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Supratik Banerjee

Publications and source records attributed to Supratik Banerjee.

33 records · Page 2Linked to original sources
arXiv2020

Anisotropy of Electric Field Fluctuations Spectrum of Solar Wind Turbulence

To investigate the power and spectral index anisotropy in the inertial range of solar wind turbulence, we use 70 intervals of electric field data accumulated by Cluster spacecraft in the free solar wind. We compute the electric field fluctuation power spectra using wavelet analysis technique and study its spectral index variation with the change in angle between the heliocentric radial direction and the local mean magnetic field. We find clear power and spectral index anisotropy in the frequency ranging from 0.01 Hz to 0.1 Hz, with more power in parallel fluctuations than perpendicular. We also report our study of anisotropy as a function of solar activity.

physics.space-ph↗
arXiv2020

Sub-Pixel Back-Projection Network For Lightweight Single Image Super-Resolution

Convolutional neural network (CNN)-based methods have achieved great success for single-image superresolution (SISR). However, most models attempt to improve reconstruction accuracy while increasing the requirement of number of model parameters. To tackle this problem, in this paper, we study reducing the number of parameters and computational cost of CNN-based SISR methods while maintaining the accuracy of super-resolution reconstruction performance. To this end, we introduce a novel network architecture for SISR, which strikes a good trade-off between reconstruction quality and low computational complexity. Specifically, we propose an iterative back-projection architecture using sub-pixel convolution instead of deconvolution layers. We evaluate the performance of computational and reconstruction accuracy for our proposed model with extensive quantitative and qualitative evaluations. Experimental results reveal that our proposed method uses fewer parameters and reduces the computational cost while maintaining reconstruction accuracy against state-of-the-art SISR methods over well-known four SR benchmark datasets. Code is available at "https://github.com/supratikbanerjee/SubPixel-BackProjection_SuperResolution".

eess.IV↗
arXiv2020

Scale-to-scale energy transfer rate in compressible two-fluid plasma turbulence

We derive the exact relation for the energy transfer in three-dimensional compressible two-fluid plasma turbulence. In the long-time limit, we obtain an exact law which expresses the scale-to-scale average energy flux rate in terms of two point increments of the fluid variables of each species, electric and magnetic field and current density, and puts a strong constraint on the turbulent dynamics. The incompressible single fluid and two-fluid limits and the compressible single fluid limit are recovered under appropriate assumption. In the single fluid limits, analyses are done with and without neglecting the electron mass thereby making the exact relation suitable for a broader range of application. In the compressible two fluid regime, the total energy flux rate, unlike the single fluid case, is found to be unaltered by the presence of a background magnetic field. The exact relation provides a way to test whether a range of scales in a plasma is inertial or dissipative and is essential to understand the nonlinear nature of both space and dilute astrophysical plasmas.

physics.plasm-ph↗
arXiv2019

Determination of energy flux rate in homogeneous ferrohydrodynamic turbulence using two-point statistics

In ferrofluids the suspended ferromagnetic particles agglomerate due to the interaction between the particle magnetic moment and the external magnetic field, which in turn, influences the turbulence and relaxation time. The relaxation time becomes large when we are considering turbulence drag force instead of viscous drag force in Brownian motion. We investigate that the total energy conservation in ferrofluids taking into interaction between the external magnetic field and the ferrofluid.

physics.flu-dyn↗
arXiv2019

On exact laws in incompressible Hall magnetohydrodynamic turbulence

A comparison is made between several existing exact laws in incompressible Hall magnetohydrodynamic (IHMHD) turbulence in order to show their equivalence, despite stemming from different mathematical derivations. Using statistical homogeneity, we revisit the law proposed by Hellinger et al. (2018) and show that it can be written, after being corrected by a multiplicative factor, in a more compact form implying only flux terms expressed as increments of the turbulent fields. The Hall contribution of this law is tested and compared to other exact laws derived by Galtier (2008) and Banerjee & Galtier (2017) using direct numerical simulations (DNSs) of three-dimensional electron MHD (EMHD) turbulence with a moderate mean magnetic field. We show that the studied laws are equivalent in the inertial range, thereby offering several choices on the formulation to use depending on the needs. The expressions that depend explicitly on a mean (guide) field may lead to residual errors in estimating the energy cascade rate ; however, we demonstrate that this guide field can be removed from these laws after mathematical manipulation. Therefore, it is recommended to use an expression independent of the mean guide field to analyze numerical or in-situ spacecraft data.

