Local models of stellar convection. II. Rotation dependence of the mixing length relations

We study the mixing length concept in comparison to three-dimensional numerical calculations of convection with rotation. In a limited range, the velocity and temperature fluctuations are linearly proportional to the superadiabaticity, as predicted by the mixing length concept and in accordance with published results. The effects of rotation are investigated by varying the Coriolis number, Co = 2 Ω τ, from zero to roughly ten, and by calculating models at different latitudes. We find that α decreases monotonically as a function of the Coriolis number. This can be explained by the decreased spatial scale of convection and the diminished efficiency of the convective energy transport, the latter of which leads to a large increase of the superadibaticity, δ = nabla - nabla_ad as function of Co. Applying a decreased mixing length parameter in a solar model yields very small differences in comparison to the standard model within the convection zone. The main difference is the reduction of the overshooting depth, and thus the depth of the convection zone, when a non-local version of the mixing length concept is used. Reduction of α by a factor of roughly 2.5 is sufficient to reconcile the difference between the model and helioseismic results. The numerical results indicate reduction of α by this order of magnitude.