arXiv subjects

Arijit Halder

Publications and source records attributed to Arijit Halder.

7 recordsLinked to original sources

arXiv2026

An integration-free method for calculating curl and divergence in space plasmas using multi-spacecraft data

The knowledge of local spatial gradients (curl, divergence etc.) is crucial to examine the three-dimensional variation of flow fields including velocity and magnetic fields in space plasmas like the solar wind. Here we propose a simple method to calculate the same using the in-situ data of multi-spacecraft systems. Unlike the popular Curlometer method which depends on the vector integration theorems, our integration-free method is based on the construction of a local orthonormal coordinate system and the associated finite difference approximations. The Curlometer is applicable to a four spacecraft system arranged in a tetrahedron and yields a single volume-averaged estimate of the curl. Using our proposed method over 107 intervals of MMS (NASA) data, on the other hand, we successfully calculate the spatial derivatives at the position of each spacecraft of the tetrahedron and a three-spacecraft (non-collinear) subset of the same. The average value of all the curls calculated for a given tetrahedron shows an excellent agreement (correlation coeffcient ~ 0:99) with the curls calculated using Curlometer formula. The quality of the calculated curl (using our method) is found to improve if the spacecraft configuration approaches a regular tetrahedron. The current framework facilitates investigation of turbulent heating rates and the exploration of local flow features like Beltramization, existence of current sheets, etc., in present and future multi-spacecraft mission, including those involving more than four spacecraft.

physics.space-ph↗

arXiv2025

Universal energy cascade and relaxation in three-dimensional inertial electron magnetohydrodynamic turbulence

Electron magnetohydrodynamics (EMHD) provides a realistic model for electron-scale heating and acceleration in weakly collisional space plasmas. A divergence-free Banerjee-Galtier type (Banerjee and Galtier, JoPA, 2017) exact relation is derived for three-dimensional homogeneous and not necessarily isotropic EMHD turbulence. By explicit calculation, it has been shown that the energy cascade is not affected by the presence of a uniform background magnetic field Bo. Using direct numerical simulations, a Kolmogorov-like energy cascade with a constant flux rate is observed across the electron inertial scale $d_e$. However, as expected, for length scales greater than $d_e$, a magnetic power spectra of $k^{-7/3}$ is obtained whereas for scales smaller than $d_e$, a $k^{-5/3}$ spectra is obtained. Similar universal cascade rate is also calculated from the scale-by-scale budget in Fourier space and is found to be equal to the one calculated using the exact law in real space. Finally, quenching the turbulence drive, the relaxation of a fully-developed EMHD turbulence is studied using the recently proposed principle of vanishing nonlinear transfers (Banerjee, Halder and Pan, PRE(L), 2023) which convincingly shows the existence of a pressure-balanced relaxed state.

physics.plasm-ph↗

arXiv2025

On local and non-local energy transfers in Hall magnetohydrodynamic turbulence

A systematic study of inertial energy cascade in three-dimensional incompressible Hall magnetohydrodynamic turbulence is conducted to probe into the locality of energy conserving triads and the subsequent transfers. Based on the nature of triadic conservations, the energy transfer due to the Hall term is further decomposed into two channels BB and JB corresponding to the terms $d_i ({\bf j}\cdot\nabla){\bf b}$ and $ d_i ({\bf b}\cdot\nabla){\bf j}$, respectively (Halder et al., 2023; Banerjee and Halder,2024). Here ${\bf b}$ and ${\bf j}$ represent the magnetic field and the current in Alfv\'en units, whereas $d_i$ is the ion inertial scale. Using direct numerical simulations, we calculate the shell-to-shell energy transfer rates corresponding to both the channels, and convincingly show each of them to comprise a combination of local and non-local energy transfers. A local inverse transfer is consistently observed at all scales of the channel BB whereas for the channel JB, the local exchange of energy is associated with a gradual increase in strength as the scale is decreased, together with a transition from inverse to direct transfer across the Hall wavenumber, characterized by the ion inertial length $d_i$. Calculating mediator-specific transfer rates, we also conclude that a considerable amount of the local energy transfer is mediated by the non-local triads, especially at small scales of the channel JB. The observed results can be explained using the power-law behaviour of the modal fields. The present study captures the intricate dynamics of energy transfer due to the Hall term and hence can be used to develop more insightful analytical models (shell models, for example) for Hall magnetohydrodynamic cascade. The framework can be extended to segregate the local and the nonlocal heating in various turbulent flows including ferrofluids, binary fluids, etc.

