arXiv subjects

B. Tripathi

Publications and source records attributed to B. Tripathi.

9 recordsLinked to original sources

arXiv2026

Large-Scale Dynamos Driven by Shear-Flow-Induced Jets

At every scale they occupy, magnetic fields affect various phenomena, including star formation, cosmic ray transport, charged particle acceleration, space weather, transport in planetary atmospheres, and laboratory plasmas. These fields are often generated and sustained by turbulent flows in a process called the dynamo. In 1955, E. N. Parker parameterized the effects of small-scale turbulence to propose a mean-field dynamo theory. The widely used theory reproduces observed large-scale fields but suffers from difficulty in tuning parameters as they are not justified from first principles: Studies of turbulent flows show tangled magnetic fields, which are folded and fragmented into small-scale structures due to shear-flow straining. Here, considering a shear flow that is unstable and driven, we develop analytic theory and perform three-dimensional (3D), advanced computer simulations of turbulence with up to 4096 x 4096 x 8192 grid points, showing ab initio generation of quasi-periodic, large-scale magnetic fields. The generation occurs via the mean-vorticity effect---an additional mean-field dynamo process postulated in 1990. Crucial to this dynamo is the prior generation of large-scale 3D jets, robustly produced as topologically protected and exact nonlinear solutions of the magnetohydrodynamic equations. The jet-driven dynamo applies to shear-driven laboratory and astrophysical systems. These include binary neutron star mergers, where the reported dynamo likely operates on microsecond timescales to produce in milliseconds some of the strongest magnetic fields in the Universe, providing signals for multimessenger astronomy.

astro-ph.SR↗

arXiv2024

Anisotropic Magnetized Asteroseismic Waves

We solve for waves in a polytropic, stratified plasmas with a spatially varying background magnetic field that points along a horizontal $x$-direction, and with gravity that is directed along the vertical $z$-direction. Force balance determines the magnitude of the background magnetic field, $B_0^2 \sim z^{n+1}$, where $n$ is the polytropic index. Using numerical and asymptotic methods, we deduce an explicit dispersion relation for fast pressure-driven waves: $Ω^2 \sim K\left(2m+n\right) \left[1 + (1/M_\mathrm{A})^2 (4-2γ+\cos^2θ-3\cos^4θ)/4 \right]$. Here, $Ω$ is the frequency, $K$ the wavenumber, $θ$ the angle the wave-vector makes with the background magnetic field, $M_\mathrm{A}$ the Alfvénic Mach number, and $m$ an integer representing the eigenstate. We discuss roles of such an explicit formula in asteroseismology.

astro-ph.SR↗

arXiv2024

Predicting the Slowing of Stellar Differential Rotation by Instability-Driven Turbulence

Differentially rotating stars and planets transport angular momentum internally due to turbulence at rates that have long been a challenge to predict reliably. We develop a self-consistent saturation theory, using a statistical closure approximation, for hydrodynamic turbulence driven by the axisymmetric Goldreich--Schubert--Fricke (GSF) instability at the stellar equator with radial differential rotation. This instability arises when fast thermal diffusion eliminates the stabilizing effects of buoyancy forces in a system where a stabilizing entropy gradient dominates over the destabilizing angular momentum gradient. Our turbulence closure invokes a dominant three-wave coupling between pairs of linearly unstable eigenmodes and a near-zero frequency, viscously damped eigenmode that features latitudinal jets. We derive turbulent transport rates of momentum and heat, and provide them in analytic forms. Such formulae, free of tunable model parameters, are tested against direct numerical simulations; the comparison shows good agreement. They improve upon prior quasi-linear or ``parasitic saturation" models containing a free parameter. Given model correspondences, we also extend this theory to heat and compositional transport for axisymmetric thermohaline instability-driven turbulence in certain regimes.

astro-ph.SR↗

arXiv2023

Three-Dimensional Shear-Flow Instability Saturation via Stable Modes

Turbulence in three dimensions ($3$D) supports vortex stretching that has long been known to accomplish energy transfer to small scales. Moreover, net energy transfer from large-scale, forced, unstable flow-gradients to smaller scales is achieved by gradient-flattening instability. Despite such enforcement of energy transfer to small scales, it is shown here not only that the shear-flow-instability-supplied $3$D-fluctuation energy is largely inverse-transferred from the fluctuation to the mean-flow gradient, but that such inverse transfer is more efficient for turbulent fluctuations in $3$D than in two dimensions ($2$D). The transfer is due to linearly stable eigenmodes that are excited nonlinearly. The stable modes, thus, reduce both the nonlinear energy cascade to small scales and the viscous dissipation rate. The vortex-tube stretching is also suppressed. Up-gradient momentum transport by the stable modes counters the instability-driven down-gradient transport, which also is more effective in $3$D than in $2$D ($\mathrm{\approx} 70\% \mathrm{\,\, vs.\,\,}\mathrm{\approx} 50\%$). From unstable modes, these stable modes nonlinearly receive energy via zero-frequency fluctuations that vary only in the direction orthogonal to the plane of $2$D shear flow. The more widely occurring $3$D turbulence is thus inherently different from the commonly studied $2$D turbulence, despite both saturating via stable modes.

