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S. Mathis - One of the best experts on this subject based on the ideXlab platform.

  • horizontal shear instabilities in rotating stellar radiation zones ii effects of the full Coriolis Acceleration
    arXiv: Solar and Stellar Astrophysics, 2020
    Co-Authors: Junho Park, S. Mathis, V. Prat, Lisa Bugnet
    Abstract:

    Stellar interiors are the seat of efficient transport of angular momentum all along with their evolution. Understanding the dependence of the turbulent transport triggered by the shear instabilities due to the differential rotation in stellar radiation zones is mandatory. Indeed, it constitutes one of the cornerstones of the rotational transport and mixing theory which is implemented in stellar evolution codes to predict the rotational and chemical evolutions of stars. We investigate horizontal shear instabilities in stellar radiation zones by considering the full Coriolis Acceleration with both the dimensionless horizontal component $\tilde{f}$ and the vertical component $f$. We performed a linear stability analysis for a horizontal shear flow with a hyperbolic tangent profile, both numerically and asymptotically using the WKBJ approximation. As in the traditional approximation, we identified the inflectional and inertial instabilities. The inflectional instability is destabilized as $\tilde{f}$ increases and its maximum growth rate increases significantly, while the thermal diffusivity stabilizes the inflectional instability similarly to the traditional case. The inertial instability is also strongly affected; for instance, the inertially unstable regime is extended in the non-diffusive limit as $0turbulence is short enough to redistribute efficiently angular momentum and mix chemicals in the radiation zones.

  • The traditional approximation of rotation, including the centrifugal Acceleration for slightly deformed stars
    Astronomy and Astrophysics, 2019
    Co-Authors: S. Mathis, V. Prat
    Abstract:

    The Traditional Approximation of Rotation (TAR) is a treatment of the dynamical equations of rotating stably stratified fluids where the action of the Coriolis Acceleration along the direction of the entropy (and chemicals) stratification is neglected while assuming that the fluid motions are mostly horizontal because of their inhibition in the vertical direction by the buoyancy force. This leads to neglect the horizontal projection of the rotation vector in the equations for the dynamics of gravito-inertial waves (GIWs) that become separable as in the non-rotating case while they are not in the case with the full Coriolis Acceleration. This approximation has been broadly applied in stellar (and planetary) astrophysics to study low-frequency GIWs. TAR is built on the assumptions that the star is spherical (i.e. its centrifugal deformation is neglected) and uniformly rotating while an adiabatic treatment of the dynamics of the waves is adopted. However, it has been recently generalised with including the effects of a differential rotation. We aim to do a new generalisation that takes into account the centrifugal Acceleration in the case of moderately uniformly rotating deformed stars. As in the case of a differentially rotating spherical star, the problem becomes 2D but can be treated analytically if assuming the Cowling, anelastic and JWKB approximations, which are relevant for low-frequency GIWs. It allows us to derive a generalised Laplace tidal equation for the horizontal eigenfunctions and asymptotic wave periods that can be used to probe the structure and dynamics of rotating deformed stars thanks to asteroseismology. A first numerical exploration of its eigenvalues and horizontal eigenfunctions shows their variation as a function of the pseudo-radius for different rotation rates and frequencies and the development of avoided crossings.

  • Mode excitation by turbulent convection in rotating stars. I. Effect of uniform rotation
    Astronomy & Astrophysics, 2009
    Co-Authors: K. Belkacem, S. Mathis, Marie-jo Goupil, Reza Samadi
    Abstract:

    We focus on the influence of the Coriolis Acceleration on the stochastic excitation of oscillation modes in convective regions of rotating stars. Our aim is to estimate the asymmetry between excitation rates of prograde and retrograde modes. We extend the formalism derived for obtaining stellar $p$- and $g$-mode amplitudes (Samadi & Goupil 2001, Belkacem et al. 2008) to include the effect of the Coriolis Acceleration. We then study the special case of uniform rotation for slowly rotating stars by performing a perturbative analysis. This allows us to consider the cases of the Sun and the CoRoT target HD 49933. We find that, in the subsonic regime, the influence of rotation as a direct contribution to mode driving is negligible in front of the Reynolds stress contribution. In slow rotators, the indirect effect of the modification of the eigenfunctions on mode excitation is investigated by performing a perturbative analysis of the excitation rates. It turns out that the excitation of solar $p$ modes is affected by rotation with excitation rates asymmetries between prograde and retrograde modes of the order of several percents. Solar low-order $g$ modes are also affected by uniform rotation and their excitation rates asymmetries are found to reach up to 10 %. The CoRoT target HD 49933 is rotating faster than the Sun ($\Omega / \Omega_\odot \approx 8$) and we show that the resulting excitation rates asymmetry is about 10 % for the excitation rates of $p$ modes. We have then demonstrated that $p$ and $g$ mode excitation rates are modified by uniform rotation through the Coriolis Acceleration. Study of the effect of differential rotation is dedicated to a forthcoming paper.

