Eddy resolving simulations of turbulent solar convection

Deep convection occurs in the outer one‐third of the solar interior and transports energy generated by nuclear reactions to the surface.It leads to a characteristic pattern of time‐averaged differential rotation, with the poles rotating significantly slower (approximately 25 per cent) than the equator. This differential rotation results from Reynolds stresses that are associated with correlations of the longitudinal velocity with the radial and latitudinal velocities. One particularly interesting feature of the solar differential rotation is that it shows significant tilting of angular velocity contours away from the rotation axis (i.e. breaking of the Taylor–Proudman state of rotation rate constant on cylinders aligned with the rotation axis), in contrast to the results from early numerical simulations. In spite of such discrepancies, numerical simulations provide the best chance of making progress in understanding the observations. Many studies have adopted the DNS approach and have justified the artificially large viscosities and thermal diffusivities used as modelling transport by unresolved eddies. LES techniques (which use a turbulence closure to relate transport coefficients to local properties of the flow) offer a superior alternative, but face the problem of defining the turbulence closure, which is potentially difficult in the presence of stratification, rotation and other complicating factors. This problem can be avoided by shifting the responsibility for truncating the turbulent cascade from an explicit turbulence closure to the numerical scheme itself. Since this approach abandons the rigorous notions of the LES approach, we refer to it as a VLES (Very Large Eddy Simulation). This paper compares results of DNS simulations carried out with a spherical‐harmonic code, and preliminary results obtained using a VLES‐type code. Both make the anelastic approximation.