Mean flow generation in rotating anelastic two-dimensional convection

Currie, Laura K.; Tobias, Steven M.

doi:10.1063/1.4939300

Cited by 13 publications

(22 citation statements)

References 47 publications

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“…Those simulations adopted the Boussinesq approximation (e.g., Spiegel & Veronis 1960), which neglects density fluctuations except where multiplied by gravity; this can be regarded as assuming a layer depth that is small compared to the scale height, and slow flows compared with the sound speed. Later studies have also simulated anelastic (Currie & Tobias 2016) and fully compressible convection with tilted rotation vectors to explore the effect of rotation on mean flows, convective transport, and convective overshooting at mid-latitudes in the Sun (see e.g., Brummell et al 1996Brummell et al , 1998Brummell et al , 2002Käpylä et al 2004;Chan 2007).…”

Section: Prior Studies Of Rotating Convectionmentioning

confidence: 99%

Convection with misaligned gravity and rotation: simulations and rotating mixing length theory

Currie

Barker

Lithwick

et al. 2020

Monthly Notices of the Royal Astronomical Society

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We present numerical simulations, using two complementary setups, of rotating Boussinesq thermal convection in a three-dimensional Cartesian geometry with misaligned gravity and rotation vectors. This model represents a small region at a non-polar latitude in the convection zone of a star or planet. We investigate the effects of rotation on the bulk properties of convection at different latitudes, focusing on determining the relation between the heat flux and temperature gradient. We show that our results may be interpreted using rotating mixing length theory (RMLT). The simplest version of RMLT (due to Stevenson) considers the single mode that transports the most heat. This works reasonably well in explaining our results, but there is a systematic departure from these predictions (up to approximately 30% in the temperature gradient) at mid-latitudes. We develop a more detailed treatment of RMLT that includes the transport afforded by multiple modes, and we show that this accounts for most of the systematic differences. We also show that convectively-generated zonal flows and meridional circulations are produced in our simulations, and that their properties depend strongly on the dimensions of the box. These flows also affect the heat transport, contributing to departures from RMLT at some latitudes. However, we find the theoretical predictions of the multi-mode theory for the mid-layer temperature gradient, the root-mean-square (RMS) vertical velocity, the RMS temperature fluctuation, and the spatial spectrum of the heat transport at different latitudes, are all in reasonably good agreement with our numerical results when zonal flows are small.

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Section: Prior Studies Of Rotating Convectionmentioning

confidence: 99%

Convection with misaligned gravity and rotation: simulations and rotating mixing length theory

Currie

Barker

Lithwick

et al. 2020

Monthly Notices of the Royal Astronomical Society

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“…Ra c increases (see e.g. Currie & Tobias 2016). Thus, in order to make meaningful comparisons between the three cases, we increase Ra for the AC runs in order to maintain the same degree of supercriticality at reference level z = 0; the parameter values are summarized in Table 2.…”

Section: Stratified Anelastic Convection: Numerical Resultsmentioning

confidence: 99%

Scale Selection in the Stratified Convection of the Solar Photosphere

Kessar

Hughes

Kersalé

et al. 2019

ApJ

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We examine the role of stratification in determining the scale for turbulent anelastic convection. Motivated by the range of scales observed in convection at the solar photosphere, we perform local numerical simulations of convection for a range of density contrasts in large domains. We analyse both the Eulerian and Lagrangian statistics of the convection and demonstrate that increasing the stratification shifts the scale of the most energetic structures in the flow to smaller scales; furthermore, the relative amplitude of vertical to horizontal flows in the convection decreases with increasing stratification. We discuss the implications of our results to the issue of solar mesogranulation.

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“…It may be that this hinders large-scale dynamo action; indeed in the study of Cattaneo and Hughes (2006) the convection had no large scale shear and no net helicity and only small scale dynamo action was found. It is therefore of interest to examine the dynamo properties of convective systems that allow net helicity to be generated, i.e., those with stratification (Currie and Tobias 2016). We propose to extend our investigation to this stratified case in the near future.…”

Section: Discussionmentioning

confidence: 99%

“…Clearly in case (a), whilst there is a non-zero mean flow at each instance in time, on averaging over a long enough period to achieve steady statistics, the mean flows are very small (this is to be expected as there is no preferred direction in the horizontal plane). In (b), the tilting of the rotation now breaks this symmetry and this leads to systematic mean flows (such flows have been seen in many cases, e.g., Hathaway and Somerville 1983, Brummell et al 1998, Julien and Knobloch 1998, Currie and Tobias 2016. The addition of a basic state thermal wind leads to a significant increase in the strength of the mean flows, this is most obvious in the zonal direction as, by definition, the mean flow in this direction contains the basic state flow, but from (c) and (d) right-hand panels, it is also clear that the addition of a thermal wind leads to strong mean flow in the y direction also.…”

Section: Hydrodynamic Flowsmentioning

confidence: 97%

Convection-driven kinematic dynamos with a self-consistent shear flow

Currie

Tobias

2018

Geophysical & Astrophysical Fluid Dynamics

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It is widely accepted that astrophysical magnetic fields are generated by dynamo action. In many cases these fields exhibit organisation on a scale larger than that of the underlying turbulent flow (e.g., the eleven-year solar cycle). The mechanism for the generation of so-called large scale fields remains an open problem. In cases where the magnetic Reynolds number (Rm) is small, dynamo-generated fields are coherent but at (the astrophysically relevant) high Rm, the fields are overwhelmed by small scale fluctuating field. Recently Tobias and Cattaneo (2013) have shown that an imposed large scale shear flow can suppress the small scale fluctuations and allow the large scale temporal behaviour to emerge. Shear is also believed to modify the electromotive force by introducing correlations between the flow and the field. However in previous models at high Rm the shear is often artificially imposed or driven by an arbitrary body force. Here we consider a simple kinematic model of a convective dynamo in which shear is self consistently driven by the presence of a horizontal temperature gradient (resulting in a thermal wind) and a rotation vector that is oblique to gravity. By considering a 2.5-dimensional system, we are able to reach high Rm so that the dynamo approaches the asymptotic regime where the growth rate becomes approximately independent of Rm. We find the flows studied here to be excellent small-scale dynamos, but with very little systematic behaviour evident at large Rm. We attribute this to being unable to self-consistently generate flows with both large (net) helicity and strong shear in this setup.

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Mean flow generation in rotating anelastic two-dimensional convection

Cited by 13 publications

References 47 publications

Convection with misaligned gravity and rotation: simulations and rotating mixing length theory

Convection with misaligned gravity and rotation: simulations and rotating mixing length theory

Scale Selection in the Stratified Convection of the Solar Photosphere

Convection-driven kinematic dynamos with a self-consistent shear flow

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