  • Magneto‐Gravito‐Inertial waves in strongly stratified stellar interiors
    AIP Conference Proceedings, 2009
    Co-Authors: S. Mathis
    Abstract:

    Stellar radiation zones are stable strongly stratified rotating magnetic regions. The buoyancy force, the Coriolis Acceleration and the Lorentz force are thus ruling the gravity waves dynamics. In this work, we examine the behaviour of these waves in stellar interiors and we show how the approximations assumed in the non‐magnetic case (for gravito‐inertial waves) can be generalized.

Lisa Bugnet - One of the best experts on this subject based on the ideXlab platform.

  • Horizontal shear instabilities in rotating stellar radiation zones: II. Effects of the full Coriolis Acceleration
    Astronomy & Astrophysics, 2021
    Co-Authors: Junho Park, Stéphane Mathis, Vincent Prat, Lisa Bugnet
    Abstract:

    Context. Stellar interiors are the seat of efficient transport of angular momentum all along their evolution. In this context, understanding the dependence of the turbulent transport triggered by the instabilities of the vertical and horizontal shears of the differential rotation in stellar radiation zones as a function of their rotation, stratification, and thermal diffusivity is mandatory. Indeed, it constitutes one of the cornerstones of the rotational transport and mixing theory, which is implemented in stellar evolution codes to predict the rotational and chemical evolutions of stars. Aims. We investigate horizontal shear instabilities in rotating stellar radiation zones by considering the full Coriolis Acceleration with both the dimensionless horizontal Coriolis component f̃ and the vertical component f. Methods. We performed a linear stability analysis using linearized equations derived from the Navier-Stokes and heat transport equations in the rotating nontraditional f-plane. We considered a horizontal shear flow with a hyperbolic tangent profile as the base flow. The linear stability was analyzed numerically in wide ranges of parameters, and we performed an asymptotic analysis for large vertical wavenumbers using the Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) approximation for nondiffusive and highly-diffusive fluids. Results. As in the traditional f-plane approximation, we identify two types of instabilities: the inflectional and inertial instabilities. The inflectional instability is destabilized as f̃ increases and its maximum growth rate increases significantly, while the thermal diffusivity stabilizes the inflectional instability similarly to the traditional case. The inertial instability is also strongly affected; for instance, the inertially unstable regime is also extended in the nondiffusive limit as 0 < f < 1 + f̃ 2/N2, where N is the dimensionless Brunt-Väisälä frequency. More strikingly, in the high thermal diffusivity limit, it is always inertially unstable at any colatitude θ except at the poles (i.e., 0° < θ <  180°). We also derived the critical Reynolds numbers for the inertial instability using the asymptotic dispersion relations obtained from the WKBJ analysis. Using the asymptotic and numerical results, we propose a prescription for the effective turbulent viscosities induced by the inertial and inflectional instabilities that can be possibly used in stellar evolution models. The characteristic time of this turbulence is short enough so that it is efficient to redistribute angular momentum and to mix chemicals in stellar radiation zones.

  • Horizontal shear instabilities in rotating stellar radiation zones: II. Effects of the full Coriolis Acceleration
    arXiv: Solar and Stellar Astrophysics, 2020
    Co-Authors: Junho Park, Stéphane Mathis, Vincent Prat, Lisa Bugnet
    Abstract:

    Stellar interiors are the seat of efficient transport of angular momentum all along with their evolution. Understanding the dependence of the turbulent transport triggered by the shear instabilities due to the differential rotation in stellar radiation zones is mandatory. Indeed, it constitutes one of the cornerstones of the rotational transport and mixing theory which is implemented in stellar evolution codes to predict the rotational and chemical evolutions of stars. We investigate horizontal shear instabilities in stellar radiation zones by considering the full Coriolis Acceleration with both the dimensionless horizontal component $\tilde{f}$ and the vertical component $f$. We performed a linear stability analysis for a horizontal shear flow with a hyperbolic tangent profile, both numerically and asymptotically using the WKBJ approximation. As in the traditional approximation, we identified the inflectional and inertial instabilities. The inflectional instability is destabilized as $\tilde{f}$ increases and its maximum growth rate increases significantly, while the thermal diffusivity stabilizes the inflectional instability similarly to the traditional case. The inertial instability is also strongly affected; for instance, the inertially unstable regime is extended in the non-diffusive limit as $0

