Turbulence in 2D channel flow


I am trying to simulate turbulence in a two-dimensional channel flow using LBM. There have been papers by Jimenez, etc discussing the instability of plane Poiseuille flow and the subsequent chaotic flow that sets in at Reynolds number of 9000 or so. The problem is the way the flow is being driven: the instability is very sensitive to the driving force. Two standard ways to drive an incompressible fluid are by having a mass flux or pressure gradient across the channel. However, I am using a body force for LB, and the disturbances, which obey continuity and boundary conditions, decay even at a Reynolds of 10^4. Reynolds number is based on channel half width and centerline velocity. I do not know what else to try in this regard. Is there a way to drive the flow, similar to incompressible flows, in LBM? The papers I mentioned above use spectral methods.

Could anyone help me in this regard?