Non-equilibrium Thermodynamics of Rayleigh–Taylor Instability

Sengupta, Tapan K.; Sengupta, Aditi; Sengupta, Soumyo; Bhole, Ashish; Shruti, Koulgi

doi:10.1007/s10765-016-2045-1

Cited by 10 publications

(5 citation statements)

References 27 publications

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“…As a consequence frequent flare and emission of intense x-ray and extreme ultraviolet ray are very common. Therefore, the atmosphere of a planet in the habitable zone of M dwarf star is unlikely to have favorable condition for life to survive (Lissauer 2007;Sengupta 2016;Owen & Mohanty 2016). Such a situation strongly motivate the search for habitable planets around brown dwarfs.…”

Section: Introductionmentioning

confidence: 99%

Polarimetric Detection of Exoplanets Transiting T and L Brown Dwarfs

Sengupta¹

2016

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While scattering of light by atoms and molecules yields large amount of polarization at the B-band of both T and L dwarfs, scattering by dust grains in cloudy atmosphere of L dwarfs gives rise to significant polarization at the far-optical and infra-red wavelengths where these objects are much brighter. However, the observable disk averaged polarization should be zero if the clouds are uniformly distributed and the object is spherically symmetric. Therefore, in order to explain the observed large polarization of several L dwarfs, rotation-induced oblateness or horizontally inhomogeneous cloud distribution in the atmosphere is invoked. On the other hand, when an extra-solar planet of Earth-size or larger transits the brown dwarf along the line of sight, the asymmetry induced during the transit gives rise to a net non-zero, time dependent polarization. Employing atmospheric models for a range of effective temperature and surface gravity appropriate for T and L dwarfs, I derive the time dependent polarization profiles of these objects during transit phase and estimate the peak amplitude of polarization that occurs during the inner contact points of the transit ingress/egress phase. It is found that peak polarization in the range of 0.2-1.0% at I-and J-band may arise of cloudy L dwarfs occulted by Earth-size or larger exoplanets. Such an amount of polarization is higher than that can be produced by rotation-induced oblateness of even the rapidly rotating L dwarfs. Hence, I suggest that time resolved imaging polarization should be a potential technique to detect transiting exoplanets around L dwarfs.

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Section: Introductionmentioning

confidence: 99%

Polarimetric Detection of Exoplanets Transiting T and L Brown Dwarfs

Sengupta¹

2016

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“…Finite difference compact schemes exhibit superior spectral resolution [40,42] than the explicit schemes of same order, which motivated researchers to use them in many DNS and large eddy simulations [12,20,35,[43][44][45][46][47][48]. The approximation of m th derivative of a function f at i th point using a compact scheme is represented as,…”

Section: Formulation Of Compressible Navier-stokes Equation For Rtimentioning

confidence: 99%

“…In the present case, the box is considered to be thermally insulated, which enables it to be viewed as an universe, without any mass, momentum, and energy transfer with the outside. The ensuing RTI upon removal of the partition enables one to view the process as one of non-equilibrium thermodynamics, as reported for a two-dimensional (2D) flow in [14,20,21] and a three-dimensional (3D) flow with A t = 0.2, due to initial temperature differential of 149K. In Read's experiments [22], two geometrical setups were considered with the purpose of providing results for 2D and 3D flows.…”

Section: Introductionmentioning

confidence: 99%

“…In practice, there is no need to impose any length scale as there are many 2D and 3D direct numerical simulations (DNS) where the initial interface is purely taken as planar [12,14,20,21,27] to replicate the experiments reported in [17,22,28] where the fluid interface is initially plane and the onset of RTI has been shown to originate from the edges and corners of the initial interface [12].…”

Section: Introductionmentioning

confidence: 99%

“…The above discussion indicates that the onset of RTI and associated length scales are still not unambiguously resolved. We have already noted that high accuracy compact schemes used for solving compressible NSE without the Stokes' hypothesis enable one to track the onset of RTI to be from the edges and corners of the interface [14,20,21] for 2D RTI problem. The authors in [29] used a 2D multi-physics simulation package, HYDRA [31,32] with a spatial resolution of the order of 3µm and time steps of the order of 100ps.…”

Section: Introductionmentioning

confidence: 99%

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Ultrasound Triggering of Rayleigh-Taylor Instability: Solution of Compressible Navier-Stokes Equation by a Non-Overlapping Parallel Compact Scheme

Sundaram¹,

Sengupta²,

Sengupta³

2022

Preprint

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Rayleigh-Taylor instability (RTI) occurs at the interface of two media when the heavier fluid is accelerated into the lighter fluid and is a prototypical hydrodynamic event present in many physical events. In high energy physics, this manifests itself across a wide range of length scales from nuclear confinement fusion at micron-scale to supernova explosion at terra scales. RTI can also be viewed as a baroclinic instability prevalent in engineering, geophysics, and astrophysics, a pedagogic description of which is given in Sengupta et al., Comput. Fluids, 225, 104995 (2021) with respect to the experimental results of Read, Physica D, 12 45-58 (1984). Here, a recently proposed non-overlapping parallel algorithm is used to solve this three-dimensional canonical problem, having the unique property of not distinguishing between sequential and parallel computing, using 4.19 billion points and a refined time step of 7.69 × 10 −8 sec. The problem achieves the required density gradient by considering two volumes of air at different temperatures (with a temperature difference of 200K) separated by a non-conducting, impermeable partition at the onset of the experiment, which is removed impulsively at t = 0. The resulting buoyancy force at the interface acting from top to bottom is the seed of the baroclinic instability. Present high precision computation enables one to capture the ensuing RTI triggered by ultrasonic waves created at the interface.

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Effects of Error on the Onset and Evolution of Rayleigh–Taylor Instability

Sengupta

et al. 2017

Notes on Numerical Fluid Mechanics and Multidisciplinary Design

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Here we investigate effects of error in simulating Rayleigh Taylor instability (RTI). The error metrics are evaluated based on the correct spectral analysis of a model equation by Sengupta et al. (J Comput Phys 226:1211-1218, 2007) [13]. The geometry for RTI consists of a rectangular box with a partition at mid-height separating two volumes of air kept at a temperature difference of 70 K. This helps avoiding Boussinesq approximation and the present time-accurate computations for compressible Navier-Stokes equation (NSE) in 2D are reported. Computations for CFL numbers of 0.09 and 0.009 shows completely different onset of RTI, while the terminal mixed stage appears similar. The difference is traced to very insignificant difference in the value of numerical amplification factor for the two CFL numbers.

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Non-equilibrium Thermodynamics of Rayleigh–Taylor Instability

Cited by 10 publications

References 27 publications

Polarimetric Detection of Exoplanets Transiting T and L Brown Dwarfs

Polarimetric Detection of Exoplanets Transiting T and L Brown Dwarfs

Ultrasound Triggering of Rayleigh-Taylor Instability: Solution of Compressible Navier-Stokes Equation by a Non-Overlapping Parallel Compact Scheme

Effects of Error on the Onset and Evolution of Rayleigh–Taylor Instability

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