Euler Was Right, Prandtl Was Wrong I

Euler vs Prandtl

In 1755 the great mathematician Euler formulated the Euler equations for slightly viscous nearly incompressible flow (of air and water) with the following prophetic declaration:

• My two equations contain all what is contained in the theory of fluid mechanics. It is not the principles of mechanics we lack to pursue this analysis but only Analysis (computation), which is not sufficiently developed for this purpose.  

Euler's equations are formulated in terms of fluid velocity and fluid pressure depending on space and time as an expression of force balance (Newton's 2nd Law) and incompressibility complemented by a slip boundary condition with only pressure forces from a solid wall meeting the fluid, that is, with zero skin friction allowing the tangential flow velocity to be non-zero restricting only the normal flow velocity to be zero on a wall.  Euler's equations are parameter-free (formally zero viscosity), thus meeting Einstein's ideal of a mathematical model. The only force acting on fluid particles is pressure and shear forces are assumed to be negligible.  Euler made the assumption about zero skin friction from experiments showing very small skin friction in slightly viscous flow with massive evidence in modern times. 

Eulers adversary d'Alembert quickly crushed Euler's grand plan by showing that Euler's equations admitted certain solutions (potential solutions) showing zero net forces (drag, lift) of a body moving through air or water, in direct contradiction to observation. This was coined d'Alembert's Paradox which from start, as expressed by Chemistry Nobel Laureate Hinshelwood:

• separated practical fluid mechanics (hydraulics) describing phenomena (drag, lift), which cannot be explained, from theoretical fluid mechanics explaining phenomena (zero drag, lift), which cannot be observed.       

Zero lift is incompatible with flight and so d'Alembert's Paradox had to be resolved, in particular after powered human flight was shown to be possible by the Wright brothers in 1903, and so the young fluid mechanician Prandtl presented a resolution in a sketchy 8-page conference contribution in 1904, where he discriminated potential flow with zero skin friction claiming that a real fluid always meets a solid wall with zero tangential velocity named no-slip.  Prandtl thus "resolved" d'Alembert's Paradox by declaring that Euler's equations with slip had to be replaced by the Navier-Stokes equations including small viscosity and no-slip. But no-slip was an ad hoc assumption which Prandtl could not justify since the exact nature of the microscopic contact between fluid and wall was unknown to him and so has remained into our days. 

Prandtl in 1904 with his self-built fluid test channel resolving d'Alembert's Paradox.

Anyway, the scientific community was by Prandtl relieved from a main headache making theory of fluid mechanics into a joke and accordingly Prandtl was named Father of Modern Fluid Mechanics based on the Navier-Stokes equations with no-slip and not Euler's equations with slip. 

But there was one main caveat: The Navier-Stokes equations with no-slip have solutions with boundary layers so thin that computational resolution is impossible with any forseeable computational power.  Prandtl's resolution thus came with the cost of making Computational Fluid Dynamics CFD into an impossibility asking for resolution of atomistic scales in a macroscopic setting.

In 2010, Hoffman and Johnson published in Journal of Mathematical Fluid Mechanics a different resolution of d'Alembert's paradox showing that the reason zero-drag/lift of potential flow cannot observed, is that potential flow (in fact any laminar flow) is unstable and thus turns into turbulent flow. This was shown by computing turbulent solutions to Eulers equations with slip with drag and lift in close correspondence to observations supported by stability analysis, as exposed in detail in the book Computational Turbulent Incompressible Flow. As a spin off a New Theory of Flight was developed revealing the true Secret of Flight in physical terms, very different from the unphysical lifting line theory advocated by Prandtl. 

Since then massive evidence has been accumulated by Johan Jansson showing that computing turbulent solutions of Euler's equations with slip opens basically all of slightly viscous nearly incompressible flow to predictive simulation without parameter input and need to resolve thin no-slip boundary layers, thus with readily available computing power, all along Euler's prophecy. More evidence: HighLift Workshop.

Euler was thus right, and he understood that he just had to wait for computing power to see his prophecy become true. It took 250 years, but now it is here.

It means that Prandtl was wrong claiming drag and lift to be effects of thin no-slip boundary layers thereby making CFD into an impossibility. 

Question

How will the fluid dynamics community react to replacing Prandtl by Euler as Father of Modern Fluid Mechanics thus changing CFD from impossible to possible? 

