Arnab Basak - Academia.edu (original) (raw)

Papers by Arnab Basak

Physica Scripta, 2021

We present dynamic models of dynamo action in the low-Prandtl-number ( Pr≤0.1 ) regime which high... more We present dynamic models of dynamo action in the low-Prandtl-number ( Pr≤0.1 ) regime which highlight the role of pure thermal convection in magnetic field generation. The essential condition for dynamo to occur is non-zero values of the magnetic Prandtl number Pm. Magnetic energy is generated in conducting fluids close to the convective instability if the reduced Rayleigh number r is raised above a critical value r d , otherwise only pure convection is prevalent. The dynamo threshold decreases with increase in Pm for a fixed value of Pr while for a fixed Pm, it increases with increase in Pr. For a fixed Pr, the induced magnetic energy is excited in the form of irregular bursts for lower values of Pm. The magnetic energy is found to be quasi-periodic or oscillatory for relatively larger values of Pm. The bursts of magnetic energy also show the possibility of flow reversals. In the chaotic regime, the probability density function of the heights of magnetic energy bursts show scaling...

Physics Letters A, 2019

We explore the modifications brought about by gravity modulation in self-aligned two-dimensional ... more We explore the modifications brought about by gravity modulation in self-aligned two-dimensional (2D) stationary rolls and higher-order convective instabilities with horizontal magnetic field. The Chandrasekhar number plays no role in determining critical values of the forcing parameters for convection to begin. The onset is in the form of 2D rolls with periodically varying intensity. The external magnetic field is solely responsible for aligning the rolls while the induced magnetic field comes into play after three-dimensional convection sets in. Gravity modulation destabilizes the system and results in chaotic flow much earlier above onset.

Nonlinear Dynamics, 2018

We present a detailed study of Rayleigh-Bénard magnetoconvection with periodic gravity modulation... more We present a detailed study of Rayleigh-Bénard magnetoconvection with periodic gravity modulation and uniform vertical magnetic field. Linear stability analysis is carried out using Floquet theory to construct the stability boundaries in order to estimate the magnitude of forcing amplitude required for having convection in the system for a fixed Rayleigh number Ra, wave number k and modulating frequency. The effects of varying Prandtl number Pr and Chandrasekhar number Q on the threshold of convection are also investigated. A higher Pr value reduces the value of the threshold, whereas a higher Q value increases it. Bicritical states are also observed at which the minimum forcing amplitude needed for convection to begin occurs at two different k values in harmonic and sub-harmonic regions, respectively. We also construct a nonlinear Galerkin model and compare the results with those obtained from linear stability analysis. Twodimensional (2D) oscillatory convection is observed at the onset, while quasiperiodic and chaotic behaviours are found at higher Ra values. 2D as well as nonlinear convective flow patterns are observed for primary and higher-order instabilities, respectively. Bifurcation diagrams with respect to different parameters such as , Ra and Q are provided for thorough understanding of the forced nonlinear system.

