A dynamic scale-similarity model for dynamo simulations in a rotating plane layer

We test a dynamic version of the scale-similarity model in plane-layer dynamo simulations. Previous work has shown that the scale-similarity model reproduces the spatial pattern of the SGS heat flux, even near the boundaries, when a correction is added for the commutation error. However, the average amplitude of the SGS terms deviates from the estimate inferred from a fully resolved calculation. In this study, we attempt to improve the average amplitude of the SGS terms by applying the dynamic scheme of Germano et al. (1991) to the scale-similarity model. This procedure yields estimates for the coefficients in the SGS model, which we evaluate as a function of vertical position in the plane layer. The resulting SGS heat flux is compared with the value determined from a resolved dynamo solution on a finer grid. The results show that the dynamic scheme improves the amplitude of the SGS heat flux. Furthermore, the results show that the coefficients for each SGS term in the dynamo simulation (heat flux, momentum flux, Maxwell stress, and magnetic induction) should be evaluated independently because the predicted coefficients for each SGS term have different values.