The grid distribution is horizontally uniform. In vertical direction, the grid spacing decreases smoothly with the height. All cases use a $64\times 64\times 96$ mesh.

Numerical Scheme: ADISM
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We adopted the ADISM (Alternating Direction Implicit method on Staggered Mesh) scheme of [@chan82] to solve the full NS equations (\[ns1\])$\sim$(\[ns3\]). This method has second-order-accuracy in space which is adequate for simulating the turbulent situation. As an implicit scheme, it can avoid the time step restriction imposed by sound waves associated with the Courant-Friedriches-Lewy(CFL) condition (see [@richtmyer1968]). Numerical tests show that the ADISM scheme can maintain stability for a time-step over 100 times the normal value suitable for explicit schemes. In contrast with most other implicit methods, the CPU time consumption of the ADI method is linearly proportional to the number of grid points. A detailed examination of the ADISM approach has been given by [@chan86]. The hydrodynamic code we used was initially developed and used by [@chan89] and then adopted by [@kim98] to study the upper solar transition layer. Therefore, it has been well debugged.

Input Physics: EOS and Opacity
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In the simulated region, the temperature is high enough that all kinds of atoms are fully ionized. For a 