arXiv subjects

Supratik Banerjee

Publications and source records attributed to Supratik Banerjee.

At least 19 recordsLinked to original sources

arXiv2026

Determination of turbulent heating rate and relaxed states in finite Larmor radius magnetohydrodynamic turbulence with helicity barrier

Finite Larmor radius magnetohydrodynamics (FLR-MHD) provides a hybrid model of plasma that explains how turbulent energy cascade extends to sufficiently small parallel length scales, potentially leading to perpendicular heating of the ions in the solar corona and the solar wind. In this work, we derive exact laws for the cascades of energy and generalized helicity in fully developed FLR-MHD turbulence. In large and small scale limits, we obtain the exact laws for reduced MHD and electron reduced MHD turbulence respectively. Unlike ordinary or reduced MHD turbulence, a global stationary state is shown to be absent in the case of a strong imbalance between the Elsasser variables. This is due to the so-called helicity barrier, which leads to two separate stationary energy cascades with different cascade rates. Our derived exact laws enable us to calculate these two cascade rates and therefore their difference, which effectively provides the heating rate of the ions. In addition, we also derive alternative Banerjee-Galtier forms for the exact laws and hence obtain the relaxed states of FLR-MHD turbulence using the framework of recently proposed principle of vanishing nonlinear transfer. The relaxed states show alignment between the velocity and magnetic field fluctuations. However, due to strong anisotropy, no Beltrami alignment is possible for velocity and magnetic fields. Similarly to the exact laws, the relaxed states of reduced and electron reduced MHD emerge in the large and small scale limits, respectively.

physics.plasm-ph↗

arXiv2026

Exact scaling laws in isotropic binary fluid turbulence

Binary fluid turbulence distinguishes itself from ordinary fluid turbulence by virtue of interfacial dynamics. Whether Kolmogorov-like scaling laws also exist for binary fluid turbulence is a fundamental question to explore. Starting from tensor formalism \`a la von K\'arm\'an and Howarth, here we derive exact scaling laws for isotropic Cahn-Hilliard-Navier-Stokes (CHNS) turbulence both in terms of two point correlators and increments. In particular, we derive the CHNS analogs for $1/3$, $4/3$, $2/15$ and $4/5$ laws known for isotropic hydrodynamic turbulence and show that the new scaling laws contain contributions both from the bulk flow and interface. The $2/15$ and $4/5$ laws of CHNS turbulence are found to be expressed purely in terms of two-point correlators and structure functions and their derivatives, respectively. However, unlike their hydrodynamic counterparts, these relations involve additional contributions from non-longitudinal directions. By means of direct numerical simulations with up to $1024^3$ grid points, all the derived exact laws are numerically verified and the scale dependence of the cascade rates obtained from different exact laws are thoroughly compared. As one moves from the homogeneous (but not necessarily isotropic) divergence form to the isotropic $4/5$ form, the inertial range is found to shift towards larger scales with a comparatively flatter cascade rate profile as a result of successive integrations over the small scales.

physics.flu-dyn↗

arXiv2026

Turbulent Properties of Interplanetary Coronal Mass Ejections Observed by Solar Orbiter in the Inner Heliosphere

We investigate the turbulent properties of 12 interplanetary coronal mass ejections (ICMEs) observed by Solar Orbiter between 0.29 and 1.0 AU. We analyze fluctuation power, spectral indices, break scales, and correlations between magnetic and velocity fluctuations (v-b) to quantify differences between ICME substructures (sheath and magnetic ejecta (ME)) and the surrounding solar wind. The ICME sheath is consistently the most turbulent region at all distances. In the solar wind, Alfv\'enicity influences inertial-range scaling, resulting in either single power laws near f^-3/2 or f^-5/3, or a coexistence of both, whereas ICME substructures consistently exhibit Kolmogorov-like f^-5/3 spectra. Alfv\'enicity is reduced within ICMEs, particularly in the ejecta, indicating more balanced Alfv\'enic fluctuations than in the solar wind. Spectral breaks shift to higher frequencies in ICME regions, with average break frequencies of 0.53 +/- 0.35 Hz (solar wind), 1.87 +/- 1.46 Hz (sheath), and 1.46 +/- 1.28 Hz (ME), reflecting differences in underlying microphysical scales. Our findings highlight distinct turbulence regimes in ICMEs compared to the solar wind and support the use of fluctuation power, spectral breaks, and v-b correlations as effective diagnostics for identifying ICME boundaries.