Further Important Facts

Turbulent solutions to Euler's equations are computed as best possible approximate solutions in the sense of having residuals which are small in a weak sense and not too large in a strong sense, in a situation when all solutions with small residual in a strong sense (laminar solutions) are unstable and do not persist over time. We thus face a new situation where only turbulent flow is computable and laminar not, as an expression of the fluctuating nature of turbulence, as seen in a waving flag showing the only motion which can persist. The control of the residual in strong sense introduces a viscous effect as a form of turbulent viscosity set by computation alone without need to model or measure turbulent viscosity beyond human comprehension.  

Euler was a mathematician while Prandtl as Father of Modern Fluid Mechanics was more of an engineer. Replacing Prandtl by Euler means freeing the full power of mathematics with computation in a rare example of parameter-free mathematical model with very rich applicability.

Standard CFD under a Planck dictate of no-slip has developed complicated wall models as well as turbulence models including many parameters, and an agreement has been made to adjust parameters to give  50% or more of total drag to skin friction. Turbulent Euler computations with zero skin friction show correct drag in a large variety of situations, which is incompatible with the 50% skin friction from standard CFD.

Total drag consists of pressure drag and skin friction drag. Turbulent Euler computations show that pressure drag dominates skin friction by a factor of at least 10, and so standard CFD claiming 50% skin friction must underestimate pressure drag by a factor 2. The CFD community is now wrestling under this contradiction. The investments in standard CFD are huge and will loose their value if Euler is allowed to take over from Prandtl...Compare with posts on Prandtl Medal.

Incompressible flow is well captured by the Euler equations  for Reynolds numbers (scaling with 1/viscosity) larger than about 500.000 associated with the so called drag crisis when drag of a bluff body drastically decreases with a factor 2-3 as the boundary condition effectively turns into slip from limited velocity strains, with late separation and small wake of low pressure, in particular with lift/drag around 15 for a wing allowing flight at affordable power.

Euler vs Navier-Stokes: What is viscosity?

The Navier-Stokes equations connect fluid velocity strains (derivatives in space) with shear forces through a positive coefficient of viscosity $\nu$ as a parameter to be supplied as input, assumed to be constant independent of fluid velocity in the basic case, but in general with a very complex unknown non-linear dependence on local flow velocities. Formally $\nu =0$ in the parameter-free Euler's equations.

In slightly viscous flow the coefficient of viscosity is small with a Reynolds number $Re = \frac{UL}{\nu}$ beyond drag crisis (bigger than 100.000- 500.000) with $U$ typical flow speed and $L$ typical spatial scale L. 

The Navier-Stokes equations can be complemented by a (skin) friction boundary condition with a friction parameter $\beta$ connecting (tangential) shear stress to tangential flow velocity, with slip corresponding to $\beta =0$ and effective no-slip for $\beta >1$, thus covering a range from slip to no-slip with important effects on flow separation and drag (as exposed in Computational Turbulent Incompressible Flow). 

To determine the viscosity as input to the Navier-Stokes equation experimentally or theoretically has shown to be virtually impossible in the case of slightly viscous flow, which is always partially turbulent with a very complex expression of viscosity. Using Navier-Stokes equations for true prediction of slightly viscous flow has not been shown to be possible. With parameter fitting in viscosity models standard CFD can match measured drag, but generally fail in blind tests without prior knowledge of the correct value to match.

Computing turbulent solution to the Euler equations includes automatic modeling of viscosity

through weighted strong residual control as a dissipative effect with a complex flow dependence beyond viscous shear stress.  It appears as a solution to the open problem of turbulence modeling. In particular, size of the strong residual measures the turbulent dissipation as a mesh independent quantity meeting Kolmogorov's conjecture. 

The Navier-Stokes equation model (1823) with constant positive viscosity is generally viewed to be a better/more complete model then the Euler equations (1755) with formally zero viscosity. This was picked up by Prandtl in 1904 using in particular no-slip from the presence of positive viscosity as a way to discriminate potential flow and get around d'Alembert's paradox. But the more complete model showed to be boundary layer uncomputable and asking for parameter input and so non-predictive, while the basic Euler model showed to be more useful by being both computable (no boundary layers) and predictive as parameter free. 

The ultimate quest for a physicist is to find a Theory of Everything ToE as a parameter free model explaining all of basic physics. Computing turbulent solutions to the Euler equations is a ToE for fluid mechanics. 

