A mechanism for differential rotation based on angular momentum transport by compressible convection

Kichatinov, L. L.

doi:10.1080/03091928708210111

Cited by 39 publications

(16 citation statements)

References 18 publications

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“…Therefore, analytical theory by capturing shearing effect (such as quasi-linear theory with timedependent wavenumber) would be extremely useful in obtaining physical insights into the problem as well as guiding future computational investigations. We note that the previous works by Kichatinov and Rudiger and collaborators [17,18,19,20,21] using quasi-linear theory are valid only in the limit of weak shear. Forced sheared turbulence was proposed for the first time by [22] in the context of two-dimensional near-wall turbulence to explain the logarithmic dependence of the large scale velocity on the distance to the wall.…”

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confidence: 99%

Analytical theory of forced rotating sheared turbulence: The parallel case

Leprovost

Kim

2008

Phys. Rev. E

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Forced turbulence combined with the effect of rotation and shear flow is studied. In a previous paper [Leprovost and Kim, PRE in press (2008)], we considered the case where the shear and the rotation are perpendicular. Here, we consider the complementary case of parallel rotation and shear, elucidating how rotation and flow shear influence the generation of shear flow (e.g. the direction of energy cascade), turbulence level, transport of particles and momentum. We show that turbulence amplitude and transport are always quenched due to strong shear (ξ = νk 2 y /A ≪ 1, where A is the shearing rate, ν is the molecular viscosity and ky is a characteristic wave-number of small-scale turbulence), with stronger reduction in the direction of the shear than those in the perpendicular directions. In contrast with the case where rotation and shear are perpendicular, we found that rotation affects turbulence amplitude only for very rapid rotation (Ω ≫ A) where it reduces slightly the anisotropy due to shear flow. Also, concerning the transport properties of turbulence, we find that rotation affects only the transport of particle and only for rapid rotation, leading to an almost isotropic transport (whereas, in the case of perpendicular rotation and shear, rotation favors isotropic transport even for slow rotation). Furthermore, the interaction between the shear and the rotation is shown to give rise to non-diffusive flux of angular momentum (Λ-effect), even in the absence of external sources of anisotropy, which can provide a mechanism for the creation of shearing structures in astrophysical and geophysical systems.

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confidence: 99%

Analytical theory of forced rotating sheared turbulence: The parallel case

Leprovost

Kim

2008

Phys. Rev. E

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“…Starting from Navier-Stokes equation, it is possible to show that these fluxes arise when there is a cause of anisotropy in the system, either due to an anisotropic background turbulence (see [33] and references therein) or else due to inhomogeneities such as an underlying stratification. We will show that non trivial Λ-effect can result from an anisotropy induced by shear flow on the turbulence even when the driving force is isotropic, in contrast to the case without shear flow where this effect exists only for anisotropic forcing [32].…”

Section: B Main Objectives and Methodologymentioning

confidence: 99%

“…Therefore, analytical theory by capturing shearing effect (such as quasi-linear theory with timedependent wavenumber) would be extremely useful in obtaining physical insights into the problem as well as guiding future computational investigations. We note that the previous works by Kichatinov and Rudiger and collaborators [30,31,32,33,34] using quasi-linear theory are valid only in the limit of weak shear. We further note that physically, the local nonlinear interactions in Navier-Stokes equation can be captured by an external forcing [35,36].…”