physics.flu-dyn↗
arXiv2019

Statistics of incompressible hydrodynamic turbulence: an alternative approach

Using a recent alternative form of the Kolmogorov-Monin exact relation for fully developed hydrodynamics (HD) turbulence, the incompressible energy cascade rate $\varepsilon$ is computed. Under this current theoretical framework, for three-dimensional (3D) freely decaying homogeneous turbulence, the statistical properties of the fluid velocity (${\bf u}$), vorticity ($\boldsymbol ω= \boldsymbol\nabla \times {\bf u}$) and Lamb vector ($\boldsymbol{\cal L}= \boldsymbol ω\times {\bf u})$ are numerically studied. For different spatial resolutions, the numerical results show that $\varepsilon$ can be obtained directly as the simple products of two-point increments of ${\bf u}$ and $\boldsymbol{\cal L}$, without the assumption of isotropy. Finally, the results for the largest spatial resolutions show a clear agreement with the cascade rates computed from the classical 4/3 law for isotropic homogeneous HD turbulence.

physics.flu-dyn↗
arXiv2018

Energy transfer in compressible magnetohydrodynamic turbulence for isothermal self-gravitating fluids

Three-dimensional, compressible, magnetohydrodynamic turbulence of an isothermal, self-gravitating fluid is analyzed using two-point statistics in the asymptotic limit of large Reynolds numbers (both kinetic and magnetic). Following an alternative formulation proposed by S. Banerjee and S. Galtier (Phys. Rev. E,93, 033120, 2016) and S. Banerjee and S. Galtier (J. Phys. A, Math. and Theor.,50, 015501, 2017), an exact relation has been derived for the total energy transfer. This approach results in a simpler relation expressed entirely in terms of mixed second-order structure functions. The kinetic, thermodynamic, magnetic and gravitational contributions to the energy transfer rate can be easily separated in the present form. By construction, the new formalism includes such additional effects as global rotation, the Hall term in the induction equation, etc. The analysis shows that solid-body rotation cannot alter the energy flux rate of compressible turbulence. However, the contribution of a uniform background magnetic field to the flux is shown to be non-trivial unlike in the incompressible case. Finally, the compressible, turbulent energy flux rate does not vanish completely due to simple alignments, which leads to a zero turbulent energy flux rate in the incompressible case.

physics.flu-dyn↗
arXiv2017

Exact relations for energy transfer in self-gravitating isothermal turbulence

Self-gravitating isothermal supersonic turbulence is analyzed in the asymptotic limit of large Reynolds numbers. Based on the inviscid invariance of total energy, an exact relation is derived for homogeneous, (not necessarily isotropic) turbulence. A modified definition for the two-point energy correlation functions is used to comply with the requirement of detailed energy equipartition in the acoustic limit. In contrast to the previous relations (Galtier and Banerjee, Phys. Rev. Lett., 107, 134501, 2011; Banerjee and Galtier, Phys. Rev. E, 87, 013019, 2013), the current exact relation shows that the pressure dilatation terms plays practically no role in the energy cascade. Both the flux and source terms are written in terms of two-point differences. Sources enter the relation in a form of mixed second-order structure functions. Unlike kinetic and thermodynamic potential energy, gravitational contribution is absent from the flux term. An estimate shows that for the isotropic case, the correlation between density and gravitational acceleration may play an important role in modifying the energy transfer in self-gravitating turbulence. The exact relation is also written in an alternative form in terms of two-point correlation functions, which is then used to describe scale-by-scale energy budget in spectral space.

physics.flu-dyn↗
arXiv2016

An alternative formulation for exact scaling relations in hydrodynamic and magnetohydrodynamic turbulence

We propose an alternative formulation for the exact relations in three-dimensional homogeneous turbulence using two-point statistics. Our finding is illustrated with incompressible hydrodynamic, standard and Hall magnetohydrodynamic turbulence. In this formulation, the cascade rate of an inviscid invariant of turbulence can be expressed simply in terms of mixed second-order structure functions. Besides the usual variables like the velocity ${\bf u}$, vorticity $ω$, magnetic field ${\bf b}$ and the current ${\bf j}$, the vectors ${\bf u } \times {\boldsymbol ω}$, ${\bf u} \times {\bf b}$ and ${\bf j} \times {\bf b}$ are also found to play a key role in the turbulent cascades. The current methodology offers a simple algebraic form which is specially interesting to study anisotropic space plasmas like the solar wind, with in principle a faster statistical convergence than the classical laws written in terms of third-order correlators.

