Corruption of Modern Physics 14: Prandtl's Boundary Layer Theory

Turbulent solution of Euler's equations with a slip boundary condiition with a turbulent wake arising from opposing flow instability at rear separation creating drag.

Ludwig Prandtl is named Father of Modern Fluid Mechanics motivated by his boundary layer theory with a no-slip boundary condition as key element,  which has dominated fluid mechanics since the 1920s. No-slip means that a fluid meets a fixed solid boundary with zero velocity thus creating a boundary layer connecting free flow velocity away from the boundary with thickness scaling with $\sqrt{\nu}$ with $\nu$ fluid viscosity of typical size $0.000001$. A typical boundary layer is thus very thin of size $0.001$ which requires so many mesh points in computation that the required computational power is far away still today. In addition, small viscosity fluid mechanics is turbulent with small scales also asking for resolution.

Father Prandtl with his no-slip boundary condition thus forced modern fluid mechanics into a fruitless  search for wall models seeking to circumvent the need of boundary layer resolution, which made modern fluid mechanics into a nightmare of wall modeling.

How could this be? The reason is that with the no-slip condition Prandtl could present a resolution of d'Alembert's Paradox remaining unresolved since its formulation in 1755, with the paradox comparing prediction of zero drag or resistance to motion in theoretical potential flow satisfying a slip boundary condition as a model of small skin friction of size $0.001$ allowing the fluid to slide without friction along a solid boundary, with observation of real flow with substantial drag. 

As noted by Nobel Laureate Hinshelwood, this made fluid mechanics from start into a joke when divided into

• practical fluid mechanics or hydraulics observing phenomena which cannot be explained (non-zero drag) 
• theoretical fluid mechanics explaining phenomena which cannot be observed (zero drag).    

Prandtl suggested to resolve the paradox by declaring potential flow satisfying Euler's equations for slightly viscous flow as an illegal solution because of violation of the no-slip condition. This simple trick brought relief to fluid mechanics from start viewed as a joke, but it came with the side effect of making fluid mechanics instead into a computational night-mare. From ashes into the fire.

In 2010 I published together with Johan Hoffman a real resolution of d'Alembert's paradox in the prestigious Journal of Mathematical Fluid Mechanics, which showed that the reason the zero-drag potential solution with slip cannot be observed, is that it is unstable and so is replaced by a turbulent solution of Euler's equations with slip but non-zero drag from a turbulent wake. Main drag is thus not an effect of skin friction as Prandtl claimed, but from free flow turbulence as shown in the fig above.  

This work changed the premises for fluid mechanics freeing it for the computational impossibility of no-slip, since slip does not generate any boundary layer. The full potential is exposed in Euler Right! Prandtl Wrong? including a revelation of the Secret of Flight. Take a look and free yourself from the prison of no-slip.