CATENA, 2019

The present paper describes the design of a comprehensive rainfall simulator which is particularl... more The present paper describes the design of a comprehensive rainfall simulator which is particularly meant for the assessment of soil erosion at plot scale by considering various soil grain types, soil slope angles, and surface exposures under different rainfall conditions. The entire setup is divided into four major parts: (a) water supply system with single spray nozzle, (b) supporting metal frame, (c) hydraulic jack attached container table for slope adjustment, and (d) temperature simulator. It covers an area of 3 m 2 , out of which 0.5 m 2 is the target area or experimental plot and the simulated raindrops fall from a height of 2.3 m. Four types of full-jet spray nozzles are used to simulate rainfall intensities of 65, 93, 112, and 148 mm/h. The experimental plot can attain a maximum slope angle of 40°using a hydraulic jack unit. A temperature simulator is designed to replicate the natural conditions in the laboratory. Physical and numerical simulations are carried out to measure the characteristics of simulated rainfall and compare with those of natural rainfall conditions. The Christiansen coefficient (Cu) of the designed rainfall simulator varies from 81% to 88%. The rain droplet size ranges from roughly 1 mm to 5 mm and their corresponding terminal velocities range from 4.76 m/s to 10.64 m/s, striking velocities are found between 5.56 m/s and 9.63 m/s, and kinetic energies ranging from 0.0081 mJ to 3.0342 mJ. The total kinetic energy of the raindrops striking the soil surface in the entire plot area of 0.5 m 2 depends on the rainfall intensity and varies from about 6 J to 12 J. The designed setup is capable of simulating rainfall inside the laboratory with properties very close to those of natural rainfall. We adopt the Taguchi fractional factorial design of experiments to investigate the effects of different factors on soil erosion. Furthermore, statistical analysis of the experimental data is carried out by using signal-to-noise (S/N) ratio and the optimum condition for maximum soil erosion is predicted. The main objectives of this study are to design a comprehensive rainfall simulator setup, evaluate the properties of the simulated rainfall, provide a theoretical model and assess the several factors affecting soil erosion using reduced number of experiments in the laboratory.

The European Physical Journal B, 2015

A model for three-dimensional Rayleigh-Bénard convection in low-Prandtl-number fluids near onset ... more A model for three-dimensional Rayleigh-Bénard convection in low-Prandtl-number fluids near onset with rigid horizontal boundaries in the presence of a uniform vertical magnetic field is constructed and analyzed in detail. The kinetic energy K, the convective entropy Φ and the convective heat flux (N u − 1) show scaling behaviour with ǫ = r − 1 near onset of convection, where r is the reduced Rayleigh number. The model is also used to investigate various magneto-convective structures close to the onset. Straight rolls, which appear at the primary instability, become unstable with increase in r and bifurcate to three-dimensional structures. The straight rolls become periodically varying wavy rolls or quasiperiodically varying structures in time with increase in r depending on the values of Prandtl number P r. They become irregular in time, with increase in r. These standing wave solutions bifurcate first to periodic and then quasiperiodic traveling wave solutions, as r is raised further. The variations of the critical Rayleigh number Raos and the frequency ωos at the onset of the secondary instability with P r are also studied for different values of Chandrasekhar's number Q.

Physical review. E, Statistical, nonlinear, and soft matter physics, 2014

We present the results of direct numerical simulations of Rayleigh-Bénard convection in the prese... more We present the results of direct numerical simulations of Rayleigh-Bénard convection in the presence of a uniform vertical magnetic field near instability onset. We have done simulations in boxes with square as well as rectangular cross sections in the horizontal plane. We have considered the horizontal aspect ratio η=L(y)/L(x)=1 and 2. The onset of the primary and secondary instabilities are strongly suppressed in the presence of the vertical magnetic field for η=1. The Nusselt number Nu scales with the Rayleigh number Ra close to the primary instability as [{Ra-Ra(c)(Q)}/Ra(c)(Q)](0.91), where Ra(c)(Q) is the threshold for onset of stationary convection at a given value of the Chandrasekhar number Q. Nu also scales with Ra/Q as (Ra/Q)(μ). The exponent μ varies in the range 0.39≤μ≤0.57 for Ra/Q≥25. The primary instability is stationary as predicted by Chandrasekhar. The secondary instability is temporally periodic for Pr=0.1 but quasiperiodic for Pr=0.025 for moderate values of Q. ...

arXiv (Cornell University), Mar 8, 2023

Monthly Notices of the Royal Astronomical Society, 2021

Based on 3D compressible magnetohydrodynamic simulations, we explore the interactions between the... more Based on 3D compressible magnetohydrodynamic simulations, we explore the interactions between the magnetized wind from a solar-like star and a Mars-like planet – with a gravitionally stratified atmosphere – that is either non-magnetized or hosts a weak intrinsic dipolar field. The primary mechanism for the induction of a magnetosphere around a non-magnetized conducting planet is the pile-up of stellar magnetic fields in the day-side region. The magnetopause stand-off distance decreases as the strength of the planetary dipole field is lowered and saturates to a minimum value for the case of a planet with no magnetic field. Global features such as bow shock, magnetosheath, magnetotail, and strong current sheets are observed in the imposed magnetosphere. We explore variations in atmospheric mass loss rates for different stellar wind strengths to understand the impact of stellar magnetic activity and plasma winds – and their evolution – on (exo)planetary habitability. In order to simula...