astro-ph.SR↗

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↗

arXiv2025

Universal relations between parallel and perpendicular spectral power law exponents in non-axisymmetric magnetohydrodynamic turbulence

Following a general heuristic approach, algebraic constraints are established between the parallel and perpendicular power-law exponents of non-axisymmetric, highly aligned magnetohydrodynamic turbulence, both with and without strong imbalance between the Els\"asser variables. Such relations are universal both for the regimes of weak and strong turbulence and are useful to predict the corresponding turbulent power spectra. For scale-dependent alignment, a Boldyrev-type $k^{-3/2}$ perpendicular spectrum emerges transverse to the direction of alignment whereas a $k^{-5/3}$ spectrum is obtained for the same if the alignment becomes scale-independent. However, regardless of the nature of alignment, our analysis consistently yields a $k_{\parallel}^{-2}$ spectrum - commonly observed in both numerical simulations and in-situ data of solar wind. In appropriate limit, previously obtained algebraic relations and power spectra for axisymmetric MHD turbulence (Galtier, Pouquet and Mangeney, Physics of Plasmas, 2005) are successfully recovered. Finally, more realistic relations capturing weak Alfv\'enic turbulence (with constant $k_{\parallel}$) and the transition to strong turbulence are derived along with their corresponding power spectra.

physics.plasm-ph↗

arXiv2025

Universal energy cascade in homogeneous binary fluid turbulence: A direct comparison of different exact relations

Below critical temperature, turbulence prevents the spontaneous phase separation of binary mixtures, resulting in a phase arrested state of emulsion which is of significant interest for scientific and industrial applications. The current work is an extensive continuation of our initial theoretical investigation into the nature and universality of associated energy cascade (Pan and Banerjee, PRE, 2022). In addition to the previously derived divergence and correlator forms of the exact relations, a Banerjee-Galtier type divergence-free form of the exact relation is derived under the explicit assumption of homogeneity. By performing three-dimensional direct numerical simulations with up to $1024^3$ grid points, we show that the sum of the kinetic and active energy associates a Kolmogorov-like universal cascade with constant flux rate across inertial scales. Despite term-by-term deviations, the cascade rates computed from all three exact laws show excellent agreement, thereby confirming the equivalence of different exact relations and hence the feasibility of determining the net cascade rate from any of the three formulations. Notably, the two dominant flux rates of the divergence form are found to cross each other roughly at the domain size, which also serves as an infrared cut-off for the inverse cascade of the small scale active energy. This behaviour is phenomenologically justified based on the interplay between the flow and surface dynamics of a phase arrested binary fluid.

physics.flu-dyn↗

arXiv2024

Universal energy cascade in critically balanced homogeneous ferrofluid turbulence

In ferrofluids, the vorticity is balanced by the rate of particle rotation, which is known here as critical balance. The universal energy cascade is investigated for a stationary and non-stationary incompressible ferrofluid turbulent system using exact relations. The findings reveal that under moderate magnetic fields, kinetic and total energy cascades occur at identical rates. As the external magnetic field strength increases, the total energy cascade becomes non-stationary and differs from the kinetic one. However, the cascade's universal, scale-independent nature remains unaffected. The suppression of turbulence in ferrofluids is observable at strong magnetic fields.

physics.flu-dyn↗

arXiv2024

Universal cascade and relaxation of strong anisotropic turbulence in fusion plasmas

Starting from the governing equations, exact relations have been derived for three-dimensional reduced magnetohydrodynamic turbulence corresponding to the inertial range cascade of energy and cross-helicity. Justifications are provided for not attempting to recover the said exact relations as a limit of the exact relations previously derived for incompressible magnetohydrodynamic turbulence. Assuming axial symmetry, anisotropic energy spectrum has been predicted from the exact relation and is found to be consistent with the critical balance thus leading to a -5/3 perpendicular energy spectrum. In the case of a strong alignment between the velocity and the magnetic field fluctuations, the derived exact relation implies a generalized anisotropic spectrum with a -3/2 power-law dependence in the direction of alignment. Using the alternative form of the exact relations, it is shown that the flow naturally relaxes towards a state of dynamic alignment in the limit of negligible kinetic and magnetic pressure. Finally, despite having different equations of dynamics, the exact relations for energy and cross-helicity and the relaxed states of a two-dimensional MHD are found to be identical to those in reduced magnetohydrodynamic flow.