Laminar Slip Layer vs Turbulent No-Slip Layer: Change of Paradigm

A turbulent no-slip  boundary layer is uncomputable and lacks mathematical model. A troublesome concept. Modern fluid dynamics has been obsessed with the problem of tackling this problem, without success. The result is CFD which is not predictive  and thus not very useful.

DFS Direct Finite Element Simulation as a new paradigm in Computational Fluid Dynamics CFD exhibits a new basic phenomenon of

• laminar slip boundary layer 

to be compared with the basic elements identified by Prandtl as the Father of modern fluid mechanics of:

• laminar no-slip boundary layer, 
• turbulent no-slip layer.

The appearance of a laminar slip boundary is connected to the so called drag crisis occurring in bluff body slightly viscous flow such as air and water at a Reynolds number $Re\approx 500.000$ with the drag of a bluff body drastically dropping beyond $500.000$. 

The reduction is the result of delayed separation with reduced wake as an effect of a shift from a laminar no-slip boundary layer, which trips the flow to early separation,  to effectively a laminar slip boundary layer, which allows a different form of separation as 3d rotational slip separation without tripping.

The appearance of a turbulent no-slip layer is typically artificially induced in experiments through a transversal ribbon/strip attached to the body thus effectively changing the shape of the body, which trips the flow into separation and turbulent wake. The idea is that this way force the experiment to fit with a preconceived notion by Prandtl of a turbulent no-slip boundary layer, but this is against the most basic principle of science to fit theory to observation and not the other way around.    

The result of using an effective laminar slip boundary condition without any artificial tripping, is that fluid flow beyond the drag crisis is computable by DFS because impossible computational resolution of thin turbulent boundary layers required in Prandtl CFD,  is no longer needed. A non-computable turbulent no-slip boundary is thus replaced by a computable laminar slip layer. 

DFS shows to accurately predict fluid flow beyond the drag crisis by computing best possible turbulent solutions of Euler's equations as first principle physics without parameters with slip as wall model and a turbulence model as emergent from computation. This makes CFD computable from being uncomputable to all Prandtl followers, and thus represents a veritable change of paradigm.

A key to the breakthrough is the concept of laminar slip boundary layer of a fluid which is viscous-plastic with fluid particles sliding along a smooth wall with skin friction coefficient of size 0.001 at drag crisis and decreasing beyond. 

DFS shows that slightly viscous flow is not Newtonian with a constant (small) viscosity since the emergent turbulence model in DFS does not reflect a constant viscosity, nor does the viscosity-plastic slip boundary condition. 

This gives perspective on the Clay Navier-Stokes problem which concerns a Newtonian fluid seemingly without relevance for slightly viscous flow as the main challenge of fluid mechanics.           

Prandtl's Tripped Science vs Boeing Max

Prandtl making tripped experiments

Danger of tripping 

Ludwig Prandtl is viewed as the Father of Modern Fluid Mechanics because he offered a resolution of the pressing problems of fluid mechanics in the beginning of the 20th century including d'Alembert's paradox through his discovery of the laminar and turbulent boundary layer in wall bounded fluid flow.

The legacy of Prandtl is described in Prandtl-Essentials of Fluid Mechanics edited by Herbert Oertel, Springer 2004, with the following introduction

• The development of modern fluid mechanics is closely connected to the name of its founder, Ludwig Prandtl. 
• In 1904 it was his famous article on fluid motion with very small friction that introduced boundary-layer theory. 
• His article on airfoil theory, published the following decade, formed the basis for the calculation of friction drag, heat transfer, and flow separation.
• Prandtl was particularly successful in bringing together theory and experiment, with the experiments serving to verify his theoretical ideas. 
• It was this that gave Prandtl’s experiments their importance and precision. His famous experiment with the tripwire, through which he discovered the turbulent boundary layer and the effect of turbulence on flow separation, is one example. 
• The tripwire was not merely inspiration, but rather was the result of consideration of discrepancies in Eiffel’s drag measurements on spheres. 
• Two experiments with different tripwire positions were enough to establish the generation of turbulence and its effect on the flow separation. For his experiments Prandtl developed wind tunnels and measuring apparatus, such as the Göttingen wind tunnel and the Prandtl stagnation tube. 
• His scientific results often seem to be intuitive, with the mathematical derivation present only to provide service to the physical understanding, although it then does indeed deliver the decisive result and the simplified physical model. 
• According to a comment by Werner Heisenberg, Prandtl was able to “see” the solutions of differential equations without calculating them.

