Abstract

Blasius’s exact solution of the boundary layer equation and von Kármán’s approximate method have significantly influenced our understanding of Fluid Mechanics and related mathematical domains since the last century. However, the classical formulation of these centennial solutions is ill-suited to describe mathematically or physically the original model. Both solutions admit that the effect of a uniform flow passing over a flat plate is analogous to towing the same plate through the stationary fluid. Blasius’s solution, based on a unique point on the asymptotic curve, contradicts the existence of the potential flow, and is a result of an artificial fourth boundary condition. Consequently, these classical solutions cannot precisely determine the limits of the boundary layer or predict the laminar/turbulent transition despite the typical interaction with the local Reynolds number. The main technical approaches to predict potential transition occurrence are those based on small disturbance methods or the two-equation turbulence models. Unlike classical models, the present flat plate boundary layer model enables the natural detection of regime changes without inducing flow using external forces, or relying on empirical formulations for successful closure. Comparing the proposed model results with existing classical models helps us, based on these new concepts, understand the advancements in the state-of-the-art boundary layer.

Keywords:General fluid mechanics; Boundary integral method; Boundary layer control; Transition to turbulence; Computational method