physics.flu-dyn↗
arXiv2016

Scaling of compressible magnetohydrodynamic turbulence in the fast solar wind

The role of compressible fluctuations in the energy cascade of fast solar wind turbulence is studied using a reduced form of an exact law derived recently (Banerjee and Galtier, PRE, 2013) for compressible isothermal magnetohydrodynamics and in-situ observations from the THEMIS B/ARTEMIS P1 spacecraft. A statistical survey of the data revealed a turbulent energy cascade over two decades of scales, which is broader than the previous estimates made from an exact incompressible law. A term-by-term analysis of the compressible model reveals new insight into the role played by the compressible fluctuations in the energy cascade. The compressible fluctuations are shown to amplify (2 to 4 times) the turbulent cascade rate with respect to the incompressible model in 10 % of the analyzed samples. This new estimated cascade rate is shown to provide the adequate energy dissipation required.

physics.space-ph↗
arXiv2016

Chiral Exact Relations for Helicities in Hall Magnetohydrodynamic Turbulence

Besides total energy, three-dimensional incompressible Hall magnetohydrodynamics (MHD) possesses two inviscid invariants which are the magnetic helicity and the generalized helicity. New exact relations are derived for homogeneous (non-isotropic) stationary Hall MHD turbulence (and also for its inertialess electron MHD limit) with non-zero helicities and in the asymptotic limit of large Reynolds numbers. The universal laws are written only in terms of mixed second-order structure functions, i.e. the scalar product of two different increments. It provides, therefore, a direct measurement of the dissipation rates for the corresponding invariant flux. This study shows that the generalized helicity cascade is strongly linked to the left polarized fluctuations while the magnetic helicity cascade is linked to the right polarized fluctuations.

physics.flu-dyn↗
arXiv2015

The density structure and star formation rate of non-isothermal polytropic turbulence

The interstellar medium of galaxies is governed by supersonic turbulence, which likely controls the star formation rate (SFR) and the initial mass function (IMF). Interstellar turbulence is non-universal, with a wide range of Mach numbers, magnetic fields strengths, and driving mechanisms. Although some of these parameters were explored, most previous works assumed that the gas is isothermal. However, we know that cold molecular clouds form out of the warm atomic medium, with the gas passing through chemical and thermodynamic phases that are not isothermal. Here we determine the role of temperature variations by modelling non-isothermal turbulence with a polytropic equation of state (EOS), where pressure and temperature are functions of gas density, P~rho^Gamma, T~rho^(Gamma-1). We use grid resolutions of 2048^3 cells and compare polytropic exponents Gamma=0.7 (soft EOS), Gamma=1 (isothermal EOS), and Gamma=5/3 (stiff EOS). We find a complex network of non-isothermal filaments with more small-scale fragmentation occurring for Gamma<1, while Gamma>1 smoothes out density contrasts. The density probability distribution function (PDF) is significantly affected by temperature variations, with a power-law tail developing at low densities for Gamma>1. In contrast, the PDF becomes closer to a lognormal distribution for Gamma<=1. We derive and test a new density variance - Mach number relation that takes Gamma into account. This new relation is relevant for theoretical models of the SFR and IMF, because it determines the dense gas mass fraction of a cloud, from which stars form. We derive the SFR as a function of Gamma and find that it decreases by a factor of ~5 from Gamma=0.7 to Gamma=5/3.

astro-ph.GA↗
arXiv2013

Exact Relation with Two-point Correlation Functions and Phenomenological Approach for Compressible Magnetohydrodynamic Turbulence

Compressible isothermal magnetohydrodynamic turbulence is analyzed under the assumption of statistical homogeneity and in the asymptotic limit of large kinetic and magnetic Reynolds numbers. Following Kolmogorov we derive an exact relation for some two-point correlation functions which generalizes the expression recently found for hydrodynamics. We show that the magnetic field brings new source and flux terms into the dynamics which may act on the inertial range similarly as a source or a sink for the mean energy transfer rate. The introduction of a uniform magnetic field simplifies significantly the exact relation for which a simple phenomenology may be given. A prediction for axisymmetric energy spectra is eventually proposed.

physics.flu-dyn↗
arXiv2011

Exact relation for correlation functions in compressible isothermal turbulence

Compressible isothermal turbulence is analyzed under the assumption of homogeneity and in the asymptotic limit of a high Reynolds number. An exact relation is derived for some two-point correlation functions which reveals a fundamental difference with the incompressible case. The main difference resides in the presence of a new type of term which acts on the inertial range similarly as a source or a sink for the mean energy transfer rate. When isotropy is assumed, compressible turbulence may be described by the relation, $- {2 \over 3} ε_{\rm{eff}} r = {\cal F}_r(r)$, where ${\cal F}_r$ is the radial component of the two-point correlation functions and $ε_{\rm{eff}}$ is an effective mean total energy injection rate. By dimensional arguments we predict that a spectrum in $k^{-5/3}$ may still be preserved at small scales if the density-weighted fluid velocity, $ρ^{1/3} \uu$, is used.

astro-ph.SR↗