Turbulent convection models (TCMs) based on hydrodynamic moment equations are compared with the classical mixing‐length theory (MLT) in solar models. The aim is to test the effects of some physical processes on the structure of the solar convection zone, such as the dissipation, diffusion and anisotropy of turbulence that have been ignored in the MLT. Free parameters introduced by the TCMs are also tested in order to find appropriate values for astrophysical applications. It is found that the TCMs usually give larger convective heat fluxes than the MLT does, and the heat transport efficiency is sensitively related to the dissipation parameters used in the TCMs. As a result of calibrating to the present solar values, our solar models usually have rather smaller values of the mixing length to local pressure scaleheight ratio than the standard solar model. The turbulent diffusion is found to have important effects on the structure of the solar convection zone. It leads to significantly lowered and expanded profiles for the Reynolds correlations, and a larger temperature gradient in the central part of the superadiabatic convection region but a smaller one near the boundaries of the convection zone. It is interesting to note that, due to a careful treatment of turbulence developing towards isotropic state, our non‐local TCM results in radially dominated motion in the central part and horizontally dominated motion near the boundaries of the convection zone, just as what has been observed in many 3D numerical simulations. Our solar models with the TCMs give small but meaningful differences in the temperature and sound speed profiles compared with the standard solar model using the MLT.

The Carte Synoptique catalogue of solar filaments from 1919 March to 1957 July, corresponding to complete cycles 16‐18, is utilized to show the latitudinal migrations of solar filaments at low (≤50°) and high (>50°) latitudes and the latitudinal distributions of solar filaments for all solar filaments, solar filaments whose maximum lengths during solar disk passage are less than or equal to 70° and solar filaments whose maximum lengths during solar disk passage are larger than 70°. The results show the following. (1) The latitudinal migrations of all low‐latitude solar filaments and low‐latitude solar filaments whose maximum lengths during solar disk passage are less than or equal to 70° follow the Spörer sunspot law. However, the latitudinal migration of low‐latitude solar filaments whose maximum lengths during solar disk passage are larger than 70° do not follow the Spörer sunspot law: there is no equatorward and no poleward drift. The latitudinal migration of high‐latitude solar filaments whose maximum lengths during solar disk passage are larger than 70° is more significant than those of all high‐latitude solar filaments and high‐latitude solar filaments whose maximum lengths during solar disk passage are less than or equal to 70°: there is a poleward migration from the latitude of about 50° to 70° and an equatorward migration from the latitude of about 70° to 50° of all high‐latitude solar filaments and high‐latitude solar filaments whose maximum lengths during solar disk passage are less than or equal to 70° and there is a poleward migration from the latitude of about 50° to 80° and an equatorward migration from the latitude of about 80° to 50° of high‐latitude solar filaments whose maximum lengths during solar disk passage are larger than 70°. (2) The statistical characteristics of latitudinal distribution of solar filaments whose maximum lengths during solar disk passage are larger than 70° is different from those of all solar filaments and solar filaments whose maximum lengths during solar disk passage are less than or equal to 70° (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The free parameters involved in the turbulent convection models are determined in the solar interior with the aid of helioseismology. We calculated solar p‐mode oscillation of l= 150 for a series of solar models described by Li & Yang, and compared the calculated frequencies with the helioseismic observations. It is found that, with appropriate choices of the turbulent parameters, solar model with both local and non‐local turbulent convection models can give the calculated p‐mode frequencies that are better consistent with the observations than the standard solar model does. The turbulent dissipation plays a major role in the frequency corrections, while the turbulent diffusion makes further improvements in the frequencies. Decreasing the values of parameters Ct and Ce or increasing the values of parameters Ct1 and Ce1 helps reduce the calculated frequencies, indicating that the turbulent dissipation is weak and the turbulent diffusion is strong in the convection zone of the Sun. The parameters Ck and Cs have no obvious effect on the p‐mode frequencies. The temperature is found to have a bump near the surface of the convection zone and a mild depression over the inner convection zone. It is just this temperature depression that makes the sound speed a little less, and the p modes spending a little longer time to travel in the convection zone. Combined with better values of the free parameters, our solar models with the TCMs can reduce the frequency differences between the model calculations and observation as much as 30 per cent for the modes of middle and high l. This result can give a clue to solar modelling, i.e., including turbulence in solar models is helpful to reproduce the observed solar p‐mode frequencies.