Three‐dimensional Spherical Simulations of Solar Convection. I. Differential Rotation and Pattern Evolution Achieved with Laminar and Turbulent States

Stochastic Fluctuations in a Babcock‐Leighton Model of the Solar Cycle

“…A reasonable correspondence with the observed amplitude-duration anticorrelation is obtained with Ñuctuation amplitudes of 100% in the circulation, and 200% in the poloidal source term. While such Ñuctuation amplitudes may seem rather high, the simulations of Miesch et al (2000) do support Ñuctuations in the meridional circulation at that level (and perhaps even higher). Strong Ñuc-tuations in sunspot numbers are also observed at all phases of the cycle, supporting the idea that strong temporal Ñuc-tuations are also to be expected in the Babcock-Leighton poloidal source term.…”

“…Consequently, this circulation can be expected to be strongly inÑuenced by stochastic Ñuctuations due to the much more vigorous turbulent velocity Ðeld pervading the convection zone. This expectation is certainly borne out by observations of the solar surface meridional Ñow as well as numerical simulations, with both suggesting rms Ñuctuations comparable to, or even exceeding, the mean meridional Ñow speed (Hathaway 1996 ;Miesch et al 2000). It is essential to ascertain whether Ñux transport models can still operate under such strongly Ñuctuating conditions, and this is in fact a primary objective of this paper.…”

“…A poleward meridional Ñow is a well-established fact at the solar surface (Duvall 1979), and recent helioseismic studies have demonstrated that this Ñow is not a mere surface feature, but extends at least as deep as (Giles et al 1997 ; r/R _^0 .85 Braun & Fan 1998 ;Schou & Bogart 1998). In addition, the numerical simulations of Miesch (1998 ; see also Miesch et al 2000), although carried out in a parameter regime relatively far removed from solar interior conditions, suggest the presence of a mean, large-scale equatorward return Ñow at the base of the convective envelope.…”

“…The introduction of meridional circulation is far from an ad hoc hypothesis ; both analytic theory (e.g., Kitchatinov & 1995 ;Durney 1996b) and numerical simulations Rudiger (e.g., Brummell, Hulburt, & Toomre 1998 ;Miesch et al 2000) have shown that rotational inÑuences on thermally driven convective motions in a rotating spherical shell lead to net cross-correlations between turbulent velocity components that can drive both a mean zonal Ñow and a largescale circulation in meridional planes. A poleward meridional Ñow is a well-established fact at the solar surface (Duvall 1979), and recent helioseismic studies have demonstrated that this Ñow is not a mere surface feature, but extends at least as deep as (Giles et al 1997 ; r/R _^0 .85 Braun & Fan 1998 ;Schou & Bogart 1998).…”

Advection‐dominated solar dynamo model with two‐cell meridional flow and a positive α ‐effect in the tachocline

“…Global convection models for solar differential rotation tend to produce complex patterns for the meridional flow with several 'cells' between the pole and the equator (Miesch et al 2000;Elliott et al 2000;Brun & Toomre 2002;Brun et al 2004).…”