Significance of the thin-layer Navier-Stokes approximation

The terms neglected in the thin-layer approximation are evaluated by transforming the equations into curvilinear surface coordinates and comparing these equations with the second order Navier-Stokes equations. In this formulation of the thin-layer equations, it is determined that the longitudinal curvature terms of second-order boundary layer theory are missing. The complete Navier-Stokes equations are required before the surface coordinate transformation in order to retain the curvature terms in the resulting governing equations. In addition, it is shown that the thin-layer equations with the Cartesian velocity components as dependent varables are not readily reduced to he boundary layer equations.