The Mathematical Problems of Aerodynamics

Extract

The equations governing the motion of a viscous fluid were first obtained by Navier more than 100 years ago (“ Memoire sur les Lois du Mouvement des Fluides,” Mem. de l’Acad. des Sciences, vi. 389, 1822), and in spite of their close study by Stokes, Helmholtz, Kelvin, Rayleigh, Lamb and numerous other mathematicians of great eminence, no complete unrestricted solution for any case of practical importance has yet been discovered. As they stand, the mathematical difficulties presented by the equations have so far been found to be too formidable, and whatever progress has been achieved has been by imposing restrictions on the form of the equations, and therefore serious limitations on the nature of the fluid motion studied. It may be that the mathematical symbolism in the formulation of the problem of viscous fluid flow as usually presented is not that best adapted for its purpose, that it is not as natural a medium of expression as for example Tensor Analysis is for Relativity ; that in fact the essential factors that govern the eddying, for instance, in the wake of a moving body are not presented as governing the structure of the equations.