Differential rotation and turbulent convection: A new Reynolds stress model and comparison with solar data

Canuto, V. M.; Minotti, F.; Schilling, Oleg

doi:10.1086/173986

Cited by 40 publications

(37 citation statements)

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“…4c), i.e., at considerably higher latitudes than predicted by Canuto et al (1994). Yet, we emphasize that in this latitudinal range the results based on the PLS sample are ambiguous (see the 10-deg bin sampling in Fig.…”

Section: Relationship Between ∆V Rot and V Mermentioning

confidence: 70%

“…In this respect it is worth comparing our results with some theoretical considerations. According to the model by Canuto et al (1994), the covariance ∆v rot v mer should have a maximum value at the latitude B ≈ 30…”

Section: Relationship Between ∆V Rot and V Mermentioning

confidence: 99%

“…beyond the maximum predicted by Canuto et al (1994). On the other hand, note that the "operational form" of the model by Canuto et al (1994), denoted as M5, utilizes several approximations (e.g., the meridional flow and the radial gradient of the rotational velocity are neglected), and it is not clear how much these approximations affect the predicted location of the extreme in the Q(B) dependence.…”

Section: Relationship Between ∆V Rot and V Mermentioning

confidence: 99%

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Properties of the solar velocity field indicated by motions of coronal bright points

Vršnak

Brajša

Wöhl³

et al. 2003

A&A

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Abstract. Full-disc solar images obtained with the Extreme Ultraviolet Imaging Telescope (EIT) on board the Solar and Heliospheric Observatory (SOHO) are used to analyse properties of the solar velocity field by tracing coronal bright points from June 4, 1998 to May 22, 1999. Rotation velocity residuals, meridional motions and their relationship are investigated. Zones of slow and fast rotation found in motions of coronal bright points are consistent with the pattern of torsional oscillations, indicating that the statistical velocity pattern of bright point motions reflects the large-scale plasma flows. A complex pattern of meridional motion is deduced: The equatorward flows are found to dominate at low (B < 10• ) and high (B > 40 • ) latitudes, whereas at mid-latitudes (B ≈ 10• −40 • ) a poleward flow is inferred. The complete data set shows no significant correlation between rotation residuals and meridional motions. However, when a subsample of coronal bright points including only the "point-like structures" (predominantly young bright points) is considered, a statistically significant correlation is found. On average, faster tracers show equatorward motion and the slower ones show poleward motion. Such a segregation is reflected in a statistically significant covariance of the rotation residuals and meridional velocities in the order of −1000 m 2 s −2 , revealing an equatorward transport of angular momentum. The negative value of the covariance is provided by the high velocity tail in the velocity distribution of point-like structures, representing less than 15% of the population. The latitude dependence of the covariance can be expressed as Q = −62 B + 200 m 2 s −2 covering the range B = 0 • -60• .

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Section: Relationship Between ∆V Rot and V Mermentioning

confidence: 70%

Section: Relationship Between ∆V Rot and V Mermentioning

confidence: 99%

Section: Relationship Between ∆V Rot and V Mermentioning

confidence: 99%

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Properties of the solar velocity field indicated by motions of coronal bright points

Vršnak

Brajša

Wöhl³

et al. 2003

A&A

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“…While the spectral information is lost in this Reynolds Stress formalism, the method is easy to apply to non-local and space-dependent problems and has the potential to treat stellar convective overshooting (Canuto 1993). The method has already been successfully applied to the planetary boundary layer (PBL) which is the seat of strong convection (Canuto et al 1994a) as well as to study the interaction between shear, vorticity and buoyancy at the surface of the sun (Canuto et al 1994b). Work is in progress (Gabriel 1996, Houdeck 1996 to apply the same method to the study of helioseismology.…”

Section: Discussionmentioning

confidence: 99%

Stellar Turbulent Convection: A Self‐consistent Model

Canuto

Goldman

Mazzitelli³

1996

ApJ

Self Cite

268

313

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We present a selfconsistent model for stellar turbulent convection which is similar in spirit to the CM model (Canuto & Mazzitelli 1991) since it accounts for the full spectrum of the turbulent eddies rather than only one eddy, as done in the mixing length theory (MLT). The model differs from the CM model in the treatment of the rate of energy input n s (k) from the source that generates the turbulence. In the present model, n s (k) is controlled by both the source and the turbulence it ultimately generates, thus ensuring a selfconsistent modeling of the turbulence. This improves the CM model in which n s (k) was taken to be equal to the growth rate of the linear unstable convective modes.However, since the formulation of a selfconsistent treatment is far from simple, we were forced to use a representation of the nonlinear interactions less complete than the one in the CM model. The ensuing equations were solved numerically for a wide range of convective efficiencies. The results are the convective flux, the mean square turbulent velocity, the root mean squared turbulent pressure and the turbulent viscosity.We implemented the model in the ATON stellar structure code and computed the evolution of a solar model. The results are generally similar to those of the CM model and thus quite different from the MLT. The present model requires a smaller overshoot into the upper radiative zone than does the CM model, -2 -in accord with recent empirical estimates. Application to POP II stars and comparison with the very metal-poor globular cluster M68 yields an age in the range 11 ÷ 12 Gyr. This is somewhat younger than the CM age, which in turn is younger than the corresponding MLT age, a result of possible cosmological interest.

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“…In particular, the first two combinations in (3c) gave the wrong sign in both hemispheres. Only the combination vorticity + buoyancy (3d) was able to reproduce the data (Canuto et al 1994), a conclusion that should be viewed as a useful hint when describing regimes removed from the surface. However, as already discussed, thus far all the solutions of the angular momentum equation, which yielded results in disagreement with helio data, were based on the same assumption, the first of (3c), which failed to reproduce the surface values of (3b).…”

Section: Previous Results Of the Rsm Modelmentioning

confidence: 97%

Stellar Mixing

Canuto

2011

A&A

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We present a formalism that provides the Reynolds stresses needed to solve the angular momentum equation. The traditional Reynolds stress model assumes that the only contribution comes from shear (a down-gradient flux), but this leads to an extraction of angular momentum from the interior that is far too small compared to what is required to explain the helio seismological data. An illustrative solution of the new Reynolds stress equations shows that the presence of vorticity in a stably stratified regime, such as the one in the radiative zone, contributes a new term to the angular momentum equation that has an up-gradient flux like the one provided by the IGW model (internal gravity waves). The time scale entailed by such a term may be of the same order of 10 7 yrs produced by the IGW model. It would be instructive to solve the new angular momentum equation together with the formalism developed in Paper III to study not only the solar angular momentum distribution vs. helio data, but also the evolution of elements such as 7 Li and 4 He. These results would allow a more quantitative assessment of the overall model. The complete model yields Reynolds stresses that include differential rotation, unstable/stable stratification, double diffusion, radiative losses (arbitrary Peclet number), and meridional currents.

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Differential rotation and turbulent convection: A new Reynolds stress model and comparison with solar data

Cited by 40 publications

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Properties of the solar velocity field indicated by motions of coronal bright points

Properties of the solar velocity field indicated by motions of coronal bright points

Stellar Turbulent Convection: A Self‐consistent Model

Stellar Mixing

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