First-Order Boundary-Layer Equations

Abstract

Consider the surface of an arbitrary body which is defined in the (x^1’ x^2’ , x^3’) Cartesian (right-handed) reference coordinate system, Fig. 2.1. The boundary-layer coordinate system, a nonorthogonal curvilinear right-handed coordinate system (x¹, x², x³), is defined on the surface of the body. Although the lines x¹ = const. and x² = const. are defined on the surface, the x¹- and x²-coordinate need not necessarily be measured along the surface of the body or wing (for details see chapter 10 .) . In general the lines x¹ = const. and x² = const. are non-orthogonal. The x³-coordinate is rectilinear and normal to both, and therefore normal to the surface, too. Thus the (x¹, x², x³)-system is a locally monoclinic coordinate system. x¹, x² - or x^α, α = 1, 2 - are the Gaussian surface parameters.