  • horizontal shear instabilities in rotating stellar radiation zones ii effects of the full Coriolis Acceleration
    arXiv: Solar and Stellar Astrophysics, 2020
    Co-Authors: Junho Park, S. Mathis, V. Prat, Lisa Bugnet
    Abstract:

    Stellar interiors are the seat of efficient transport of angular momentum all along with their evolution. Understanding the dependence of the turbulent transport triggered by the shear instabilities due to the differential rotation in stellar radiation zones is mandatory. Indeed, it constitutes one of the cornerstones of the rotational transport and mixing theory which is implemented in stellar evolution codes to predict the rotational and chemical evolutions of stars. We investigate horizontal shear instabilities in stellar radiation zones by considering the full Coriolis Acceleration with both the dimensionless horizontal component $\tilde{f}$ and the vertical component $f$. We performed a linear stability analysis for a horizontal shear flow with a hyperbolic tangent profile, both numerically and asymptotically using the WKBJ approximation. As in the traditional approximation, we identified the inflectional and inertial instabilities. The inflectional instability is destabilized as $\tilde{f}$ increases and its maximum growth rate increases significantly, while the thermal diffusivity stabilizes the inflectional instability similarly to the traditional case. The inertial instability is also strongly affected; for instance, the inertially unstable regime is extended in the non-diffusive limit as $0turbulence is short enough to redistribute efficiently angular momentum and mix chemicals in the radiation zones.

V. Prat - One of the best experts on this subject based on the ideXlab platform.

  • horizontal shear instabilities in rotating stellar radiation zones ii effects of the full Coriolis Acceleration
    arXiv: Solar and Stellar Astrophysics, 2020
    Co-Authors: Junho Park, S. Mathis, V. Prat, Lisa Bugnet
    Abstract:

    Stellar interiors are the seat of efficient transport of angular momentum all along with their evolution. Understanding the dependence of the turbulent transport triggered by the shear instabilities due to the differential rotation in stellar radiation zones is mandatory. Indeed, it constitutes one of the cornerstones of the rotational transport and mixing theory which is implemented in stellar evolution codes to predict the rotational and chemical evolutions of stars. We investigate horizontal shear instabilities in stellar radiation zones by considering the full Coriolis Acceleration with both the dimensionless horizontal component $\tilde{f}$ and the vertical component $f$. We performed a linear stability analysis for a horizontal shear flow with a hyperbolic tangent profile, both numerically and asymptotically using the WKBJ approximation. As in the traditional approximation, we identified the inflectional and inertial instabilities. The inflectional instability is destabilized as $\tilde{f}$ increases and its maximum growth rate increases significantly, while the thermal diffusivity stabilizes the inflectional instability similarly to the traditional case. The inertial instability is also strongly affected; for instance, the inertially unstable regime is extended in the non-diffusive limit as $0turbulence is short enough to redistribute efficiently angular momentum and mix chemicals in the radiation zones.

  • The traditional approximation of rotation, including the centrifugal Acceleration for slightly deformed stars
    Astronomy and Astrophysics, 2019
    Co-Authors: S. Mathis, V. Prat
    Abstract:

    The Traditional Approximation of Rotation (TAR) is a treatment of the dynamical equations of rotating stably stratified fluids where the action of the Coriolis Acceleration along the direction of the entropy (and chemicals) stratification is neglected while assuming that the fluid motions are mostly horizontal because of their inhibition in the vertical direction by the buoyancy force. This leads to neglect the horizontal projection of the rotation vector in the equations for the dynamics of gravito-inertial waves (GIWs) that become separable as in the non-rotating case while they are not in the case with the full Coriolis Acceleration. This approximation has been broadly applied in stellar (and planetary) astrophysics to study low-frequency GIWs. TAR is built on the assumptions that the star is spherical (i.e. its centrifugal deformation is neglected) and uniformly rotating while an adiabatic treatment of the dynamics of the waves is adopted. However, it has been recently generalised with including the effects of a differential rotation. We aim to do a new generalisation that takes into account the centrifugal Acceleration in the case of moderately uniformly rotating deformed stars. As in the case of a differentially rotating spherical star, the problem becomes 2D but can be treated analytically if assuming the Cowling, anelastic and JWKB approximations, which are relevant for low-frequency GIWs. It allows us to derive a generalised Laplace tidal equation for the horizontal eigenfunctions and asymptotic wave periods that can be used to probe the structure and dynamics of rotating deformed stars thanks to asteroseismology. A first numerical exploration of its eigenvalues and horizontal eigenfunctions shows their variation as a function of the pseudo-radius for different rotation rates and frequencies and the development of avoided crossings.

