Hi, could anybody tell me how to formulate the 2-d naiver-stokes equations with turbulence model in them by using stream function and vorticity method? I guess stream function and vorticity technics can only be applied to handle laminar flow, am I right?

Thanks a lot

I'll answer your question in just a few words : go to the vorticity equation, find the viscosity, and replace the viscosity by the effective viscosity (=turbulent eddy viscosity + viscosity). Look for 0-equation, 1-equation, 2-equation turbulence model for the turbulent eddy viscosity. Now you are ready for turbulent flow solutions.There is a very old book on "Heat and Mass Transfer in Recirculating Flows" by Gossman, Pun, Runchal, Spalding and Wolfshtein of Imperial College,London by Academic Press 1969. This book will give you some ideas about the early CFD activities by the Imperial College group. ( The book includes the Fortran code listing ). As I said it is a very old book.