Nineteenth-Century Roots of the Boundary-Layer Idea

Ludwig Prandtl is properly credited with the development of the boundary-layer idea in viscous flow, which was generalized to the method of matched asymptotic expansions. However, the idea of matching a global and a local approximation was previously applied to specific problems in the nineteenth century by a number of well-known natural philosophers, starting with Laplace in 1805. The author summarizes their applications in hydrostatics, hydrodynamics, elasticity, electrostatics, and acoustics, with particular attention to the process of matching.