Section: Rotating Turbulencementioning

confidence: 99%

Analytical theory of forced rotating sheared turbulence: The perpendicular case

Leprovost

Kim

2008

Phys. Rev. E

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Rotation and shear flows are ubiquitous features of many astrophysical and geophysical bodies. To understand their origin and effect on turbulent transport in these systems, we consider a forced turbulence and investigate the combined effect of rotation and shear flow on the turbulence properties. Specifically, we study how rotation and flow shear influence the generation of shear flow (e.g. the direction of energy cascade), turbulence level, transport of particles and momentum, and the anisotropy in these quantities. In all the cases considered, turbulence amplitude is always quenched due to strong shear (ξ = νk 2 y /A ≪ 1, where A is the shearing rate, ν is the molecular viscosity and ky is a characteristic wave-number of small-scale turbulence), with stronger reduction in the direction of the shear than those in the perpendicular directions. Specifically, in the large rotation limit (Ω ≫ A), they scale as A −1 and A −1 | ln ξ|, respectively, while in the weak rotation limit (Ω ≪ A), they scale as A −1 and A −2/3 , respectively. Thus, flow shear always leads to weak turbulence with an effectively stronger turbulence in the plane perpendicular to shear than in the shear direction, regardless of rotation rate. The anisotropy in turbulence amplitude is however weaker by a factor of ξ 1/3 | ln ξ| (∝ A −1/3 | ln ξ|) in the rapid rotation limit (Ω ≫ A) than that in weak rotation limit (Ω ≪ A) since rotation favors almost-isotropic turbulence. Compared to turbulence amplitude, particle transport is found to crucially depend on whether rotation is stronger or weaker than flow shear. When rotation is stronger than flow shear (Ω ≫ A), the transport is inhibited by inertial waves, being quenched inversely proportional to the rotation rate (i.e. ∝ Ω −1 ) while in the opposite case, it is reduced by shearing as A −1 . Furthermore, the anisotropy is found to be very weak in the strong rotation limit (by a factor of 2) while significant in the strong shear limit. The turbulent viscosity is found to be negative with inverse cascade of energy as long as rotation is sufficiently strong compared to flow shear (Ω ≫ A) while positive in the opposite limit of weak rotation (Ω ≪ A). Even if the eddy viscosity is negative for strong rotation (Ω ≫ A), flow shear, which transfers energy to small scales, has an interesting effect by slowing down the rate of inverse cascade with the value of negative eddy viscosity decreasing as |νT | ∝ A −2 for strong shear. Furthermore, the interaction between the shear and the rotation is shown to give rise to a novel non-diffusive flux of angular momentum (Λ-effect), even in the absence of external sources of anisotropy. This effect provides a mechanism for the existence of shearing structures in astrophysical and geophysical systems.

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“…Furthermore, Coriolis forces can give rise to the so-called Λ effect (similar to the α effect in dynamos) from the non-diffusive part of Reynolds stress which is proportional to the rotation itself if the background turbulence in the absence of Coriolis forces is anisotropic (e.g. Rüdiger 1983) or inhomogeneous (Kichatinov 1987). In the case of strong rotation, the Λ effect due to the anisotropy in the background turbulence also decreases as Ω −2 (Rüdiger 1983).…”

Section: Introductionmentioning

confidence: 99%

“…This effect of Coriolis forces has been studied in the context of the transport of angular momentum (e.g. Rüdiger 1983;Kichatinov 1987;Rüdiger 1989;Kichatinov & Rüdiger 1993) and heat (Rüdiger 1989;Kichatinov et al 1994;Kichatinov & Rüdiger 1995) in the convection zone to understand the prominent latitudinal differential rotation in that region. In particular, in the limit of strong rotation such that the rotation rate exceeds the background turbulence decorrelation rate, which is the case for the Sun and most single main-sequence stars (Basri 1985), the turbulent viscosity (eddy viscosity) and heat diffusivity are shown to be reduced inversely proportional to the average rotation rate Ω while their values parallel to the rotation axis are a factor of 2 and 4 larger than those in the perpendicular directions, respectively (e.g.…”

Section: Introductionmentioning

confidence: 99%

Self-consistent theory of turbulent transport in the solar tachocline

Kim¹

2005

A&A

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Abstract.We present a self-consistent theory of turbulent transport in the solar tachocline by taking into account the effect of the radial differential rotation on turbulent transport. We show that the shearing by the radial differential rotation leads to reduction in turbulent transport of particles and momentum and the amplitude of turbulent flow via shear stabilization. The degree of reduction depends on the direction as well as the quantity that is transported. Specifically, particle transport in the vertical (radial) direction, orthogonal to the shear flow, is reduced with the scaling ∝A −2 while it is less reduced in the horizonal plane with the scaling ∝A −4/3 . Here, A is shearing rate, representing the radial differential rotation. A similar, but weaker, anisotropy also develops in the amplitude of turbulent flow. The results suggest that the radial differential rotation in the tachocline can cause anisotropy in turbulence intensity and particle transport with weaker turbulence in the radial direction even in the absence of density stratification and even when the turbulence is mainly driven radially by plumes from the convection zone. We also assess the efficiency of the transport by a meridional circulation by taking into account the interaction with the radial differential rotation. Implications for mixing and angular momentum transport in the solar interior is discussed.

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A mechanism for differential rotation based on angular momentum transport by compressible convection

Cited by 39 publications

References 18 publications

Analytical theory of forced rotating sheared turbulence: The parallel case

Analytical theory of forced rotating sheared turbulence: The parallel case

Analytical theory of forced rotating sheared turbulence: The perpendicular case

Self-consistent theory of turbulent transport in the solar tachocline

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