Similarity and dynamic similarity models for large-eddy simulations of a rotating convection-driven dynamo

Numerical simulations of rotating convection-driven dynamos have been found very useful to understand the inner workings of the geodynamo. Parametrization of small-scale processes can allow the simulations to approach a more realistic parameter range provided that these processes are modelled properly. In line with this effort, two turbulent models, the scale-similar model of Bardina et al. and a dynamic similarity model, have been applied to a rotating convection-driven plane-layer dynamo simulation with an infinite Pr number in this paper. The results from the similarity model are satisfactory: the large-scale magnetic/kinetic energies and rms magnetic/velocity field fluctuations are in much better agreement with the highly resolved solution than with the low-resolution direct simulation. The model is found to be much less sensitive to the filter scale than the a priori test. Implementation of a dynamic procedure to the similarity model gives better agreement provided that the two filtering scales are properly chosen. Effect of aspect ratio on the performance of the models is also studied by carrying out simulations with aspect ratio 1 and 2. The results show that performances of the models are not influenced by the aspect ratio chosen.