Decomposition of fluid-dynamics balance equations

The paper formulates the complete set of fluid-dynamics balance equations, for Newtonian fluids, in terms of the projections normal and tangential to a surface. This surface can be either a coordinate surface of an arbitrary curvilinear orthogonal coordinate system or a fixed, sufficiently smooth and regular arbitrary surface. The formulation presented in this paper finds its application in all those cases in which one of the three independent direction-fields in a three-dimensional space needs to be differentiated, for one reason or another, from the other two. Such cases arise in the study of discontinuity surfaces (e.g. higher order boundary layer theories) or surface-tension driven phenomena, and in the analysis of parabolic or quasi-parabolic approximations to the Navier-Stokes equations.