Wallace Woon-fong Leung - One of the best experts on this subject based on the ideXlab platform.

  • Flow and mixing in rotating zigzag microchannel
    Chemical Engineering Journal, 2013
    Co-Authors: Yong Ren, Wallace Woon-fong Leung
    Abstract:

    The flow and mixing in rotating zigzag microchannel was investigated experimentally and numerically with objective of improving mixing, which is largely due to recirculating crossflow in the cross-sectional plane of the channel and the bend connecting tilted channel segments. Unlike the conventional rotating radial channel, crossflow in the zigzag channel is highly intensified from a combination of: (a) centrifugal Acceleration component in the cross-sectional plane due to the inclined channel segments, (b) centrifugal Acceleration generating Görtler vortices at " channel bends" , and (c) Coriolis Acceleration. When the channel segment in the zigzag channel is inclined towards rotation direction (prograde), all three Accelerations are aligned intensifying the crossflow; however, when it is inclined opposite to rotation (retrograde), Coriolis Acceleration competes with the other two Accelerations producing complex flow. Unlike a stationary zigzag channel, flow in a rotating prograde bend with outlet in the direction of rotation further induces Coriolis Acceleration which adds onto the centrifugal Acceleration producing enhanced crossflow and mixing, vice versa for a retrograde bend. A numerical model has been developed accurately accounting for the interactions of throughflow, crossflow and material dispersion by diffusion and convection in a rotational platform. An experimental microfluidic platform with rotating zigzag microchannel has also been developed. Experimental results on mixing quality carried out at two rotation speeds compared well with prediction from the numerical model. The overall mixing quality of a rotating zigzag channel is much improved compared with that of a stationary zigzag channel and of a rotating radial channel, due to the intensified crossflow driven by the additional Acceleration components. A study on different bend angle on mixing quality in zigzag channel revealed that there is no optimal bend angle to achieve superior mixing enhancement, as a result of the complex flow pattern generated by the three competing Accelerations.Department of Mechanical Engineerin

  • Flow and Mixing in Rotating Zigzag Microchannel
    Chemical Engineering Journal, 2012
    Co-Authors: Yong Ren, Wallace Woon-fong Leung
    Abstract:

    Abstract The flow and mixing in rotating zigzag microchannel was investigated experimentally and numerically with objective of improving mixing, which is largely due to recirculating crossflow in the cross-sectional plane of the channel and the bend connecting tilted channel segments. Unlike the conventional rotating radial channel, crossflow in the zigzag channel is highly intensified from a combination of: (a) centrifugal Acceleration component in the cross-sectional plane due to the inclined channel segments, (b) centrifugal Acceleration generating Gortler vortices at “channel bends”, and (c) Coriolis Acceleration. When the channel segment in the zigzag channel is inclined towards rotation direction (prograde), all three Accelerations are aligned intensifying the crossflow; however, when it is inclined opposite to rotation (retrograde), Coriolis Acceleration competes with the other two Accelerations producing complex flow. Unlike a stationary zigzag channel, flow in a rotating prograde bend with outlet in the direction of rotation further induces Coriolis Acceleration which adds onto the centrifugal Acceleration producing enhanced crossflow and mixing, vice versa for a retrograde bend. A numerical model has been developed accurately accounting for the interactions of throughflow, crossflow and material dispersion by diffusion and convection in a rotational platform. An experimental microfluidic platform with rotating zigzag microchannel has also been developed. Experimental results on mixing quality carried out at two rotation speeds compared well with prediction from the numerical model. The overall mixing quality of a rotating zigzag channel is much improved compared with that of a stationary zigzag channel and of a rotating radial channel, due to the intensified crossflow driven by the additional Acceleration components. A study on different bend angle on mixing quality in zigzag channel revealed that there is no optimal bend angle to achieve superior mixing enhancement, as a result of the complex flow pattern generated by the three competing Accelerations.

Junho Park - One of the best experts on this subject based on the ideXlab platform.

