Father of Modern Fluid Mechanics Dead

· fluid mechanics
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The Father of Modern Aerodynamics inspecting the Ho III 1938 Rhön Contest Challenger.

1. The Legacy of Prandtl

Ludwig Prandtl (1875-1953) is named Father of Modern Aerodynamics and Founder of Modern Fluid Mechanics. Wikipedia tells the story: (full story)

Ludwig Prandtl performing experiments in his fluid mechanics lab in Göttingen.

The historical survey Fluid Mechanics in the First Half of This Century (20th), by S. Goldstein sends the same message:

  • In 1904 Prandtl read his paper On Motion of Fluids Flow with Very Little Viscosity to the Third International Congress of Mathematicians at Heidelberg.
  • This was a most extraordinary paper of less than eight pages. In 1928 I asked Prandtl why he had kept it so short, and he replied that he had been given ten minutes for his lecture at the Congress and that, being still quite young, he had thought he could publish only what he had had time to say. 
  • The paper will certainly prove to be one of the most extraordinary papers of this century, and probably of many centuries.
  • However, for some years after it was published Prandtl’s lecture was almost, if not completely, unnoticed. Perhaps this is not surprising. It was so very short, and it was published where no one who was likely to appreciate it might be expected to look for it.      
  • The influence of Prandtl’s boundary-layer theory has been enormous. It has been used to make clear physical phenomena that were, or would have been, otherwise baffling or at least murky.

Goldstein continues with a discussion about the crucial aspect of  slip or no-slip boundary condition:

  • I suppose that it is still correct that for practical purposes in most situa­tions our quantitative knowledge of resistance is mainly empirical. However, much more is understood now of the underlying physical processes, and we may ask what was the main cause of the difficulties and confusion. Certainly it did not lie in any lack of intellectual ability of the very distinguished scientists who wrestled with the problems from Newton to Stokes and Rayleigh. The real trouble was doubt about the boundary conditions to be applied at the dividing surface between a solid and a liquid or gas. In the theory of the irrotational motion of an inviscid fluid, the relative normal velocity at the surface of an impermeable solid must be zero, and no other boundary condition is required or can be imposed. For the motion of a viscous fluid, on the other hand, according to the dynamical differential equations published during the period 1822 to 1845 (Navier, 1822; Poisson, 1829; Saint-Venant, 1843; Stokes, 1845), another boundary condition is re­quired for a solution. There was doubt and vacillation for a long time. On the whole, one thing seems to have been agreed: that there is no slip, i.e., no relative tangential velocity, at the surface of a solid body in the case of a very slow motion in a viscous fluid; but all else was in doubt. 
  • The discrepancies between the actual motions of a real fluid of small viscosity, when laminar, and the results calculated for the irrotational motion of an inviscid fluid arise mainly, in most cases, from the condition in a real fluid of no slip at a boundary. If a fluid could slip freely over the surface of a solid body it would be a very different world. Those, among them Lamb and Levi-Civita, who have asserted in the past that viscosity cannot be considered a predominant cause of direct resistance, were correct in this sense in most ordinary circumstances.
  • In his 1904 lecture to the International Congress of Mathematicians Prandtl stated briefly but definitely that by far the most important question in the problem (of the flow of a fluid of small viscosity past a solid body) is the behavior of the fluid at the walls of the solid body. 

Prandtl introduces the concept of boundary layer in his 1904 a paper as follows:

  • The physical processes in the boundary layer (Grenzschicht) between fluid and solid body can be calculated in a sufficiently satisfactory way if it is assumed that the fluid adheres to the wans, so that the total velocity there is zero-or equal to the velocity of the body. If the viscosity is very small and the path of the fluid along the wall not too long, the velocity will have again its usual value very near to the wall. In the thin transition layer (Ubergangsschicht) the sharp changes of velocity, in spite of the small viscosity coefficient, produce noticeable effects.

John D. Anderson gives full praise to in Prandtl’s Boundary Layer:

  • In 2005, concurrent with the World Year of Physics celebration of, among other things, Albert Einstein and his famous papers of 1905, we should also celebrate the 100th anniversary of Prandtl’s seminal paper. The modern world of aerodynamics and fluid dynamics is still dominated by Prandtl’s idea. By every right, his boundary-layer concept was worthy of the Nobel Prize. He never received it, however; some say the Nobel Committee was reluctant to award the prize for accomplishments in classical physics.
  • Prandtl’s boundary-layer idea revolutionized how scientists conceptualized fluid dynamics. 
  • Prandtl died in 1953. He was clearly the father of mod- ern aerodynamics and a monumental figure in fluid dy- namics. The impact of his work will reverberate for as long as fluid dynamics is studied and applied.

 2. The Unfortunate Influence of Prandtl

Prandtl resolved d’Alembert’s paradox in his 8 page 1904 article by dictating the necessity of using a no-slip boundary condition with a boundary layer, even if the viscosity and skin friction is vanishingly small. Prandtl thereby resolved d’Alembert’s paradox by disqualifying the zero drag potential solution because it satisfies a slip boundary condition without boundary layer and not a no-slip boundary condition with boundary layer.

The scientific community thanked Prandtl for resolving the paradox and saving fluid mechanics from collapse by elevating him to the role of Father leading the way into modernity, based on his 8 page 1904 sketch.

But Prandtl’s resolution of d’Alembert’s paradox was not correct: The real reason that potential flow is unphysical and cannot be observed is not the slip boundary condition, which is perfectly fine for vanishingly small viscosity and skin friction, but the fact that it is unstable because of a specific exponential instability at separation.

Slightly viscous flow is uncomputable with no-slip, since resolution of thin boundary layers requires quadrillions of mesh points. Slightly viscous flow with slip boundary condition is computable using millions of mesh points.

3. Instead of Prandtl

Prandtl made modern fluid mechanics uncomputable and thus beyond understanding and thereby reduced its usefulness. Prandtl saved fluid mechanics from imminent collapse in 1904 but the price was high and his salvation was not constructive and threw 20th century fluid mechanics into scientific backwater.

A different constructive approach to slightly viscous flow is presented on this site under Fluid Mechanics and in the book Computational Turbulent Incompressible Flow including a a revelation of The Secret of Flight, which Prandtl did not help to uncover.


1 Comment

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  1. cementafriend

    Thanks for the links to Prandtl’s 1904 paper and to Anderson’s paper.

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