To give the highlighted parts perspective recall that when I was awarded the Prandtl Medal in 2014 by ECCOMAS, I stated that I would receive the medal under the condition that it would be expressed that the New Theory/Computation of Flight developed together with Johan Hoffman and Johan Jansson showed that Prandtl had misled modern fluid mechanics into a fruitless search for the origin lift and drag of an airplane wing in a boundary layer so thin that it could never be resolved in computation. This was not allowed to be expressed and the result was that I did not accept to receive the medal. The story can be read here.

The New Theory of Flight supported by refined computations since 2014 shows that contrary to Prandtl wall bounded slightly viscous flow can be modeled by a slip boundary condition without any boundary layer, which makes the flow computable as time variable turbulent flow. There is thus now massive evidence that Prandtl was wrong, seriously wrong. 

Signs that there is something fishy with Prandtl's boundary layers as the origin of drag and lift can be seen in the above highlights: 

1. Prandtl use a tripwire to change the flow to fit what he could "see" without mathematics and computation. 
2. His results were intuitive.     

The effect of artificially tripping the flow in experiments has led to the misconception that skin friction drag is a major part of total drag with form/pressure drag a minor part, viewed to be relevant  also for an airplane wing without tripping device. The New Theory gives hard evidence that this is seriously misleading by computing drag and lift with slip in close accordance to observations.

The lesson is that if you rely on intuition rather than correct mathematics and are ready to trip experiments to fit, then you can end up with something with little connection to reality. Evidently Prandtl did so. The consequences are severe with the Boeing Max debacle a result of misconceived engineering computation following Prandtl.

PS The following question/answer appears on FAQ at Secret ion Flight:

Q30: Why is the flow tripped by a wire, strip or ribbon in wind tunnel measurements of drag of wing, when a real wing does not have any tripping device and the tripping thus appears to be artficial?

A30: The rationale presented is that the tripping will force the development of a turbulent boundary layer with substantial skin friction,  which according to Prandtl should be present. The tripping is thus done to artificially fit reality to theory, which is opposite to the basic principle of science to fit theory to reality. In the New Theory, which fits with untripped experiments, the flow of air meets the wing with a slip boundary condition modeling vanishing skin friction.

Flying Impossible with Prandtl No-Slip Flow Separation

Ludwig Prandtl is named Father of Modern Fluid Mechanics because of his proposed resolution in 1904 of d'Alembert's paradox from 1755 based on the concept of no-slip boundray layer as a thin region connecting free flow velocity with zero relative velocity at a solid wall.

Prandtl thus proposed that the drag or resistance to motion of a more or less streamlined body like an airplane wing moving through air, is an effect of boundary layer separation causing a turbulent wake. Prandtl's scenario which has dominated 20th century fluid mechanics is illustrated in the above generic text book picture with the following elements:

1. No-slip: the flow velocity is zero on the surface of the (still) wing.
2. The boundary layer starts laminar at the leading edge stagnation point, grows in thickness with the flow and quickly after the crest of the wing turns turbulent and even thicker.
3. The flow decelerates after the crest by increasing pressure in the flow direction (adverse pressure gradient), which ultimately leads to reverse flow followed by flow separation into a turbulent wake creating drag.         

But Prandtl's picture does not describe the actual flow dynamics around a wing, because this would not allow the wing to generate lift, which is the purpose of a wing. In short, this is because a flow with no-slip will separate already on the crest of the wing and little lift will be generated. The math is given below. You can see this effect in Prandtl's famous film of an airfoil dragged through a viscous fluid showing separation on the crest already at small angle of attack. Prandtl's wing would not fly.

Compare with DNS with heavily tripped turbulent boundary, which also shows separation quickly after the crest with loss of lift (real wings do not have such tripping devices).  

The New Theory of Flight shows that drag and lift do not originate from a thin no-slip Prandtl boundary layer, but instead from an effective slip boundary condition, which keeps the flow attached to the upper wing surface until the trailing edge (before stall) and thus creates lift by suction.

Prandtl has misled generations of fluid dynamicists to search for explanations in boundary layers so thin that they cannot be resolved computationally and thus cannot explain anything. 

