Convective Velocity Suppression via the Enhancement of the Subadiabatic Layer: Role of the Effective Prandtl Number

Abstract

It has recently been recognized that the convective velocities achieved in the current solar convection simulations might be over-estimated. The newly-revealed effects of the prevailing small-scale magnetic field within the convection zone may offer possible solutions to this problem. The small-scale magnetic fields can reduce the convective amplitude of small-scale motions through the Lorentz-force feedback, which concurrently inhibits the turbulent mixing of entropy between upflows and downflows. As a result, the effective Prandtl number may exceed unity inside the solar convection zone. In this paper, we propose and numerically confirm a possible suppression mechanism of convective velocity in the effectively high-Prandtl number regime. If the effective horizontal thermal diffusivity decreases (the Prandtl number accordingly increases), the subadiabatic layer which is formed near the base of the convection zone by continuous depositions of low entropy transported by adiabatically downflowing plumes is enhanced and extended. The global convective amplitude in the high-Prandtl thermal convection is thus reduced especially in the lower part of the convection zone via the change in the mean entropy profile which becomes more subadiabatic near the base and less superadiabatic in the bulk.

Consequences of high effective Prandtl number on solar differential rotation and convective velocity

“…The resulting buoyant acceleration then establishes the convection. Similar behavior is also seen in the previous local non-rotating simulations of Bekki et al [21], although they do not have fixed entropy boundary condition at the top.…”

“…We find that at larger Pr the convective velocity is suppressed and a subadiabatic layer is formed near the base of the CZ due to continuous deposition of low entropy plumes. However, our results are quantitatively different than the previous non-rotating (local) Cartesian simulations [7,21]. The most interesting and unforeseen result of our simulations is that the inward transport of angular momentum by plumes leads to an anti-solar differential rotation in high-Pr regime, despite the stronger rotational influence as quantified by the lower Rossby number.…”

“…At this end, O'Mara et al [7] carried out a set of convection simulations at varying Pr and they showed that the convective velocity decreases with the increase of Pr eff . In local Cartesian simulations, Bekki et al [21] also find a similar result of decreasing convection velocity with the increase of Pr. They further demonstrated that a subadiabatic layer near the base of the CZ is formed by continuous deposition of low-entropy downward plumes.…”

Effects of a subadiabatic layer on convection and dynamos in spherical wedge simulations

“…We note that only in Runs HD3 and HD4 the domain is deep enough to allow the formation of an RZ and that the depths of the DZ and/or OZ are thus underestimated for Runs HDp, HD1, and HD2. A similar argument applies to the runs presented by Bekki et al (2017) and Karak et al (2018). In Runs HD3 and HD4, the subadiabatic but mixed layers (DZ and OZ) cover 38 and 44 per cent of the total depth of the mixed zone.…”

“…Recent numerical simulations indeed suggest that convection is driven by cooling near the surface (Cossette andRast 2016, Käpylä et al 2017b) and that the lower part of the convection zone is weakly subadiabatic (e.g. Tremblay et al 2015, Käpylä et al 2017b, Hotta 2017, Bekki et al 2017, Karak et al 2018, Nelson et al 2018). Evidence of a changing structure of convection from a tree-like (decreasing number of downflow plumes with increasing depth) to a forest-like structure (constant number of plumes) has also been reported (Käpylä et al 2017b).…”