyc} \propto |S|^{-1}$ at small shear, and it becomes nearly independent of shear as shear becomes too strong.This asymptotic behaviour at weak and strong shear has implications for magnetic activity cycles of stars in recent observations. Our study thus essentially generalizes the standard $αΩ$ (or $α^2Ω$) dynamo as also the $α$ effect is affected by shear and the modelled random flow has a finite memory.

astro-ph.SR↗

arXiv2019

$f$-mode strengthening from a localized bipolar subsurface magnetic field

Recent numerical work in helioseismology has shown that a periodically varying subsurface magnetic field leads to a fanning of the $f$-mode, which emerges from the density jump at the surface. In an attempt to model a more realistic situation, we now modulate this periodic variation with an envelope, giving thus more emphasis on localized bipolar magnetic structures in the middle of the domain. Some notable findings are: (i) compared to the purely hydrodynamic case, the strength of the $f$-mode is significantly larger at high horizontal wavenumbers $k$, but the fanning is weaker for the localized subsurface magnetic field concentrations investigated here than the periodic ones studied earlier; (ii) when the strength of the magnetic field is enhanced at a fixed depth below the surface, the fanning of the $f$-mode in the $kω$ diagram increases proportionally in such a way that the normalized $f$-mode strengths remain nearly the same in different such cases; (iii) the unstable Bloch modes reported previously in case of harmonically varying magnetic fields are now completely absent when more realistic localized magnetic field concentrations are imposed beneath the surface, thus suggesting that the Bloch modes are unlikely to be supported during most phases of the solar cycle; (iv) the $f$-mode strength appears to depend also on the depth of magnetic field concentrations such that it shows a relative decrement when the maximum of the magnetic field is moved to a deeper layer. We argue that detections of $f$-mode perturbations such as those being explored here could be effective tracers of solar magnetic fields below the photosphere before these are directly detectable as visible manifestations in terms of active regions or sunspots.

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arXiv2018

Magnetic Helicity Reversal in the Corona at Small Plasma Beta

Solar and stellar dynamos shed small-scale and large-scale magnetic helicity of opposite signs. However, solar wind observations and simulations have shown that some distance above the dynamo both the small-scale and large-scale magnetic helicities have reversed signs. With realistic simulations of the solar corona above an active region now being available, we have access to the magnetic field and current density along coronal loops. We show that a sign reversal in the horizontal averages of the magnetic helicity occurs when the local maximum of the plasma beta drops below unity and the field becomes nearly fully force free. Hence, this reversal is expected to occur well within the solar corona and would not directly be accessible to in-situ measurements with the Parker Solar Probe or SolarOrbiter. We also show that the reversal is associated with subtle changes in the relative dominance of structures with positive and negative magnetic helicity.

astro-ph.SR↗

arXiv2018

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

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 $α$ parameter of dynamo theory. We derive a linear integro-differential equation for the evolution of large-scale magnetic field, using the first-order smoothing approximation and the Galilean invariance of the $α$-statistics. This enables construction of a model that is non-perturbative in the shearing rate $S$ and the $α$-correlation time $τ_α$. After a brief review of the salient features of the exactly solvable white-noise limit, we consider the case of small but non-zero $τ_α$. 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 $α$-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 $γ\propto |S|$.

astro-ph.GA↗

arXiv2018

E and B polarizations from inhomogeneous and solar surface turbulence

Gradient- and curl-type or E- and B-type polarizations have been routinely analyzed to study the physics contributing to the cosmic microwave background polarization and galactic foregrounds. They characterize the parity-even and parity-odd properties of the underlying physical mechanisms, for example hydromagnetic turbulence in the case of dust polarization. Here we study spectral correlation functions characterizing the parity-even and parity-odd parts of linear polarization for homogeneous and inhomogeneous turbulence to show that only the inhomogeneous helical case can give rise to a parity-odd polarization signal. We also study nonhelical turbulence and suggest that a strong nonvanishing (here negative) skewness of the E polarization is responsible for an enhanced ratio of the EE to the BB (quadratic) correlation in both helical and nonhelical cases. This could explain the enhanced EE/BB ratio observed recently for dust polarization. We close with a preliminary assessment of using linear polarization of the Sun to characterize its helical turbulence without being subjected to the pi ambiguity that magnetic inversion techniques have to address.

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