The crucial difference between no-slip and slip is seen in mathematical terms as follows: Put a coordinate system with coordinates $x=(x_1,x_2,x_3)$ on top of the crest of the wing with the $x_1$-axis in the main flow direction, the $x_2$-axis perpendicular to the wing and the $x_3$-axis along the wing span. Consider momentum balance in the $x_2$ direction in velocity $u=(u_1,u_2,u_3)$ and pressure $p$ in the presence of vanishingly small viscosity, stationary state and no exterior forcing:

• $u_1\frac{\partial u_2}{\partial x_1}+u_2\frac{\partial u_2}{\partial x_2}+\frac{\partial p}{\partial x_2}=0$ for $x_2\gt 0$,

with $u_2=0$ for $x_2=0$ for both no-slip and slip, and $u_1=0$ for $x_2=0$ in the case of no-slip, while $u_1$ is the free stream velocity with slip. The normal velocity $u_2$ is very mall close to the wall, and so the momentum balance can be reduced to

• $\frac{\partial p}{\partial x_2}=-u_1\frac{\partial u_2}{\partial x_1}$ close to wall,     (1)

In order for the flow to not separate on the crest, the flow must be accelerated by a positive pressure gradient in the normal direction depending on the curvature of the crest, that is $\frac{\partial p}{\partial x_2}$ must be positive large enough. But with no-slip and $u_1=0$ on the surface, this is not compatible with (1) stating that

• $\frac{\partial p}{\partial x_2}$ is vanishingly small close to wall.  

The effect is that flow with no-slip will separate on the crest and lift will be lost. Flying with no-slip is impossible.

Recall that Prandtl focussed on explaining drag, leaving lift to the (likewise unphysical) Kutta-Zhukovsky circulation theory, forgetting that it is incompatible with his boundary layer theory. Flying must have been a complete mystery to Prandtl.

On the other hand, flow with slip can separate only at stagnation, which cannot occur on the crest where the flow speed is maximal, and thus with $u_1 \gt 0$ the free flow velocity in the relation (1) (with a proper negative $\frac{\partial u_2}{\partial x_1}$) can be satisfied with required positive normal pressure gradient. Flying with slip is possible.

The New Theory of Flight thus is based a new theory for flow separation (see previous post) based on 3d rotational slip separation, which shows that the text book theory of Prandtl based on adverse pressure gradients does not correctly capture the true physics of flow separation. The consequences are far-reaching.

New Theory of Flight: Time Line

Potential flow around circular cylinder with zero drag and lift (left). 
Real flow with non-stationary turbulent 3d rotational slip separation and non-zero drag (right). 

The New Theory of Flight published in J Mathematical Fluid Mechanics, can put be into the following time line:

1750 formulation by Euler of the Euler equations describing incompressible flow with vanishing viscosity expressing Newton's 2nd law and incompressibility in Euler coordinates of a fixed Euclidean coordinate system.

1752 d'Alembert's Paradox as zero drag and lift of potential flow around a wing defined as stationary flow which is

1. incompressible
2. irrotational
3. of vanishing viscosity
4. satisfies slip boundary condition 

as exact solution of the Euler equations.

1904 resolution of d'Alembert's paradox of zero drag by Prandtl stating that potential flow is unphysical, because 4. violates a requirement that real flow must satisfy

• no slip boundary condition.

1904 resolution of d'Alembert's paradox of zero lift by Kutta-Zhukovsky stating that potential flow is unphysical, because 2. violates that a sharp trailing edge in real flow creates 

• rotational flow.

2008 resolution of d'Alembert's paradox of zero drag and lift by Hoffman-Johnson stating that potential flow is unphysical, because 

• potential flow it is unstable at separation and develops into non-stationary turbulent 3d rotational slip separation as a viscosity solution of the Euler equations with substantial drag and lift.  

Recall that d'Alembert's paradox had to be resolved, in one way or the other, to save theoretical fluid mechanics from complete collapse, when the Wright brothers managed to get their Flyer off ground into sustained flight in 1903 with a 10 hp engine. 

Prandtl, named the Father of Modern Fluid Mechanics, discriminated the potential solution by an ad hoc postulate that 4. was unphysical (without touching 2.) and obtained drag without lift.

Kutta-Zhukovsky, named Fathers of Modern Aero Dynamics, discriminated the potential solution by an ad hoc postulate that 2. was unphysical (without touching 4.) and obtained lift without drag. 

