how to set the periodic BC in channel?

Bin Li

the channel flow is computed with 3d compressible NS code using MacMarco scheme. in stream wise the periodic bc is used, denoted f_x. in aiaa paper 98-3315, it was -2.*u_taw**2. another paper suggest that it is evaluated using f(d_u/dy). which is better? my code is not valid for this problem now. in initial conditions, all flow parameters is uniform. u=1,v=w=0, density r=1, temperature T=1.(non-dimension) and i add a fluctuate to u within [-0.05,0.05] at inlet boundary in certain time-step. the flow can not develop. i think maybe the initial u is wrong. anyone can send me a velocity profile datas with any Mach number any Renoly number, only compressible. thanks. maybe you would give some advice about it. best regards