Rotating convective turbulence in Earth and planetary cores

TLDR: In this paper, a closely coupled suite of advanced asymptotically-reduced theoretical models, efficient Cartesian direct numerical simulations (DNS) and laboratory experiments are presented.

About: This article is published in Physics of the Earth and Planetary Interiors.The article was published on 2015-09-01 and is currently open access. It has received 156 citations till now. The article focuses on the topics: Planetary core & Convection.

Figures

Fig. 3. Comparison of outer boundary radial magnetic field intensities, BrðroÞ, from two dynamo simulations carried out in Sreenivasan (2010). (a) More moderate case carried out with E ¼ 5 10 5; Ra=Racrit ¼ 11; Pr ¼ Pm ¼ 1. (b) More extreme case with E ¼ 1:5 10 6; Ra=Racrit ¼ 50; Pr ¼ 1, and Pm ¼ 0:1. In both images, red (blue) denotes positive (negative) values. Image adapted from Sreenivasan (2010).

Fig. 7. Snapshot visualizations showing the cellular, Taylor column, plume and geostrophic turbulence regimes, as defined in Sprague et al. (2006) and Julien et al. (2012b). Top row: flake visualizations from the laboratory experiments made in Cheng et al. (2015). Bottom row: temperature fluctuation field h from the non-slip DNS cases in Stellmach et al. (2014).

Fig. 12. Large-scalevortices (LSVs) in rotating, three-dimensional convection. (a)Renderingof axial vorticityfield, f, fromfree-slipDNScarriedout atE ¼ 10 7; Pr ¼ 1; Ra=Racrit ¼ 10:4, and computational domain width W ’ 20‘conv . Adapted from Stellmach et al. (2014). (b) Axial vorticity field from the reduced model carried out at Pr ¼ 1; Ra=Racrit ¼ 11:5, and W ’ 40‘conv . Adapted fromRubio et al. (2014). (c and d) Axial integrations of f frompanel a and b, respectively. The color scheme is the same as in Fig. 1c, but the scaling ranges all differ.

Fig. 4. (Left) Schematic view of Earth’s interior. The coloration represents the buoyancy gradient that drives thermo-compositional convection in the iron-rich outer core fluid. (Right) Snapshot image of a laboratory rotating thermal convection experiment. Qualitatively similar to a polar region in the core (e.g., Sreenivasan and Jones, 2006a), the gravity and rotation and buoyancy gradient vectors are all axial. A laser light sheet hitting reflective flakes shows the shear structures in the rotating convective flow. Here the adverse temperature gradient is represented by the coloration, with vermilion (aquamarine) representing the warmer (cooler) fluid. Image adapted from Cheng et al. (2015).

Fig. 8. Snapshot visualizations of the temperature fluctuation field h for difference cases in the cellular, Taylor column, plume and geostrophic turbulence regimes, as defined in Sprague et al. (2006) and Julien et al. (2012b). Top row: free-slip DNS cases from Stellmach et al. (2014). Bottom row: Reduced modeling results from Julien et al. (2012b).

Fig. 5. Reynolds–Ekman regime diagram showing the different capabilities of various methods of studying rotating convection and dynamo physics. The salmon, dark grey, and deep violet colored boxes represent, respectively, the accessibility ranges of direct numerical simulations (e.g., Stellmach et al., 2014), global dynamo models (e.g., Sheyko, 2014; Jones, 2014; Nataf and Schaeffer, 2015) and rotating convection experiments in water (e.g., Cheng et al., 2015). The solid black line denotes Ro ¼ ReE ¼ 1, where geostrophic balance is expected to be lost at all scales in the fluid layer. The black dashed line corresponds to Ro ¼ 10 6, a typical estimate of Ro in Earth’s core. The red and green lines represent upper bounding limits on the reduced models, with the solid part of these lines marking the lower of the two bounds. The red line demarcates where the local Ro‘ ¼ RoE 1=3 = 0.1, above which the assumption of local geostrophic balance likely breaks down, thereby invalidating the reduced equations. The green line represents current-day computing capabilities for the reduced models, for which Re‘ K103 (e.g., Rubio et al., 2014).

