Inflow conditions for spatial direct numerical simulation of turbulent boundary layers

The inflow conditions for spatial direct numerical simulation(SDNS) of turbulent boundary layers should reflect the characteristics of upstream turbulence,which is a puzzle. In this paper a new method is suggested,in which the flow field obtained by using temporal direct numerical simulation(TDNS) for fully developed turbulent flow(only flow field for a single moment is sufficient) can be used as the inflow of SDNS with a proper transformation. The calculation results confirm that this method is feasible and effective. It is also found that,under a proper time-space transformation,all statistics of the fully developed turbulence obtained by both temporal mode and spatial mode DNS are in excellent agreement with each other,not only qualitatively,but also quantitatively. The normal-wise distributions of mean flow profile,turbulent Mach number and the root mean square(RMS) of the fluctuations of various variables,as well as the Reynolds stresses of the fully developed turbulence obtained by using SDNS,bear similarity in nature.