Solar Differential Rotation and Meridional Flow: The Role of a Subadiabatic Tachocline for the Taylor‐Proudman Balance

Abstract

We present a simple model for the solar differential rotation and meridional circulation based on a mean field parameterization of the Reynolds stresses that drive the differential rotation. We include the subadiabatic part of the tachocline and show that this, in conjunction with turbulent heat conductivity within the convection zone and overshoot region, provides the key physics to break the Taylor-Proudman constraint, which dictates differential rotation with contour lines parallel to the axis of rotation in case of an isentropic stratification. We show that differential rotation with contour lines inclined by 10 • − 30 • with respect to the axis of rotation is a robust result of the model, which does not depend on the details of the Reynolds stress and the assumed viscosity, as long as the Reynolds stress transports angular momentum toward the equator. The meridional flow is more sensitive with respect to the details of the assumed Reynolds stress, but a flow cell, equatorward at the base of the convection zone and poleward in the upper half of the convection zone, is the preferred flow pattern.

Meridional Circulation in Solar and Stellar Convection Zones

“…Here the MC profile is determined mainly by the nondiffusive component of the convective angular momentum transport, which is typically modeled by the Λ-effect in the zonal momentum Equation (Rempel 2005(Rempel , 2007. This is the process of gyroscopic pumping that will be described in detail in Section 5.1 and that is responsible for the establishment of MC in our convection simulations, as demonstrated in Section 5.2.…”

“…We note that contours in these simulations are noticeably cylindrical with respect to the Sun. This may be attributed to the lack of an underlying stable zone, which is thought to promote conical Ω profiles by inducing baroclinic torques (Rempel 2005;Balbus & Schaan 2012). At rotation rates less than  Ω , the solar-like DR transitions to a state characterized by a weakly retrograde equator and rapidly prograde poles.…”

“…We also neglected the Lorentz force, which is less justified in stars but appropriate here because the simulations we consider are non-magnetic. Full expressions are given in MH11 (see also Kitchatinov & Rüdiger 1995;Rempel 2005).…”

Numerical Simulations of a Rotating Red Giant Star. I. Three-Dimensional Models of Turbulent Convection and Associated Mean Flows

“…This is a well-known dynamical property of rotating fluids, in which the fluid velocity tends to be uniform along lines parallel to the rotation axis (Pedlosky 1987). The Taylor-Proudman constrain on rotating flows and the way of potentially braking it have been extensively studied in the context of the conical rotation profile of the Sun (e.g., Kitchatinov & Rüdiger 1995;Durney 1999;Brun & Toomre 2002;Rempel 2005;Miesch et al 2006). In these papers, it has been shown that along with the Reynolds stresses, the baroclinic term involving latitudinal gradient of the temperature and entropy fluctuations plays a significant role in shaping the solar differential rotation.…”

Numerical calculation of convection with reduced speed of sound technique

“…We refer to the technique as the Reduced Speed of Sound Technique (RSST). This technique was used previously by Rempel (2005Rempel ( , 2006 in mean field models of solar differential rotation and nonkinematic dynamos, which essentially solve the full set of timedependent axisymmetric MHD equations. Those solutions were however restricted to the relaxation toward a stationary state or very slowly varying problems on the timescale of the solar cycle.…”