The Astrophysical Journal, 2019

The outflowing magnetized wind from a host star shapes planetary and exoplanetary magnetospheres ... more The outflowing magnetized wind from a host star shapes planetary and exoplanetary magnetospheres dictating the extent of its impact. We carry out three-dimensional (3D) compressible magnetohydrodynamic (MHD) simulations of the interactions between magnetized stellar winds and planetary magnetospheres corresponding to a far-out star-planet system, with and without planetary dipole obliquity. We identify the pathways that lead to the formation of a dynamical steady-state magnetosphere and find that magnetic reconnection plays a fundamental role in the process. The magnetic energy density is found to be greater on the night-side than that on the day-side and the magnetotail is comparatively more dynamic. Magnetotail reconnection events are seen to associated with stellar wind plasma injection into the inner magnetosphere. We further study magnetospheres with extreme tilt angles keeping in perspective the examples of Uranus and Neptune. High dipole obliquities may also manifest due to polarity excursions during planetary field reversals. We find that global magnetospheric reconnection sites change for large planetary dipole obliquity and more complex current sheet structures are generated. We discuss the implications of these findings for injection of interplanetary species and energetic particles into the inner magnetosphere, auroral activity and magnetospheric radio emission. This study is relevant for exploring star planet interactions in the solar and extra-solar systems.

Proceedings of the International Astronomical Union, 2018

The age-dependent activity of a star dictates the extent of its planetary impact. We study the in... more The age-dependent activity of a star dictates the extent of its planetary impact. We study the interaction of the stellar wind produced by Solar-like stars with the magnetosphere of Earth-like planets using three dimensional (3D) magnetohydrodynamic (MHD) simulations. The numerical simulations reveal important features of star-planet interaction e.g. bow-shock, magnetopause, magnetotail, etc. Interesting phenomena such as particle injection into the planetary atmosphere as well as atmospheric mass loss are also observed which are instrumental in determining the atmospheric retention by the planet.

Chaos (Woodbury, N.Y.), 2016

Effects of a uniform magnetic field on homoclinic bifurcations in Rayleigh-Bénard convection in a... more Effects of a uniform magnetic field on homoclinic bifurcations in Rayleigh-Bénard convection in a fluid of Prandtl number Pr = 0.01 are investigated using direct numerical simulations (DNS). A uniform magnetic field is applied either in the vertical direction or in the horizontal direction. For a weak vertical magnetic field, the possibilities of both forward and backward homoclinic bifurcations are observed leading to a spontaneous gluing of two limit cycles into one as well as a spontaneous breaking of a limit cycle into two for lower values of the Chandrasekhar's number ( Q≤5). A slightly stronger magnetic field makes the convective flow time independent giving the possibility of stationary patterns at the secondary instability. For horizontal magnetic field, the x⇋y symmetry is destroyed and neither a homoclinic gluing nor a homoclinic breaking is observed. Two low-dimensional models are also constructed: one for a weak vertical magnetic field and another for a weak horizont...

Proceedings of the International Astronomical Union, 2018

Concentrated magnetic structures such as sunspots and starspots play a fundamental role in drivin... more Concentrated magnetic structures such as sunspots and starspots play a fundamental role in driving solar and stellar activity. However, as opposed to the sun, observations as well as numerical simulations have shown that stellar spots are usually formed as high-latitude patches extended over wide areas. Using a fully spectral magnetohydrodynamic (MHD) code, we simulate polar starspots produced by self-consistent dynamo action in rapidly rotating convective shells. We carry out high resolution simulations and investigate various properties related to stellar dynamics which lead to starspot formation.