Hoffman-Johnson showed without ad hoc postulate that the potential solution is unstable at separation and develops into non-stationary turbulent 3d rotational slip separation causing drag and lift. 

The length of the time-line 1750-1752-1904-2008 is remarkable from scientific point of view. Little happened between 1752 and 1904 and between 1904 and 2008, and what happened in 1904 was not in touch with reality. For detailed information, see The Secret of Flight.

1946 Nobel Laureate Hinshelwood made the following devastating analysis:

• D’Alembert’s paradox separated fluid mechanics from its start into theoretical fluid mechanics explaining phenomena which cannot be observed and practical fluid mechanics or hydraulics observing phenomena which cannot be explained.

The only glimpse in the darkness was offered by the mathematician Garret Birkhoff in his 1950 book Hydrodynamics, by asking if any potential flow is stable, a glimpse of light that was directly blown out by a devastating critique of the book from fluid dynamics community, which made Birkhoff remove his question in the 2nd edition of the book and to never return to hydrodynamics.

The 2008 resolution of d'Alembert's Paradox leading into the New Theory of Flight by Hoffman-Johnson,  has been met with complete silence/full oppression by the fluid mechanics community still operating under the paradigm of Hinshelwoods analysis. 

Response from ECCOMAS General Assembly

Here is the response to my letter to the General Assembly of ECCOMAS recorded in the previous post:

Dear Professor Johnson, 
your email of July 21, 2014, was discussed in the ECCOMAS General Assembly meeting on July 22, 2014. The members of the General Assembly unanimously arrived at the following conclusions:

1. The selection procedure followed the official dedication of the ECCOMAS Ludwig Prandtl Medal, acknowledging your outstanding and sustained contributions in the area of computational fluid dynamics.
2. It was confirmed that the award ceremony had to follow the established procedure consisting of a short introduction of the awardees and a brief summary of their major scientific achievements, not providing the possibility for addresses by the awardees. The award ceremony on Monday, July 21, 2014, executed by the organizers of the joint WCCM-ECCM-ECFD conference, exactly followed these rules.
3. The ECCOMAS General Assembly regrets your decision not to accept the award of the Ludwig Prandtl Medal. However, it respects your decision.
4. The ECCOMAS General Assembly considers the discussion on this matter as finished.

Best regards,
Ekkehard Ramm, Ferdinando Auricchio, Pedro Diez, and Josef Eberhardsteiner
President, Vicepresidents, and Secretary of ECCOMAS

Here is my comment on this conclusion of the General Assembly "unanimously arrived at":

My condition for accepting the Medal was that a very short statement authored by me was voiced at the award ceremony, by me or the chairman or the person presenting my work. What I wanted to express was that I through my work have found that Prandtl's boundary layer theory is not in accordance with observations. In short, that my work was not in agreement with Prandtl's.  

This could not be accepted by the Organizers, who demanded me to either give up my condition  of voicing my statement or not accept the Medal. 

When presenting my decision to not accept the Medal at the award ceremony, the Organizers stated according to reports that the reason I could not accept the Medal was that the findings of my research was in opposition to Prandtl's boundary layer theory.

This was not the true reason, which was that my voice was suppressed. I had said that I can accept the Medal if my view on Prandtl's boundary layer theory is not suppressed.

In any case, the Organizers de facto made the very statement at the award ceremony, which could not be made, namely that my view is in opposition to Prandtl's. Nothing was thus gained by forcing me to  not accept the Medal.

And No, the discussion on "this matter" is not all "finished". We are only at the beginning of a long discussion to come in the world of CFD, then outside the body of ECCOMAS, where the focus can continue to be to  "exactly follow established procedures" for  "acknowledging outstanding and sustained contributions in the area of CFD". 

There must be members of ECCOMAS, and others, who do not applaud the handling of the 2014 Prandtl Medal. To suppress expression of scientific theory and observation is to violate the most basic principle of science of free expression. It is nothing for ECCOMAS to be proud of.

If the General Assembly respects my decision to not accept the Medal, I do not respect the decision by the Organizers to force me to do so.

PS By "outstanding contributions to CFD" is apparently meant my work in the 1980s and 1990s,  "sustained constributions" must then refer to my work in the 2000s and 2010s, which is exactly the work in opposition to Prandtl which could not be mentioned at the award ceremony: In mathematics, one contradiction can give rise to any number of contradictions. 

