Shear instabilities in a fully compressible polytropic atmosphere

Witzke, V.; Silvers, L. J.; Favier, Benjamin

doi:10.1051/0004-6361/201425285

Cited by 5 publications

(15 citation statements)

References 27 publications

(37 reference statements)

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“…Furthermore, the boundary conditions introduced in equation (5) restrict the shear profile to values of L u that will result in a low enough value of the z-derivative of u 0 at the boundaries. A visualisation of the general form of shear, density and temperature profiles used in this paper can be found in Witzke, Silvers & Favier (2015). The force term, F, in equation (2) aims to model external forces resulting from large-scale global effects (such as Reynolds stresses associated with thermal convection in global-scale calculations for example) that are not included in our local approach.…”

Section: Modelmentioning

confidence: 99%

“…This was achieved by changing U 0 = 0.07 and 1/L u = 60, and the dynamical viscosity was fixed to be 10 −5 . We compared the growth rate and the most unstable mode predicted by means of a linear stability analysis as used in Witzke et al (2015) to that found in all cases of the secular instability. Furthermore, we checked that the instability is a consequence of the destabilising mechanism at low Péclet numbers, by conducting test cases with the same dynamical viscosity as used in cases O to R but C k = 0.0002.…”

Section: Secular Instabilitymentioning

confidence: 99%

“…In addition, complex gas dynamics in stellar interiors is not only important for mixing processes but also plays a crucial role in magnetic field generation (see Miesch & Toomre 2009;Jones, Thompson & Tobias 2010). Therefore, ongoing research focuses on understanding possible hydrodynamical and magnetohydrodynamical instabilities leading to turbulence in various stellar regions (Rüdiger, Kitchatinov & Elstner 2012;Witzke, Silvers & Favier 2015;Garaud & Kulenthirarajah 2016). E-mail:Veronika.Witzke.1@city.ac.uk (VW); Lara.Silvers.1@city.ac.uk (LJS); Favier@irphe.univ-mrs.fr (BF) Main-sequence stars have common dynamical elements, such as large-scale shear flows resulting from differential rotation.…”

Section: Introductionmentioning

confidence: 99%

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Evolution and characteristics of forced shear flows in polytropic atmospheres: large and small Péclet number regimes

Witzke

Silvers

Favier

2018

Monthly Notices of the Royal Astronomical Society

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Complex mixing and magnetic field generation occurs within stellar interiors particularly where there is a strong shear flow. To obtain a comprehensive understanding of these processes, it is necessary to study the complex dynamics of shear regions. Due to current observational limitations, it is necessary to investigate the inevitable small-scale dynamics via numerical calculations. Here, we examine direct numerical calculations of a local model of unstable shear flows in a compressible polytropic fluid primarily in a two-dimensional domain, where we focus on determining how key parameters affect the global properties and characteristics of the resulting saturated turbulent phase. We consider the effect of varying both the viscosity and the thermal diffusivity on the non-linear evolution. Moreover, our main focus is to understand the global properties of the saturated phase, in particular estimating for the first time the spread of the shear region from an initially hyperbolic tangent velocity profile. We find that the vertical extent of the mixing region in the saturated regime is generally determined by the initial Richardson number of the system. Further, the characteristic quantities of the turbulence, i.e. typical length-scale and the root-mean-square velocity are found to depend on both the Richardson number, and the thermal diffusivity. Finally, we present our findings of our investigation into saturated flows of a 'secular' shear instability in the low Péclet number regime with large Richardson numbers.

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Section: Modelmentioning

confidence: 99%

Section: Secular Instabilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Evolution and characteristics of forced shear flows in polytropic atmospheres: large and small Péclet number regimes

Witzke

Silvers

Favier

2018

Monthly Notices of the Royal Astronomical Society

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“…We do not consider shear instabilities triggered by thermal diffusion for which larger values of Ri can be used (Dudis 1974;Zahn 1974;Lignières et al 1999). Because the 1/4 criterion is a necessary, but not sufficient, requirement for instability we also solve the corresponding linear stability problem based on the approach used in Witzke, Silvers & Favier (2015) in addition to conducting the non-linear calculations. For simplicity, the Prandtl number is fixed to be unity whereas the dimensionless thermal diffusivity C k is varied from 10 −4 to 10 −5 .…”

Section: Linear Regimementioning

confidence: 99%

“…For simplicity, the Prandtl number is fixed to be unity whereas the dimensionless thermal diffusivity C k is varied from 10 −4 to 10 −5 . Taking the previous linear study by Witzke, Silvers & Favier (2015) into account, our parameters satisfy the following requirements: To ensure a stable stratification the polytropic index is set to be m = 1.6, the amplitude U 0 of the shear flow is chosen such that the Mach number in the middle of the domain remains less than 0.08, which avoids additional stabilisation by compressible effects. Furthermore, we take the initial Péclet number, which we define as…”

Section: Linear Regimementioning

confidence: 99%

Evolution of forced shear flows in polytropic atmospheres: a comparison of forcing methods and energetics

Witzke¹,

Silvers²,

Favier³

2016

Mon. Not. R. Astron. Soc.

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Shear flows are ubiquitous in astrophysical objects including planetary and stellar interiors, where their dynamics can have significant impact on thermo-chemical processes. Investigating the complex dynamics of shear flows requires numerical calculations that provide a long time evolution of the system. To achieve a sufficiently long lifetime in a local numerical model the system has to be forced externally. However, at present, there exist several different forcing methods to sustain large-scale shear flows in local models. In this paper we examine and compare various methods used in the literature in order to resolve their respective applicability and limitations. These techniques are compared during the exponential growth phase of a shear flow instability, such as the Kelvin-Helmholtz (KH) instability, and some are examined during the subsequent non-linear evolution. A linear stability analysis provides reference for the growth rate of the most unstable modes in the system and a detailed analysis of the energetics provides a comprehensive understanding of the energy exchange during the system's evolution. Finally, we discuss the pros and cons of each forcing method and their relation with natural mechanisms generating shear flows.

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