Physica Scripta, 2021

We present dynamic models of dynamo action in the low-Prandtl-number ( Pr≤0.1 ) regime which high... more We present dynamic models of dynamo action in the low-Prandtl-number ( Pr≤0.1 ) regime which highlight the role of pure thermal convection in magnetic field generation. The essential condition for dynamo to occur is non-zero values of the magnetic Prandtl number Pm. Magnetic energy is generated in conducting fluids close to the convective instability if the reduced Rayleigh number r is raised above a critical value r d , otherwise only pure convection is prevalent. The dynamo threshold decreases with increase in Pm for a fixed value of Pr while for a fixed Pm, it increases with increase in Pr. For a fixed Pr, the induced magnetic energy is excited in the form of irregular bursts for lower values of Pm. The magnetic energy is found to be quasi-periodic or oscillatory for relatively larger values of Pm. The bursts of magnetic energy also show the possibility of flow reversals. In the chaotic regime, the probability density function of the heights of magnetic energy bursts show scaling...

Physics Letters A, 2019

We explore the modifications brought about by gravity modulation in self-aligned two-dimensional ... more We explore the modifications brought about by gravity modulation in self-aligned two-dimensional (2D) stationary rolls and higher-order convective instabilities with horizontal magnetic field. The Chandrasekhar number plays no role in determining critical values of the forcing parameters for convection to begin. The onset is in the form of 2D rolls with periodically varying intensity. The external magnetic field is solely responsible for aligning the rolls while the induced magnetic field comes into play after three-dimensional convection sets in. Gravity modulation destabilizes the system and results in chaotic flow much earlier above onset.

Nonlinear Dynamics, 2018

We present a detailed study of Rayleigh-Bénard magnetoconvection with periodic gravity modulation... more We present a detailed study of Rayleigh-Bénard magnetoconvection with periodic gravity modulation and uniform vertical magnetic field. Linear stability analysis is carried out using Floquet theory to construct the stability boundaries in order to estimate the magnitude of forcing amplitude required for having convection in the system for a fixed Rayleigh number Ra, wave number k and modulating frequency. The effects of varying Prandtl number Pr and Chandrasekhar number Q on the threshold of convection are also investigated. A higher Pr value reduces the value of the threshold, whereas a higher Q value increases it. Bicritical states are also observed at which the minimum forcing amplitude needed for convection to begin occurs at two different k values in harmonic and sub-harmonic regions, respectively. We also construct a nonlinear Galerkin model and compare the results with those obtained from linear stability analysis. Twodimensional (2D) oscillatory convection is observed at the onset, while quasiperiodic and chaotic behaviours are found at higher Ra values. 2D as well as nonlinear convective flow patterns are observed for primary and higher-order instabilities, respectively. Bifurcation diagrams with respect to different parameters such as , Ra and Q are provided for thorough understanding of the forced nonlinear system.

CATENA, 2019

The present paper describes the design of a comprehensive rainfall simulator which is particularl... more The present paper describes the design of a comprehensive rainfall simulator which is particularly meant for the assessment of soil erosion at plot scale by considering various soil grain types, soil slope angles, and surface exposures under different rainfall conditions. The entire setup is divided into four major parts: (a) water supply system with single spray nozzle, (b) supporting metal frame, (c) hydraulic jack attached container table for slope adjustment, and (d) temperature simulator. It covers an area of 3 m 2 , out of which 0.5 m 2 is the target area or experimental plot and the simulated raindrops fall from a height of 2.3 m. Four types of full-jet spray nozzles are used to simulate rainfall intensities of 65, 93, 112, and 148 mm/h. The experimental plot can attain a maximum slope angle of 40°using a hydraulic jack unit. A temperature simulator is designed to replicate the natural conditions in the laboratory. Physical and numerical simulations are carried out to measure the characteristics of simulated rainfall and compare with those of natural rainfall conditions. The Christiansen coefficient (Cu) of the designed rainfall simulator varies from 81% to 88%. The rain droplet size ranges from roughly 1 mm to 5 mm and their corresponding terminal velocities range from 4.76 m/s to 10.64 m/s, striking velocities are found between 5.56 m/s and 9.63 m/s, and kinetic energies ranging from 0.0081 mJ to 3.0342 mJ. The total kinetic energy of the raindrops striking the soil surface in the entire plot area of 0.5 m 2 depends on the rainfall intensity and varies from about 6 J to 12 J. The designed setup is capable of simulating rainfall inside the laboratory with properties very close to those of natural rainfall. We adopt the Taguchi fractional factorial design of experiments to investigate the effects of different factors on soil erosion. Furthermore, statistical analysis of the experimental data is carried out by using signal-to-noise (S/N) ratio and the optimum condition for maximum soil erosion is predicted. The main objectives of this study are to design a comprehensive rainfall simulator setup, evaluate the properties of the simulated rainfall, provide a theoretical model and assess the several factors affecting soil erosion using reduced number of experiments in the laboratory.

