High-Resolution Calculation of the Solar Global Convection With the Reduced Speed of Sound Technique. Ii. Near Surface Shear Layer With the Rotation

Abstract

We present a high-resolution, highly stratified numerical simulation of rotating thermal convection in a spherical shell. Our aim is to study in detail the processes that can maintain a near surface shear layer (NSSL) as inferred from helioseismology. Using the reduced speed of sound technique we can extend our global convection simulation to 0.99 R ⊙ and include near the top of our domain small-scale convection with short time scales that is only weakly influenced by rotation. We find the formation of a NSSL preferentially in high latitudes in the depth range r = 0.95 − 0.975R ⊙ . The maintenance mechanisms are summarized as follows. Convection under weak influence of rotation leads to Reynolds stresses that transport angular momentum radially inward in all latitudes. This leads to the formation of a strong poleward directed meridional flow and a NSSL, which is balanced in the meridional plane by forces resulting from the v ′ r v ′ θ correlation of turbulent velocities. The origin of the required correlations depends to some degree on latitude. In high latitudes a positive correlation v ′ r v ′ θ is induced in the NSSL by the poleward meridional flow whose amplitude increases with the radius, while a negative correlation is generated by the Coriolis force in bulk of the convection zone. In low latitudes a positive correlation v ′ r v ′ θ results from rotationally aligned convection cells ("banana cells"). The force caused by these Reynolds stresses is in balance with the Coriolis force in the NSSL.

Meridional Circulation in Solar and Stellar Convection Zones

“…In particular, we find a transition from single-celled to multi-celled MC profiles in the high and low Ro regimes that is directly linked to a change in the nature of F RS . This conclusion is supported by the recent high-resolution simulations of Hotta et al (2015). There they find that inward angular momentum transport by small-scale convection in the surface layers induces a poleward meridional flow as envisioned by MH11.…”

“…Meanwhile, the solar regime (Ro > 1) often exhibits multiple cells in latitude and radius, aligned with the rotation axis outside the tangent cylinder. 4 Recent high-resolution models have also begun to capture aspects of the solar NSSL wherein small-scale convection in the surface layers establishes an inward Ω gradient (Guerrero et al 2013b;Hotta et al 2015). As suggested by Miesch & Hindman (2011), the NSSL in these simulations is established by a radially inward angular momentum transport, maintained by meridional Reynolds stress (RS), and intimately linked to a poleward meridional flow.…”

The Spectral Amplitude of Stellar Convection and Its Scaling in the High-Rayleigh-Number Regime

“…In the case of the Sun, these simulations are often run by assigning solar values to most model variables, notably the rotation rate and the luminosity, while admitting diffusivities that are computationally tractable but also necessarily orders of magnitude larger than their intended microscopic counterparts (e.g., Brun et al 2004;Ghizaru et al 2010;Hotta et al 2015). It is now becoming increasingly evident that such quasi-laminar simulations have succeeded in maintaining a solar-like differential rotation and energy flux in part owingto the outsized role played by diffusion in many of those models.…”

Solar Dynamics, Rotation, Convection and Overshoot

“…2). These have been dubbed "torsional oscillations" (Howard and Labonte 1980;Schou 1999;Howe et al 2000;Vorontsov et al 2002). The causal connection between the flows and the magnetic manifestations of the solar cycle are unclear.…”

“…Proposed mechanisms for the former include the influence of rotation on convective heat transport (Kitchatinov and Rüdiger 1995;Brun and Toomre 2002;, the influence of rotational shear on convective heat transport (Balbus et al 2009;Balbus and Schaan 2012), and thermal coupling to the subadiabatic tachocline (Rempel 2005b;Miesch et al 2006). For recent perspectives on the latter puzzle (the NSSL), see Miesch and Hindman (2011), Gastine et al (2013), Guerrero et al (2013b), and Hotta et al (2014b).…”