I'm looking for a decent paper/book that will give me the underlying principles for the thin-layer approximation of the Reynolds-averaged Navier Stokes coding. I understand that the viscous terms only act in the y-direction (for a 2-D code) but not why. Any help would be greatly appreciated. Steve.

Perhaps a good starting point would be the 2nd edition (1997) of Computational Fluid Mechanics and Heat Transfer by Tannehill, Anderson and Pletcher. The authors discuss the Thin-Layer NS Equations in Section 8.2, and devote all of Chapter 8 (about 80 pages) to this and related topics, and provide numerous references for further study.

That's fantastic. I've just looked and there's a copy in my library. Thanks very much.