Shear instability of differential rotation in stars

Watson, M. J.

doi:10.1080/03091928008243663

Cited by 76 publications

(45 citation statements)

References 17 publications

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“…see Gilman 2000;Brummell et al 2002;Rogers & Glazmaier 2005), or by instabilities (e.g. see Watson 1981;Charbonneau et al 1999) -, we demonstrated how turbulence level and transport are reduced via shearing in a non-trivial manner (see also Burrell 1997;Kim 2004 in a simplified three-dimensional (3D) hydrodynamic turbulence. In particular, turbulent transport of chemical species and angular momentum are shown to become strongly anisotropic with much more efficient transport in the horizontal (latitudinal) direction than in the vertical (radial) direction due to shear stabilisation by a strong radial shear.…”

Section: Introductionmentioning

confidence: 99%

Self-consistent theory of turbulent transport in the solar tachocline

Kim¹,

Leprovost²

2007

A&A

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Aims. To understand the fundamental physical processes important for the evolution of solar rotation and distribution of chemical species, we provide theoretical predictions for particle mixing and momentum transport in the stably stratified tachocline. Methods. By envisioning that turbulence is driven in the tachocline, we compute the amplitude of turbulent flow, turbulent particle diffusivities, and eddy viscosity, by incorporating the effect of a strong radial differential rotation and stable stratification. We identify the different roles that the shear flow and stable stratification play in turbulence regulation and transport. Results. Particle transport is found to be severely quenched due to stable stratification, as well as radial differential rotation, especially in the radial direction with an effectively more efficient horizontal transport. The eddy viscosity is shown to become negative for parameter values typical of the tachocline, suggesting that turbulence in the stably stratified tachocline leads to a non-uniform radial differential rotation. Similar results also hold in the radiative interiors of stars, in general.

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Section: Introductionmentioning

confidence: 99%

Self-consistent theory of turbulent transport in the solar tachocline

Kim¹,

Leprovost²

2007

A&A

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“…Since this is rapid compared to thermal adjustment times, each set uniformly heats a low-latitude ring at the radial distances of its hot spots. Such rings can be dynamically unstable to horizontal turbulence (Watson 1981;Spiegel & Zahn 1992) and probably become warm shells. A likely observation of a warm ring or shell is discussed in Section 4.1.…”

Section: Rotation Rates and Overlappingmentioning

confidence: 99%

EFFECTS OF A DEEP MIXED SHELL ON SOLARg-MODES,p-MODES, AND NEUTRINO FLUX

Wolff

2009

ApJ

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A mixed-shell model that reflects g-modes away from the Sun's center is developed further by calibrating its parameters and evaluating a mixing mechanism: buoyancy. The shell roughly doubles g-mode oscillation periods and would explain why there is no definitive detection of their periods. But the shell has only minor effects on most p-modes. The model provides a mechanism for causing short-term fluctuations in neutrino flux and makes plausible the correlations between this flux and solar activity levels. Relations are derived for a shell heated asymmetrically by transient increases in nuclear burning in small "hot spots." The size of these spots and the timing of a heating event are governed by sets( ) of standing asymptotic g-modes, coupled by a maximal principle that greatly enhances their excitation and concentrates power toward the equator, assisting the detection of higher-sets. Signals from all sets, except one, in the range 2 8 are identified by difference periods between consecutive radial states using the method of Garcia et al. and reinterpreting their latest spectrum. This confirms two detections of sets in a similar range of by their rotation rates. The mean radius of shell mixing is r m = 0.16 R , which improves an earlier independent estimate of 0.18 by the author. The shell may cause the unexplained dip in measured sound speed at its location. Another sound speed error, centered near 0.67 R , and reversing flows in the same place with a period originally near 1.3 yr suggest that the g-modes are depositing there about 3% of the solar luminosity. That implies the shell at r m is receiving a similar magnitude of power, which would be enough energy to mix the corresponding shell in a standard solar model in 10 7 yr.

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“…However, these works were restricted to the case where the mean flow is sheared in the vertical direction while our differential rotation profile is sheared in the horizontal direction. Using a different approach, Watson (1981) studied the stability of a conical rotation profile similar to ours with respect to non-axisymmetric wavelike perturbations, but was restricted to the case of two-dimensional Rossby waves with negligible radial velocity.…”

Section: Critical Layersmentioning

confidence: 99%

Tidal inertial waves in differentially rotating convective envelopes of low-mass stars

Guenel

Baruteau

Mathis

et al. 2016

A&A

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Context. Star-planet tidal interactions may result in the excitation of inertial waves in the convective region of stars. In low-mass stars, their dissipation plays a prominent role in the long-term orbital evolution of short-period planets. Turbulent convection can sustain differential rotation in their envelopes with an equatorial acceleration (as in the Sun) or deceleration, which can modify the propagation properties of the waves. Aims. We explore in this first paper the general propagation properties of free linear inertial waves in a differentially rotating homogeneous fluid inside a spherical shell. We assume that the angular velocity background flow depends on the latitudinal coordinate alone, close to what is expected in the external convective envelope of low-mass stars. Methods. We use an analytical approach in the inviscid case to get the dispersion relation, from which we compute the characteristic trajectories along which energy propagates. This allows us to study the existence of attractor cycles and infer the different families of inertial modes. We also use high-resolution numerical calculations based on a spectral method for the viscous problem. Results. We find that modes that propagate in the whole shell (D modes) behave the same way as with solid-body rotation. However, another family of inertial modes exists (DT modes), which can only propagate in a restricted part of the convective zone. Our study shows that they are less common than D modes and that the characteristic rays and shear layers often focus towards a wedge -or point-like attractor. More importantly, we find that for non-axisymmetric oscillation modes, shear layers may cross a corotation resonance with a local accumulation of kinetic energy. Their damping rate scales very differently from the value we obtain for standard D modes, and we show an example where it is independent of viscosity (Ekman number) in the astrophysical regime in which it is small.

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Shear instability of differential rotation in stars

Cited by 76 publications

References 17 publications

Self-consistent theory of turbulent transport in the solar tachocline

Self-consistent theory of turbulent transport in the solar tachocline

EFFECTS OF A DEEP MIXED SHELL ON SOLARg-MODES,p-MODES, AND NEUTRINO FLUX

Tidal inertial waves in differentially rotating convective envelopes of low-mass stars

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