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M Rieutord - One of the best experts on this subject based on the ideXlab platform.
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gravito inertial modes in a differentially rotating Spherical Shell
EPJ Web of Conferences, 2015Co-Authors: M Rieutord, G M Mirouh, Clement Baruteau, J BallotAbstract:While many intermediate- and high-mass main sequence stars are rapidly and differentially rotating, the effects of rotation on oscillation modes are poorly known. In this communication we present a first study of axisymmetric gravito-inertial modes in the radiative zone of a differentially rotating star. We consider a simplified model where the radiative zone of the star is a linearly stratified rotating fluid within a Spherical Shell, with differential rotation due to baroclinic effects. We solve the eigenvalue problem with high-resolution spectral computations and determine the propagation domain of the waves through the theory of characteristics. We explore the propagation properties of two kinds of modes: those that can propagate in the entire Shell and those that are restricted to a sub-domain. Some of the modes that we find concentrate kinetic energy around short-period shear layers known as attractors. We describe various geometries for the propagation domains, conditioning the surface visibility of the corresponding modes.
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gravito inertial modes in a differentially rotating Spherical Shell
SF2A-2014: Proceedings of the Annual meeting of the French Society of Astronomy and Astrophysics, 2014Co-Authors: M Rieutord, G M Mirouh, Clement Baruteau, J BallotAbstract:The gravito-inertial waves propagating over a Shellular baroclinic flow inside a rotating Spherical Shell are analysed using the Boussinesq approximation. The wave properties are examined by computing paths of characteristics in the non-dissipative limit, and by solving the full dissipative eigenvalue problem using a high-resolution spectral method. Gravito-inertial waves are found to obey a mixed-type second-order operator and to be often focused around short-period attractors of characteristics or trapped in a wedge formed by turning surfaces and boundaries. We also find eigenmodes that show a weak dependence with respect to viscosity and heat diffusion just like truly regular modes. Some axisymmetric modes are found unstable and likely destabilized by baroclinic instabilities. Similarly, some non-axisymmetric modes that meet a critical layer (or corotation resonance) can turn unstable at sufficiently low diffusivities. In all cases, the instability is driven by the differential rotation. For many modes of the spectrum, neat power laws are found for the dependence of the damping rates with diffusion coefficients, but the theoretical explanation for the exponent values remains elusive in general. The eigenvalue spectrum turns out to be very rich and complex, which lets us suppose an even richer and more complex spectrum for rotating stars or planets that own a differential rotation driven by baroclinicity.
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inertial waves in a differentially rotating Spherical Shell
Journal of Fluid Mechanics, 2013Co-Authors: Clement Baruteau, M RieutordAbstract:We investigate the properties of small-amplitude inertial waves propagating in a differentially rotating incompressible fluid contained in a Spherical Shell. For cylindrical and Shellular rotation profiles and in the inviscid limit, inertial waves obey a second-order partial differential equation of mixed type. Two kinds of inertial modes therefore exist, depending on whether the hyperbolic domain where characteristics propagate covers the whole Shell or not. The occurrence of these two kinds of inertial modes is examined, and we show that the range of frequencies at which inertial waves may propagate is broader than with solid-body rotation. Using high-resolution calculations based on a spectral method, we show that, as with solid-body rotation, singular modes with thin shear layers following short-period attractors still exist with differential rotation. They exist even in the case of a full sphere. In the limit of vanishing viscosities, the width of the shear layers seems to weakly depend on the global background shear, showing a scaling in with the Ekman number , as in the solid-body rotation case. There also exist modes with thin detached layers of width scaling with as Ekman boundary layers. The behaviour of inertial waves with a corotation resonance within the Shell is also considered. For cylindrical rotation, waves get dramatically absorbed at corotation. In contrast, for Shellular rotation, waves may cross a critical layer without visible absorption, and such modes can be unstable for small enough Ekman numbers.