physics.flu-dyn↗

arXiv2023

Nonlinear mode coupling and energetics of driven magnetized shear-flow turbulence

To comprehensively understand saturation of two-dimensional ($2$D) magnetized Kelvin-Helmholtz-instability-driven turbulence, energy transfer analysis is extended from the traditional interaction between scales to include eigenmode interactions, by using the nonlinear couplings of linear eigenmodes of the ideal instability. While both kinetic and magnetic energies cascade to small scales, a significant fraction of turbulent energy deposited by unstable modes in the fluctuation spectrum is shown to be re-routed to the conjugate-stable modes at the instability scale. They remove energy from the forward cascade at its inception. The remaining cascading energy flux is shown to attenuate exponentially at a small scale, dictated by the large-scale stable modes. Guided by a widely used instability-saturation assumption, a general quasilinear model of instability is tested by retaining all nonlinear interactions except those that couple to the large-scale stable modes. These complex interactions are analytically removed from the magnetohydrodynamic equations using a novel technique. Observations are: an explosive large-scale vortex separation instead of the well-known merger of $2$D, a dramatic enhancement in turbulence level and spectral energy fluxes, and a reduced small-scale dissipation length-scale. These show critical role of the stable modes in instability saturation. Possible reduced-order turbulence models are proposed for fusion and astrophysical plasmas, based on eigenmode-expanded energy transfer analyses.

physics.plasm-ph↗

arXiv2022

Near-cancellation of up- and down-gradient momentum transport in forced magnetized shear-flow turbulence

Visco-resistive magnetohydrodynamic turbulence, driven by a two-dimensional unstable shear layer that is maintained by an imposed body force, is examined by decomposing it into dissipationless linear eigenmodes of the initial profiles. The down-gradient momentum flux, as expected, originates from the large-scale instability. However, continual up-gradient momentum transport by large-scale linearly stable but nonlinearly excited eigenmodes is identified, and found to nearly cancel the down-gradient transport by unstable modes. The stable modes effectuate this by depleting the large-scale turbulent fluctuations via energy transfer to the mean flow. This establishes a physical mechanism underlying the long-known observation that coherent vortices formed from nonlinear saturation of the instability reduce turbulent transport and fluctuations, as such vortices are composed of both the stable and unstable modes, which are nearly equal in their amplitudes. The impact of magnetic fields on the nonlinearly excited stable modes is then quantified. Even when imposing a strong magnetic field that almost completely suppresses the instability, the up-gradient transport by the stable modes is at least two-thirds of the down-gradient transport by the unstable modes, whereas for weaker fields, this fraction reaches up to $98\%$. These effects are persistent with variations in magnetic Prandtl number and forcing strength. Finally, continuum modes are shown to be energetically less important, but essential for capturing the magnetic fluctuations and Maxwell stress. A simple analytical scaling law is derived for their saturated turbulent amplitudes. It predicts the fall-off rate as the inverse of the Fourier wavenumber, a property which is confirmed in numerical simulations.

physics.flu-dyn↗

arXiv2022

Exact analytical solutions in inhomogeneous magnetic fields for linear asteroseismic waves

We solve for waves in an isothermal, stratified medium with a magnetic field that points along a direction perpendicular to that of gravity and varies exponentially in the direction of gravity. We find exact analytical solutions for two different cases: (a) waves propagating along the direction of the magnetic field and (b) waves propagating along the direction of the gravity. In each case, we find solutions in terms of either the hypergeometric functions or their confluent cousins. We solve the resultant transcendental dispersion relation numerically. The changes in the eigenfrequencies due to a spatially inhomogeneous Alfvén wave speed are significant -- there are more oscillations or leaking of nodes of the eigenfunctions in regions of lower Alfvén speed and wave reflection from regions of larger Alfvén speed. Such changes in the dispersion relation and the mode structures may allow detection of magnetic fields buried in the stellar interior.

astro-ph.SR↗

arXiv2022

Mechanism for Sequestering Magnetic Energy at Large Scales in Shear-Flow Turbulence

Straining of magnetic fields by large-scale shear flow, generally assumed to lead to intensification and generation of small scales, is re-examined in light of the persistent observation of large-scale magnetic fields in astrophysics. It is shown that, in magnetohydrodynamic turbulence, unstable shear flows have the unexpected effect of sequestering magnetic energy at large scales, due to counteracting straining motion of nonlinearly excited large-scale stable eigenmodes. This effect is quantified via dissipation rates, energy transfer rates, and visualizations of magnetic field evolution by artificially removing the stable modes. These analyses show that predictions based upon physics of the linear instability alone miss substantial dynamics, including those of magnetic fluctuations.

physics.plasm-ph↗

arXiv2022

Resummed Wentzel-Kramers-Brillouin Series: Quantization and Physical Interpretation

The Wentzel-Kramers-Brillouin (WKB) perturbative series, a widely used technique for solving linear waves, is typically divergent and at best, asymptotic, thus impeding predictions beyond the first few leading-order effects. Here, we report a closed-form formula that exactly resums the perturbative WKB series to all-orders for two turning point problem. The formula is elegantly interpreted as the action evaluated using the product of spatially-varying wavenumber and a coefficient related to the wave transmissivity; unit transmissivity yields the Bohr-Sommerfeld quantization.

quant-ph↗