Frequently asked questions

Q1. What are the contributions mentioned in the paper "Rotating convective turbulence in earth and planetary cores" ?

In particular, the authors present a closely coupled suite of advanced asymptotically-reduced theoretical models, efficient Cartesian direct numerical simulations ( DNS ) and laboratory experiments. The goal of this paper is to review these findings, and to discuss their possible implications for planetary cores dynamics. 

Q2. Why is it important to benchmark the reduced equations against reference data sets?

Due to the inherent theoretical complexity in developing novel reduced equation sets, it is essential, as with any other model, to benchmark them against reference data sets. 

Q3. Where do the authors predict that low E convective flows will also occur?

At lower latitudes, situated well outside the tangent cylinder, the authors predict that low E convective flows will also occur in the form of 3D geostrophic turbulent motions. 

Q4. How much heating power is needed to determine the minimum Ra values?

The minimum heating power is about 25 W, which, importantly, determines the minimum Ra values that can be accessed in their laboratory experiments. 

Q5. What is the advantage of the reduced equations?

Another advantage of the reduced equations is that they contain only two non-dimensional parameters, fRa and Pr, in comparison to the three parameters, Ra; Pr and E, necessary to characterize Navier–Stokes. 

Q6. What is the effect of a weak flux of kinetic energy in a columnar large?

(iii) Cartesian, 3D geostrophic turbulence generates a weak flux of kinetic energy into system-scale, quasi-2D, columnar large-scale vortices (LSVs). 

Q7. Why are the boundary layers not shown in this image?

The boundary layers located adjacent to non-slip boundaries are not shown in this image in order to provide a clear view of the bulk convective flow. 

Q8. What does the author say about the possibility of LSVs in Earth’s core?

Based on their above arguments that geostrophic turbulent convection exists in Earth’s core, the authors posit that LSVs can develop at high latitudes in Earth’s core as well and may take part in the generation of high latitude geomagnetic flux patches. 

Q9. How many small scale flows can generate ensemble electromotive forces?

In fact, a great deal of theoretical work has shown that small scale flows that have small local magnetic Reynolds numbers, Rm‘ ¼ U‘conv=g 1, can generate ensemble electromotive forces that produce dynamo action on the large scale (e.g., Childress and Soward, 1972; Soward, 1974; Moffatt, 1978; Stellmach and Hansen, 2004; McWilliams, 2012; Roberts and King, 2013; Calkins et al., 2015b). 

Q10. What is the role of the reduced equations?

Ro values correctly describe core flow, then it may prove necessary to develop higher order corrections to the reduced equations to accurately model small-scale core flows. 

Q11. How can the authors extrapolate this result to low E geophysical settings?

It should be possible to extrapolate this result to low E geophysical settings, so long as the horizontal length scale of boundary variations greatly exceeds ‘ ’ E1=3H. 

Q12. How do they explain the inverse energy cascades in laboratory experiments?

inverse energy cascades have been detected in rapidly-rotating laboratory experiments with forced turbulence (e.g., Yarom et al., 2013), suggesting that convection-driven LSVs will be detected in laboratory experiments and in non-slip DNS that are carried out at sufficiently extreme conditions (e.g., E K 10 7; Pr K 1). 

Q13. What is the axial distance over which the slow variable, Z, changes by an order one?

Note that the axial distance over which the slowvariable, Z, changes by an order one value corresponds to E 1=3 order one variations in the fast axial scale z. 

Q14. What do they suggest that Pm must be lowered in order for multi-scale turbulent processes?

Guervilly et al. (2015)’s findings suggest then that Pm must be lowered below unity in dynamo models in order for multi-scale turbulent processes to be able to develop. 

Q15. What are the capabilities of these approaches?

The capabilities of these approaches are shown schematically in Fig. 5. The authors posit that the intercomparison of these different meth-ods, each with its different strengths and weaknesses, optimizes their ability to understand rotating convection physics under extreme, planetary-core-like conditions. 

Q16. What could be the reason for the large-scale magnetic flux patches?

It could even be that localized regions of intensified magnetic flux arise simply as a by-product of their remote observations of a multi-scale field.