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inertial waves in a differentially rotating Spherical Shell
arXiv: Solar and Stellar Astrophysics, 2012Co-Authors: Clement Baruteau, M RieutordAbstract:We investigate the properties of small-amplitude inertial waves propagating in a differentially rotating incompressible fluid contained in a Spherical Shell. For cylindrical and Shellular rotation profiles and in the inviscid limit, inertial waves obey a second-order partial differential equation of mixed type. Two kinds of inertial modes therefore exist, depending on whether the hyperbolic domain where characteristics propagate covers the whole Shell or not. The occurrence of these two kinds of inertial modes is examined, and we show that the range of frequencies at which inertial waves may propagate is broader than with solid-body rotation. Using high-resolution calculations based on a spectral method, we show that, as with solid-body rotation, singular modes with thin shear layers following short-period attractors still exist with differential rotation. They exist even in the case of a full sphere. In the limit of vanishing viscosities, the width of the shear layers seems to weakly depend on the global background shear, showing a scaling in E^{1/3} with the Ekman number E, as in the solid-body rotation case. There also exist modes with thin detached layers of width scaling with E^{1/2} as Ekman boundary layers. The behavior of inertial waves with a corotation resonance within the Shell is also considered. For cylindrical rotation, waves get dramatically absorbed at corotation. In contrast, for Shellular rotation, waves may cross a critical layer without visible absorption, and such modes can be unstable for small enough Ekman numbers.
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gravito inertial waves in a rotating stratified sphere or Spherical Shell
Journal of Fluid Mechanics, 1999Co-Authors: B Dintrans, M Rieutord, Lorenzo ValdettaroAbstract:The properties of gravito-inertial waves propagating in a stably stratified rotating Spherical Shell or sphere are investigated using the Boussinesq approximation. In the perfect fluid limit, these modes obey a second-order partial differential equation of mixed type. Characteristics propagating in the hyperbolic domain are shown to follow three kinds of orbits: quasi-periodic orbits which cover the whole hyperbolic domain; periodic orbits which are strongly attractive; and finally, orbits ending in a wedge formed by one of the boundaries and a turning surface. To these three types of orbits, our calculations show that there correspond three kinds of modes and give support to the following conclusions. First, with quasi-periodic orbits are associated regular modes which exist at the zero-diffusion limit as smooth square-integrable velocity fields associated with a discrete set of eigenvalues, probably dense in some subintervals of [0,N], N being the Brunt-Vaisala frequency. Second, with periodic orbits are associated singular modes which feature a shear layer following the periodic orbit; as the zero-diffusion limit is taken, the eigenfunction becomes singular on a line tracing the periodic orbit and is no longer square-integrable; as a consequence the point spectrum is empty in some subintervals of [0,N]. It is also shown that these internal shear layers contain the two scales E 1/3 and E 1/4 as pure inertial modes (E is the Ekman number). Finally, modes associated with characteristics trapped by a wedge also disappear at the zero-diffusion limit; eigenfunctions are not square-integrable and the corresponding point spectrum is also empty.
Longshi Rao - One of the best experts on this subject based on the ideXlab platform.
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improvement in luminous efficacy and thermal performance using quantum dots Spherical Shell for white light emitting diodes
Nanomaterials, 2018Co-Authors: Songmao Chen, Caiman Yan, Yong Tang, Xinrui Ding, Longshi RaoAbstract:White light-emitting diodes (WLEDs) based on quantum dots (QDs) are gaining increasing attention due to their excellent color quality. QDs films with planar structure are universally applied in WLEDs for color conversion, while they still face great challenges in high light extraction and thermal stability. In this study, a QDs film with a Spherical Shell structure was proposed to improve the optical and thermal performance for WLEDs. Compared with the conventional planar structure, the luminous efficacy of the QDs Spherical Shell structure is improved by 12.9% due to the reduced total reflection effect, and the angular-dependent correlated color temperature deviation is decreased from 2642 to 283 K. Moreover, the highest temperature of the WLED using a QDs Spherical Shell is 4.8 °C lower than that of the conventional WLED with a planar structure, which is mainly attributed to larger heat dissipation area and separated heat source. Consequently, this QDs Spherical Shell structure demonstrates superior performance of QDs films for WLEDs applications.