  • Horizontal shear instabilities in rotating stellar radiation zones: II. Effects of the full Coriolis Acceleration
    Astronomy & Astrophysics, 2021
    Co-Authors: Junho Park, Stéphane Mathis, Vincent Prat, Lisa Bugnet
    Abstract:

    Context. Stellar interiors are the seat of efficient transport of angular momentum all along their evolution. In this context, understanding the dependence of the turbulent transport triggered by the instabilities of the vertical and horizontal shears of the differential rotation in stellar radiation zones as a function of their rotation, stratification, and thermal diffusivity is mandatory. Indeed, it constitutes one of the cornerstones of the rotational transport and mixing theory, which is implemented in stellar evolution codes to predict the rotational and chemical evolutions of stars. Aims. We investigate horizontal shear instabilities in rotating stellar radiation zones by considering the full Coriolis Acceleration with both the dimensionless horizontal Coriolis component f̃ and the vertical component f. Methods. We performed a linear stability analysis using linearized equations derived from the Navier-Stokes and heat transport equations in the rotating nontraditional f-plane. We considered a horizontal shear flow with a hyperbolic tangent profile as the base flow. The linear stability was analyzed numerically in wide ranges of parameters, and we performed an asymptotic analysis for large vertical wavenumbers using the Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) approximation for nondiffusive and highly-diffusive fluids. Results. As in the traditional f-plane approximation, we identify two types of instabilities: the inflectional and inertial instabilities. The inflectional instability is destabilized as f̃ increases and its maximum growth rate increases significantly, while the thermal diffusivity stabilizes the inflectional instability similarly to the traditional case. The inertial instability is also strongly affected; for instance, the inertially unstable regime is also extended in the nondiffusive limit as 0 < f < 1 + f̃ 2/N2, where N is the dimensionless Brunt-Väisälä frequency. More strikingly, in the high thermal diffusivity limit, it is always inertially unstable at any colatitude θ except at the poles (i.e., 0° < θ <  180°). We also derived the critical Reynolds numbers for the inertial instability using the asymptotic dispersion relations obtained from the WKBJ analysis. Using the asymptotic and numerical results, we propose a prescription for the effective turbulent viscosities induced by the inertial and inflectional instabilities that can be possibly used in stellar evolution models. The characteristic time of this turbulence is short enough so that it is efficient to redistribute angular momentum and to mix chemicals in stellar radiation zones.

  • Horizontal shear instabilities in rotating stellar radiation zones: II. Effects of the full Coriolis Acceleration
    arXiv: Solar and Stellar Astrophysics, 2020
    Co-Authors: Junho Park, Stéphane Mathis, Vincent Prat, Lisa Bugnet
    Abstract:

    Stellar interiors are the seat of efficient transport of angular momentum all along with their evolution. Understanding the dependence of the turbulent transport triggered by the shear instabilities due to the differential rotation in stellar radiation zones is mandatory. Indeed, it constitutes one of the cornerstones of the rotational transport and mixing theory which is implemented in stellar evolution codes to predict the rotational and chemical evolutions of stars. We investigate horizontal shear instabilities in stellar radiation zones by considering the full Coriolis Acceleration with both the dimensionless horizontal component $\tilde{f}$ and the vertical component $f$. We performed a linear stability analysis for a horizontal shear flow with a hyperbolic tangent profile, both numerically and asymptotically using the WKBJ approximation. As in the traditional approximation, we identified the inflectional and inertial instabilities. The inflectional instability is destabilized as $\tilde{f}$ increases and its maximum growth rate increases significantly, while the thermal diffusivity stabilizes the inflectional instability similarly to the traditional case. The inertial instability is also strongly affected; for instance, the inertially unstable regime is extended in the non-diffusive limit as $0

  • horizontal shear instabilities in rotating stellar radiation zones ii effects of the full Coriolis Acceleration
    arXiv: Solar and Stellar Astrophysics, 2020
    Co-Authors: Junho Park, S. Mathis, V. Prat, Lisa Bugnet
    Abstract:

    Stellar interiors are the seat of efficient transport of angular momentum all along with their evolution. Understanding the dependence of the turbulent transport triggered by the shear instabilities due to the differential rotation in stellar radiation zones is mandatory. Indeed, it constitutes one of the cornerstones of the rotational transport and mixing theory which is implemented in stellar evolution codes to predict the rotational and chemical evolutions of stars. We investigate horizontal shear instabilities in stellar radiation zones by considering the full Coriolis Acceleration with both the dimensionless horizontal component $\tilde{f}$ and the vertical component $f$. We performed a linear stability analysis for a horizontal shear flow with a hyperbolic tangent profile, both numerically and asymptotically using the WKBJ approximation. As in the traditional approximation, we identified the inflectional and inertial instabilities. The inflectional instability is destabilized as $\tilde{f}$ increases and its maximum growth rate increases significantly, while the thermal diffusivity stabilizes the inflectional instability similarly to the traditional case. The inertial instability is also strongly affected; for instance, the inertially unstable regime is extended in the non-diffusive limit as $0turbulence is short enough to redistribute efficiently angular momentum and mix chemicals in the radiation zones.