Turbulent kinetic energy spectra of solar convection

Understanding and characterization of solar convection is a key problem of heliophysics and astrophysics. The solar turbulence driven by convective energy transport determines the dynamical state of the solar plasma, and leads to excitation of acoustic waves (Kiti-ashvili et al. 2011), formation of magnetic structures (Brandenburg et al. 2011; Kitiashvili et al. 2010) and other dynamical phenomena. Realistic numerical simulations of solar magnetoconvection are an important tool for understanding many observed phenomena, verification and validation of theoretical models and interpretations of observations. The simulations of this type were started in pioneering works by Stein & Nordlund (1998), with the primary goal of constructing numerical models based on first physical princi-ples. The “quiet Sun ” describes a background state of the solar surface layers without sunspots and active regions, that is, without large-scale magnetic flux emergence and other strong magnetic field effects, which can significantly change properties of the tur-bulent convection. Quiet-Sun regions are characterized by a weak mean magnetic field of 1- 10 G usually concentrated in small-scale flux tubes in the intergranular lanes. The flux tubes observe