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Improvement in Luminous Efficacy and Thermal Performance Using Quantum Dots Spherical Shell for White Light Emitting Diodes
MDPI AG, 2018Co-Authors: Songmao Chen, Caiman Yan, Yong Tang, Xinrui Ding, Longshi RaoAbstract:White light-emitting diodes (WLEDs) based on quantum dots (QDs) are gaining increasing attention due to their excellent color quality. QDs films with planar structure are universally applied in WLEDs for color conversion, while they still face great challenges in high light extraction and thermal stability. In this study, a QDs film with a Spherical Shell structure was proposed to improve the optical and thermal performance for WLEDs. Compared with the conventional planar structure, the luminous efficacy of the QDs Spherical Shell structure is improved by 12.9% due to the reduced total reflection effect, and the angular-dependent correlated color temperature deviation is decreased from 2642 to 283 K. Moreover, the highest temperature of the WLED using a QDs Spherical Shell is 4.8 °C lower than that of the conventional WLED with a planar structure, which is mainly attributed to larger heat dissipation area and separated heat source. Consequently, this QDs Spherical Shell structure demonstrates superior performance of QDs films for WLEDs applications
Masahisa Tabata - One of the best experts on this subject based on the ideXlab platform.
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finite element approximation to infinite prandtl number boussinesq equations with temperature dependent coefficients thermal convection problems in a Spherical Shell
Future Generation Computer Systems, 2006Co-Authors: Masahisa TabataAbstract:A stabilized finite element scheme for infinite Prandtl number Boussinesq equations with temperature-dependent coefficients is analyzed. The domain is a Spherical Shell and the P1-element is employed for every unknown function. The finite element solution is proved to converge to the exact one in the first order of the time increment and the mesh size. The scheme is applied to Earth's mantle convection problems with viscosities strongly dependent on the temperature and some numerical results are shown.
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a stabilized finite element method for the rayleigh benard equations with infinite prandtl number in a Spherical Shell
Computer Methods in Applied Mechanics and Engineering, 2000Co-Authors: Masahisa Tabata, Atsushi SuzukiAbstract:Abstract A finite element scheme is developed and analyzed for a thermal convection problem of Boussinesq fluid with infinite Prandtl number in a Spherical Shell. This problem is a mathematical model of the Earth's mantle movement and has been a topic of interest for geophysicists. It is described by the Rayleigh–Benard equations with infinite Prandtl number, that is, a system of the Stokes equations and the convection–diffusion equation coupled with the buoyancy and the convection terms. A stabilized finite element scheme with P1/P1/P1 element is presented, and an error estimate is established. The obtained theoretical convergence order is also recognized by a numerical result. Another numerical result is shown as an example of the Earth's mantle movement simulation.
K P Rao - One of the best experts on this subject based on the ideXlab platform.
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failure analysis of laminated composite cylindrical Spherical Shell panels subjected to low velocity impact
Computers & Structures, 1998Co-Authors: S Ganapathy, K P RaoAbstract:Abstract A 4-noded, 48 d.o.f. doubly curved quadrilateral Shell finite element based on Kirchhoff–Love Shell theory, is used in the nonlinear finite element analysis to predict the damage of laminated composite cylindrical/Spherical Shell panels subjected to low-velocity impact. The large displacement stiffness matrix is formed using Green's strain tensor based on total Lagrangian approach. An incremental/iterative scheme is used for solving resulting nonlinear algebraic equations by Newton–Raphson method. The damage analysis is performed by applying Tsai–Wu quadratic failure criterion at all Gauss points and the mode of failure is identified using maximum stress criteria. The modes of failure considered are fiber breakage and matrix cracking. The progressive failure analysis is carried out by degrading the stiffness of the material suitably at all failed Gauss points. The load due to low-velocity impact is treated as an equivalent quasi-static load and Hertzian law of contact is used for finding the maximum contact force. After evaluating the nonlinear finite element analysis thoroughly for typical problems, damage analysis was carried out for cross-ply and quasi-isotropic cylindrical/Spherical Shell panels.