The European Physical Journal B, 2015

A model for three-dimensional Rayleigh-Bénard convection in low-Prandtl-number fluids near onset ... more A model for three-dimensional Rayleigh-Bénard convection in low-Prandtl-number fluids near onset with rigid horizontal boundaries in the presence of a uniform vertical magnetic field is constructed and analyzed in detail. The kinetic energy K, the convective entropy Φ and the convective heat flux (N u − 1) show scaling behaviour with ǫ = r − 1 near onset of convection, where r is the reduced Rayleigh number. The model is also used to investigate various magneto-convective structures close to the onset. Straight rolls, which appear at the primary instability, become unstable with increase in r and bifurcate to three-dimensional structures. The straight rolls become periodically varying wavy rolls or quasiperiodically varying structures in time with increase in r depending on the values of Prandtl number P r. They become irregular in time, with increase in r. These standing wave solutions bifurcate first to periodic and then quasiperiodic traveling wave solutions, as r is raised further. The variations of the critical Rayleigh number Raos and the frequency ωos at the onset of the secondary instability with P r are also studied for different values of Chandrasekhar's number Q.

Physical review. E, Statistical, nonlinear, and soft matter physics, 2014

We present the results of direct numerical simulations of Rayleigh-Bénard convection in the prese... more We present the results of direct numerical simulations of Rayleigh-Bénard convection in the presence of a uniform vertical magnetic field near instability onset. We have done simulations in boxes with square as well as rectangular cross sections in the horizontal plane. We have considered the horizontal aspect ratio η=L(y)/L(x)=1 and 2. The onset of the primary and secondary instabilities are strongly suppressed in the presence of the vertical magnetic field for η=1. The Nusselt number Nu scales with the Rayleigh number Ra close to the primary instability as [{Ra-Ra(c)(Q)}/Ra(c)(Q)](0.91), where Ra(c)(Q) is the threshold for onset of stationary convection at a given value of the Chandrasekhar number Q. Nu also scales with Ra/Q as (Ra/Q)(μ). The exponent μ varies in the range 0.39≤μ≤0.57 for Ra/Q≥25. The primary instability is stationary as predicted by Chandrasekhar. The secondary instability is temporally periodic for Pr=0.1 but quasiperiodic for Pr=0.025 for moderate values of Q. ...

arXiv (Cornell University), Mar 8, 2023

Monthly Notices of the Royal Astronomical Society, 2021

Based on 3D compressible magnetohydrodynamic simulations, we explore the interactions between the... more Based on 3D compressible magnetohydrodynamic simulations, we explore the interactions between the magnetized wind from a solar-like star and a Mars-like planet – with a gravitionally stratified atmosphere – that is either non-magnetized or hosts a weak intrinsic dipolar field. The primary mechanism for the induction of a magnetosphere around a non-magnetized conducting planet is the pile-up of stellar magnetic fields in the day-side region. The magnetopause stand-off distance decreases as the strength of the planetary dipole field is lowered and saturates to a minimum value for the case of a planet with no magnetic field. Global features such as bow shock, magnetosheath, magnetotail, and strong current sheets are observed in the imposed magnetosphere. We explore variations in atmospheric mass loss rates for different stellar wind strengths to understand the impact of stellar magnetic activity and plasma winds – and their evolution – on (exo)planetary habitability. In order to simula...