physics.plasm-ph↗

arXiv2024

Emergence of two inertial sub-ranges in solar wind turbulence: dependence on heliospheric distance and solar activity

The solar wind is highly turbulent, and intermittency effects are observed for fluctuations within the inertial range. By analyzing magnetic field spectra and fourth-order moments, we perform a comparative study of turbulence and intermittency in different types of solar wind measured during periods of solar minima and a maximum. Using eight fast solar wind intervals measured during solar minima between 0.3 au and 3.16 au, we found a clear signature of two inertial sub-ranges with $f^{-3/2}$ and $f^{-5/3}$ power laws in the magnetic power spectra. The intermittency, measured through the scaling law of the kurtosis of magnetic field fluctuations, further confirms the existence of two different power laws separated by a clear break. A systematic study on the evolution of the said sub-ranges as a function of heliospheric distance shows correlation of the break scale with both the turbulence outer scale and the typical ion scales. During solar maximum, on the contrary, the two sub-ranges are not omnipresent, thus showing more variability in the power spectra and intermittency scaling properties.

physics.space-ph↗

arXiv2024

Stationary and non-stationary energy cascades in homogeneous ferrofluid turbulence

The nonlinear transfer rate of the total energy (transfer rate of kinetic energy + transfer rate due to the work done by the magnetization) for an incompressible turbulent ferrofluid system is studied under the assumption of statistical homogeneity. Using the formalism of the two-point correlators, an exact relation connecting the second-order statistical moments to the average energy injection rate is derived for the scale-to scale transfer of the total energy. We validate the universality of the exact relation through direct numerical simulations for stationary and non-stationary cascade regimes. For a weak external magnetic field, both kinetic and the total energy cascade with nearly the same cascade rate. A stationary cascade regime is achieved and hence a good agreement between the exact energy transfer rate and the average energy injection is found. Due to the rapid alignment of the ferrofluid particles in the presence of strong external fields, the turbulence dynamics becomes non-stationary. Interestingly, there too, both kinetic and the total energy exhibit inertial range cascades but with different cascade rates which can be explained using the non-stationary form of our derived exact relation.

physics.flu-dyn↗

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

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↗

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

Energy transfer in simple and active binary fluid turbulence {\bf {-}} a false friend of incompressible MHD turbulence

Inertial range energy transfer in three dimensional fully developed binary fluid turbulence is studied under the assumption of statistical homogeneity. Using two point statistics, exact relations corresponding to the energy cascade are derived (i) in terms of two-point increments and (ii) two-point correlators. Despite having some apparent resemblances, the exact relation in binary fluid turbulence is found to be different from that of the incompressible MHD turbulence (Politano and Pouquet, GRL, 1998). Besides the usual direct cascade of energy, under certain situations, an inverse cascade of energy is also speculated depending upon the strength of the activity parameter and the interplay between the two-point increments of the fluid velocity and the composition gradient fields. An alternative form of the exact relation is also derived in terms of the `upsilon' variables and a subsequent phenomenology is also proposed predicting a $k^{-{3}/{2}}$ law for the turbulent energy spectrum.

physics.flu-dyn↗

arXiv2021

Scale dependent anisotropy of electric field fluctuations in solar wind turbulence

We study the variation of average powers and spectral indices of electric field fluctuations with respect to the angle between average flow direction and the mean magnetic field in solar wind turbulence. Cluster spacecraft data from the years 2002 and 2007 are used for the present analysis. We perform a scale dependent study with respect to the local mean magnetic field using wavelet analysis technique. Prominent anisotropies are found for both the spectral index and power levels of the electric power spectra. Similar to the magnetic field fluctuations, the parallel (or antiparallel) electric fluctuation spectrum is found to be steeper than the perpendicular spectrum. However the parallel (or antiparallel) electric power is found to be greater than the perpendicular one. Below 0.1 Hz, the slope of the parallel electric power spectra deviates substantially from that of the total magnetic power spectra, supporting the existence of Alfvénic turbulence.

physics.space-ph↗