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interlaminar stresses in laminated composite plates cylindrical Spherical Shell panels damaged by low velocity impact
Composite Structures, 1997Co-Authors: S Ganapathy, K P RaoAbstract:Prediction of damage caused by low-velocity impact in laminated composite plate cylindrical/Spherical Shell panels is an important problem faced by designers using composites. Not only the in-plane stresses but also the interlaminar normal and shear stresses play a role in estimating the damage caused. The work reported here is an effort in getting better predictions of damage in composite plate cylindrical/Spherical Shell panels subjected to low velocity impact. The low-velocity impact problem is treated as a quasi-static problem. First, the in-plane stresses are calculated by 2-D nonlinear finite element analysis using a 48 degrees of freedom laminated composite Shell element. The damage analysis is then carried out using a Tsai-Wu quadratic failure criterion and a maximum stress criteria. Interlaminar normal and shear stresses are predicted after taking into account the in-plane damage caused by low velocity impact. The interlaminar stresses are obtained by integrating the 3-D equations of equilibrium through the thickness. The deformed geometry is taken into account in the third equation of equilibrium (in the thickness direction). After evaluating the formulation and the computer program developed for correctness, the interlaminar stresses are predicted for composite plates/Shell panels which are damaged by low-velocity impact
Bing Zhang - One of the best experts on this subject based on the ideXlab platform.
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on the curvature effect of a relativistic Spherical Shell
The Astrophysical Journal, 2015Co-Authors: Lucas Z Uhm, Bing ZhangAbstract:We consider a relativistic Spherical Shell and calculate its spectral flux as received by a distant observer. Using two different methods, we derive a simple analytical expression of the observed spectral flux and show that the well-known relation (between temporal index and spectral index ) of the high-latitude emission is naturally achieved in our derivation but holds only when the Shell moves with a constant Lorentz factor Γ. Presenting numerical models in which the Shell is undergoing acceleration or deceleration, we show that the simple relation does indeed deviate as long as Γ is not constant. For the models under acceleration, we find that the light curves produced purely by the high-latitude emission initially exhibit much steeper decay than in the constant Γ case and gradually resume the relation in about one and a half orders of magnitude in observer time. For the models under deceleration, the trend is opposite. The light curves made purely by the high-latitude emission initially exhibit a shallower decay than in the constant Γ case and gradually resume the relation in a similar order of magnitude in observer time. We also show that how fast the Lorentz factor Γ of the Shell increases or decreases is the main ingredient determining the initial steepness or shallowness of the light curves.
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on the curvature effect of a relativistic Spherical Shell
arXiv: High Energy Astrophysical Phenomena, 2014Co-Authors: Lucas Z Uhm, Bing ZhangAbstract:We consider a relativistic Spherical Shell and calculate its spectral flux as received by a distant observer. Using two different methods, we derive a simple analytical expression of the observed spectral flux and show that the well-known relation $\hat \alpha = 2+\hat \beta$ (between temporal index $\hat \alpha$ and spectral index $\hat \beta$) of the high-latitude emission is achieved naturally in our derivation but holds only when the Shell moves with a constant Lorentz factor $\Gamma$. Presenting numerical models where the Shell is under acceleration or deceleration, we show that the simple $\hat \alpha = 2+\hat \beta$ relation is indeed deviated as long as $\Gamma$ is not constant. For the models under acceleration, we find that the light curves produced purely by the high-latitude emission decay initially much steeper than the constant $\Gamma$ case and gradually resume the $\hat \alpha = 2+\hat \beta$ relation in about one and half orders of magnitude in observer time. For the models under deceleration, the trend is opposite. The light curves made purely by the high-latitude emission decay initially shallower than the constant $\Gamma$ case and gradually resume the relation $\hat \alpha = 2+\hat \beta$ in a similar order of magnitude in observer time. We also show that how fast the Lorentz factor $\Gamma$ of the Shell increases or decreases is the main ingredient determining the initial steepness or shallowness of the light curves.