The Astrophysical Journal, 2019

The outflowing magnetized wind from a host star shapes planetary and exoplanetary magnetospheres ... more The outflowing magnetized wind from a host star shapes planetary and exoplanetary magnetospheres dictating the extent of its impact. We carry out three-dimensional (3D) compressible magnetohydrodynamic (MHD) simulations of the interactions between magnetized stellar winds and planetary magnetospheres corresponding to a far-out star-planet system, with and without planetary dipole obliquity. We identify the pathways that lead to the formation of a dynamical steady-state magnetosphere and find that magnetic reconnection plays a fundamental role in the process. The magnetic energy density is found to be greater on the night-side than that on the day-side and the magnetotail is comparatively more dynamic. Magnetotail reconnection events are seen to associated with stellar wind plasma injection into the inner magnetosphere. We further study magnetospheres with extreme tilt angles keeping in perspective the examples of Uranus and Neptune. High dipole obliquities may also manifest due to polarity excursions during planetary field reversals. We find that global magnetospheric reconnection sites change for large planetary dipole obliquity and more complex current sheet structures are generated. We discuss the implications of these findings for injection of interplanetary species and energetic particles into the inner magnetosphere, auroral activity and magnetospheric radio emission. This study is relevant for exploring star planet interactions in the solar and extra-solar systems.

Proceedings of the International Astronomical Union, 2018

The age-dependent activity of a star dictates the extent of its planetary impact. We study the in... more The age-dependent activity of a star dictates the extent of its planetary impact. We study the interaction of the stellar wind produced by Solar-like stars with the magnetosphere of Earth-like planets using three dimensional (3D) magnetohydrodynamic (MHD) simulations. The numerical simulations reveal important features of star-planet interaction e.g. bow-shock, magnetopause, magnetotail, etc. Interesting phenomena such as particle injection into the planetary atmosphere as well as atmospheric mass loss are also observed which are instrumental in determining the atmospheric retention by the planet.

Chaos (Woodbury, N.Y.), 2016

Effects of a uniform magnetic field on homoclinic bifurcations in Rayleigh-Bénard convection in a... more Effects of a uniform magnetic field on homoclinic bifurcations in Rayleigh-Bénard convection in a fluid of Prandtl number Pr = 0.01 are investigated using direct numerical simulations (DNS). A uniform magnetic field is applied either in the vertical direction or in the horizontal direction. For a weak vertical magnetic field, the possibilities of both forward and backward homoclinic bifurcations are observed leading to a spontaneous gluing of two limit cycles into one as well as a spontaneous breaking of a limit cycle into two for lower values of the Chandrasekhar's number ( Q≤5). A slightly stronger magnetic field makes the convective flow time independent giving the possibility of stationary patterns at the secondary instability. For horizontal magnetic field, the x⇋y symmetry is destroyed and neither a homoclinic gluing nor a homoclinic breaking is observed. Two low-dimensional models are also constructed: one for a weak vertical magnetic field and another for a weak horizont...

Proceedings of the International Astronomical Union, 2018

Concentrated magnetic structures such as sunspots and starspots play a fundamental role in drivin... more Concentrated magnetic structures such as sunspots and starspots play a fundamental role in driving solar and stellar activity. However, as opposed to the sun, observations as well as numerical simulations have shown that stellar spots are usually formed as high-latitude patches extended over wide areas. Using a fully spectral magnetohydrodynamic (MHD) code, we simulate polar starspots produced by self-consistent dynamo action in rapidly rotating convective shells. We carry out high resolution simulations and investigate various properties related to stellar dynamics which lead to starspot formation.