A theoretical description of viscous flow along a flat plate

Extract

Theoretical quantification of viscous effects in fluid flows is difficult, even if turbulence is absent, except when it is legitimate to simplify the Navier-Stokes equations in some way; for example by invoking the boundary-layer approximation in appropriate cases of interacting viscous and inviscid flow. The technical importance of viscous effects was thought sufficient incentive to re-examine a very simple flow configuration — namely plane, uniform and steady flow of an incompressible, viscous fluid toward a vanishingly-thin flat plate aligned with the undisturbed stream — in search of fresh insights into the general theory for viscous-inviscid interactions.

The strategy was to exploit the analogy between vorticity transport in a viscous fluid and heat conduction in a moving solid. The key to doing so was the realization that, if the perturbation of the undisturbed flow by the plate might be represented as the sum of a series of successive approximations, then the stream function of the viscous part of the flow field — not merely the vorticity which resulted from its existence — might be expressible at every stage as the solution of an analogous heat conduction problem.