A model of the entropy flux and Reynolds stress in turbulent convection

We propose a closure model for the transport of entropy and momentum in astrophysical turbulence, intended for application to rotating stellar convective regions. Our closure model is first presented in the Boussinesq formalism, and compared with laboratory experiments and numerical simulations on the Rayleigh–Bénard convection and homogeneous Rayleigh–Bénard convection. The predicted angular momentum transport properties of the turbulence in the slowly rotating case recover the well-known Λ-effect, with an amplitude related to the convective heat flux. The model is then extended to the anelastic case. In the special case of spherical symmetry, the predicted radial heat flux is equivalent to that of mixing-length theory. For rotating stars, our model describes the coupled transport of heat and angular momentum, and provides a unified formalism in which to study both differential rotation and thermal inhomogeneities in stellar convection zones.