This paper describes a series of 3D simulations of shallow inefficient convection in the outer layers of the Sun. The computational domain is a closed box containing the convection-radiation transition layer, located at the top of the solar convection zone. The most salient features of the simulations are that: i)The position of the lower boundary can have a major effect on the characteristics of solar surface convection (thermal structure, kinetic energy and turbulent pressure). ii)The width of the box has only a minor effect on the thermal structure, but a more significant effect on the dynamics (rms velocities). iii)Between the surface and a depth of 1 Mm, even though the density and pressure increase by an order of magnitude, the vertical correlation length of vertical velocity is always close to 600 km. iv) In this region the vertical velocity cannot be scaled by the pressure or the density scale height. This casts doubt on the applicability of the mixing length theory, not only in the superadiabatic layer, but also in the adjacent underlying layers. v) The final statistically steady state is not strictly dependent on the initial atmospheric stratification.
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