The dynamics of stratified horizontal shear flows at low Péclet number

Cope, Laura; Garaud, Pascale; Caulfield, C. P.

doi:10.1017/jfm.2020.600

Cited by 24 publications

(29 citation statements)

References 61 publications

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“…They are now tested using direct numerical simulations devoted to the stellar regime (Prat & Lignières 2013Garaud et al 2017;Prat et al 2016;Gagnier & Garaud 2018;Kulenthirarajah & Garaud 2018). The horizontal turbulence induced by horizontal gradients of the differential rotation has only been examined in the stellar regime in a few works, which again use phenomenological arguments (Zahn 1992;Maeder 2003), results from lab experiments studying differentially rotating flows (Richard & Zahn 1999;), and first devoted numerical simulations (Cope et al 2020). The systematic study of the combined effect of stable stratification, rotation, and thermal diffusion in the stellar context has only been recently undertaken.…”

Section: Introductionmentioning

confidence: 99%

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Horizontal shear instabilities in rotating stellar radiation zones

Park

Prat

Mathis

et al. 2021

A&A

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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.

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Section: Introductionmentioning

confidence: 99%

“…The behavior of the turbulence generated by horizontal shears has been recently explored in the nonrotating case by Cope et al (2020) and Garaud (2020). They find when exploring the parameter space using Direct Numerical Simulations (DNS) a turbulent stratified regime where the turbulent transport can be modeled by an eddy diffusivity.…”

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confidence: 99%

Horizontal shear instabilities in rotating stellar radiation zones

Park

Prat

Mathis

et al. 2021

A&A

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“…This corresponds to an anti-diffusive transport of angular momentum. Cope et al (2020) and Garaud (2020) estimated the vertical turbulent diffusion coefficient associated with the horizontal shear instability using scaling laws but they did not provide any proof that the transport of chemical elements is indeed diffusive. In addition, they did not discuss the transport of angular momentum.…”

Section: Discussionmentioning

confidence: 99%

“…Concerning the horizontal diffusion coefficient, since the inital model of Zahn (1992) that was based on phenomenological arguments, other models based on energetic arguments (Maeder 2003) or results of an unstratified Taylor-Couette experiment ) have been proposed, but this coefficient is still poorly constrained, and its impact on stellar evolution is clearly overlooked. The first numerical simulations of the turbulent transport triggered by the instabilities of a horizontal shear in stellar conditions have also been performed (Cope et al 2020;Garaud 2020). Finally, Park et al (2020Park et al ( , 2021 studied the linear instabilities of the horizontal differential rotation in stellar radiation zones as a function of stratification, rotation, and thermal diffusivity.…”

Section: Introductionmentioning

confidence: 99%

Anisotropic turbulent transport with horizontal shear in stellar radiative zones

Prat

Mathis

2021

A&A

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Context. Turbulent transport in stellar radiative zones is a key ingredient of stellar evolution theory, but the anisotropy of the transport due to the stable stratification and the rotation of these regions is poorly understood. The assumption of shellular rotation, which is a cornerstone of the so-called rotational mixing, relies on an efficient horizontal transport. However, this transport is included in many stellar evolution codes through phenomenological models that have never been tested. Aims. We investigate the impact of horizontal shear on the anisotropy of turbulent transport. Methods. We used a relaxation approximation (also known as τ approximation) to describe the anisotropising effect of stratification, rotation, and shear on a background turbulent flow by computing velocity correlations. Results. We obtain new theoretical scalings for velocity correlations that include the effect of horizontal shear. These scalings show an enhancement of turbulent motions, which would lead to a more efficient transport of chemicals and angular momentum, in better agreement with helio- and asteroseismic observations of rotation in the whole Hertzsprung-Russell diagram. Moreover, we propose a new choice for the non-linear time used in the relaxation approximation, which characterises the source of the turbulence. Conclusions. For the first time, we describe the effect of stratification, rotation, and vertical and horizontal shear on the anisotropy of turbulent transport in stellar radiative zones. The new prescriptions need to be implemented in stellar evolution calculations. To do so, it may be necessary to implement non-diffusive transport.

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“…Of course, much more work remains to be done before one can gain a complete understanding of shear instabilities and GSF instabilities in stars. In particular, the present study was limited to the equatorial region of a star, and the dynamics away from the equator are known to be substantially different, both for the GSF instability (Knobloch & Spruit 1982;Barker et al 2020), and for the shear instability (Cope et al 2020;Garaud 2020b). In the former case, Barker et al (2020) found that the GSF instability criterion is relaxed compared with (5), and that angular momentum layering can lead to a vast increase in the turbulent transport coefficient.…”

Section: Summary and Discussionmentioning

confidence: 99%

Modeling coexisting GSF and shear instabilities in rotating stars

Chang,

Garaud

2021

Preprint

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Zahn's widely-used model for turbulent mixing induced by rotational shear has recently been validated (with some caveats) in non-rotating shear flows. It is not clear, however, whether his model remains valid in the presence of rotation, even though this was its original purpose. Furthermore, new instabilities arise in rotating fluids, such as the Goldreich-Schubert-Fricke (GSF) instability. Which instability dominates when more than one can be excited, and how they influence each other, were open questions that this paper answers. To do so, we use direct numerical simulations of diffusive stratified shear flows in a rotating triply-periodic Cartesian domain located at the equator of a star. We find that either the GSF instability or the shear instability tends to take over the other in controlling the system, suggesting that stellar evolution models only need to have a mixing prescription for each individual instability, together with a criterion to determine which one dominates. However, we also find that it is not always easy to predict which instability "wins" for given input parameters, because the diffusive shear instability is subcritical, and only takes place if there is a finite-amplitude turbulence "primer" to seed it. Interestingly, we find that the GSF instability can in some cases play the role of this primer, thereby providing a pathway to excite the subcritical shear instability. This can also drive relaxation oscillations, that may be observable. We conclude by proposing a new model for mixing in the equatorial regions of stellar radiative zones due to differential rotation.

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The dynamics of stratified horizontal shear flows at low Péclet number

Abstract: Abstract

Cited by 24 publications

References 61 publications

Horizontal shear instabilities in rotating stellar radiation zones

Horizontal shear instabilities in rotating stellar radiation zones

Anisotropic turbulent transport with horizontal shear in stellar radiative zones

Modeling coexisting GSF and shear instabilities in rotating stars

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