physics.plasm-ph↗

arXiv2023

Fundamental units of triadic interactions in Hall magnetohydrodynamic turbulence: how far can we go?

A systematic study has been carried out to obtain the fundamental units of triad interaction in Hall magnetohydrodynamic turbulence. Instead of finding the elementary building blocks of non-unique mode-to-mode transfer rates, we have investigated the fundamental units for uniquely defined combined transfers and convincingly showed that the mode-to-mode transfers can act as a practical base element for the same. In addition to the conventional field-specific mode-to-mode transfers, here we have introduced the idea of mode-specific transfers which is found to be important for the turbulent cascade and the turbulent relaxed states. Whereas the Hall transfer is found to associate mode-to-mode transfers for mode-specific interactions (with a three-member basis), it presents a mixture of typical mode-to-mode (also with a three-member basis) and non mode-to-mode (with a five-member basis) transfers for the field-specific interactions. The non mode-to-mode transfers are shown to satisfy the triad conservation differently from the mode-to-mode transfers. However, they also possess an inherent non-uniqueness and hence cannot be determined unambiguously unlike the combined transfer rates.

physics.flu-dyn↗

arXiv2023

Universal relaxation of turbulent binary fluids

Upon quenching the forcing, a turbulent system tends to attain the state of stable equilibrium through the process of turbulent relaxation. Such relaxation in binary fluids is of surmount interest for both fundamental science understanding and industrial applications. A systematic investigation of the same has been carried out, for the first time, using direct numerical simulations of Cahn-Hilliard-Navier-Stokes equations. With the help of a thorough scanning, the bulk of each fluid and its interface are found to relax in a different way. However, using the principle of vanishing nonlinear transfer, we propose a convincing, universal pathway of obtaining the turbulent relaxed states for both the bulk and the interface which attain a relaxed state when the turbulent cascades of the inviscid invariants are suppressed. Interestingly, the relaxation of the bulk turns up to be subtly different from the turbulent relaxation of a single hydrodynamic fluid and the interface relaxation is found to follow a Helmholtz-like pressure-balanced condition.

physics.flu-dyn↗

arXiv2023

On the contribution of the Hall term in small-scale magnetohydrodynamic dynamo

A detailed study of small-scale Hall magnetohydrodynamic dynamo has been performed both analytically and numerically. Assuming the magnetic field and the current to be separate fields, the contribution of the Hall term has been decomposed into two parts and their individual contributions have been studied separately. Calculating the scale-separated transfer rates described in Dar \textit{et. al.} (Physica D, 157 (207), 2001), it is found that the small-scale current fields are the primary contributors in sustaining large scale magnetic fields. Furthermore, the nature of the scale-to-scale fluxes are found to be globally intact with the ion inertial scale.

physics.flu-dyn↗

arXiv2022

Universal turbulent relaxation of fluids and plasmas by the principle of vanishing nonlinear transfers

A seventy year old problem of fluid and plasma relaxation has been revisited. A new principle of vanishing nonlinear transfer has been proposed to develop a unified theory of turbulent relaxation of neutral fluids and plasmas. Unlike previous studies, the new principle enables us to find the relaxed states unambiguously without going through any variational principle. The general relaxed states obtained herein are found to support naturally a pressure gradient which is consistent with several numerical studies. Relaxed states are reduced to Beltrami type aligned states where the pressure gradient is negligibly small.

physics.plasm-ph↗