Letter to the General Assembly of ECCOMAS

I want to direct the attention of the General Assembly to the following actions taken by a group of representatives of ECCOMAS in connection to the Prandtl Medal, which was to be awarded to me at the opening ceremony of the IACM-ECCOMAS Conference July 21-25 in Barcelona:

1. I was informed that I had to arrange and pay travel and accomodation myself.

2. I was not invited to the Conference Banquet and informed that the cost was not covered by ECCOMAS.

3. I was not given a fair possibility of expressing my views: No very short statement authored by me was permitted to be voiced at the award ceremony. After a long hazzle I was given a last empty slot in one of 49 parallel sessions in a room of 34 m2 accomodating at most 20 people.

4. The abstract of my talk and link to a related post on my professional blog was not put up on the conference web page, despite repeated requests by me.

5. I was met by an unfriendly uncivilized attitude in a long correspondence recorded on my blog:

with related posts here, here, here and here.

As a consequence of mainly 3. I could not accept to receive the Medal.

I ask the General Assembly to study the details of this story, which to me has been a completely unexpected and unprecedented harrassment.

I expect the General Assembly to report back to me and in particular inform me if the reception I have met as Medalist is the normal standard of ECCOMAS.

Sincerely, 

Claes Johnson

PS Letter to the Organizers asking for reimbursement of my expenses created by the Prandtl Medal Award:

To the Organizers IACM-ECCOMAS Barcelona 2014

I ask you to reimburse me for the following costs in connection to the Prandtl Medal 2014 awarded to me,  which have been drawn on my personal bank account:

Hotel Rey Juan Carlos, two nights:  SEK 2897

Flight Vueling  EBRC7K: SEK 2211

Total SEK: 5108 (around €600)

Please send the remimbursement to Handelsbanken Strandvägen 5B, Box 14222, 104 40 Stockholm

Clearingnumber: 6124, Swift/BIC: HANDSESS 

account xxxxxxxxx 

Please inform me ASAP when the payment has been done,  or if you for some reason are unable to make the transaction.

Sincerely, 

Claes Johnson

The effect of the letter will be reported in upcoming post. Apparently, ECCOMAS has already refused to pay the hotel bill, since the cost has been drawn on my credit card. The chance that the flight ticket will reimbursed appears to be small, since my request has not even been acknowledged.
I really wonder if this is the standard of ECCOMAS, or if I am getting a special reception, because of my "outstanding and sustained contributions to CFD"? If so, it adds to my experience that the better results you may have, the more "outstanding and sustained contributions" you have created, the more opposition and suppression you will meet.

The End of the Prandtl Medal

Here is the last exchange of emails concerning the Prandtl Medal between me and representatives for ECCOMAS offering the Medal to me and IACM co-organizing the conference at which opening ceremony tomorrow the Medal would have been hanged around my neck.

The correspondence (full account in previous post) shows that the contradiction of giving the Prandtl Medal to me was resolved into one of the two given possibilities: My view in direct contradiction to Prandtl's legacy was not allowed to be expressed in open scientific discussion. In this case the Prandtl Medal survived but I could not accept to receive it. 

The other possibility was that my view in direct contradiction to Prandtl's legacy would have been allowed to be expressed in open scientific discussion. In this case it would have been possible for me to accept the Medal, but further issues of the Prandtl Medal may have become meaningless. 

The Organizers chose the first option. The Medal Committee having voted for the second option was apparently run over by the Organizers. But I am still alive and can better express my happy message to the CFD community without the weight of a Prandtl Medal.

Friday July 18:

Dear Professor Johnson,

we already mentioned earlier that a very short award ceremony will take place following the tradition in our associations. This includes a brief introduction of the awardees and a short summary of their major work. Again we would like to point out that it is not possible to enter into a scientific discussion in this ceremony.

However, despite the short notice the organizers found a way for you to express your view in a subsequent CFD session, waived your registration, and include the abstract in the online version of the program. Moreover, your talk will be announced in the ceremony.

We would regret if this arrangement does not meet your expectations and you decide to decline accepting the medal.

Ekkehard Ramm, Pedro Diez, Ferdinando Auricchio, Josef Eberharsteiner- President, Vicepresidents and Secretary of ECCOMAS, Eugenio Oñate, Xavier Oliver, Antonio Huerta - Chairmen of WCCM-ECCM-ECFD 2014

Saturday July 19

Dear Professors and Organizers:

I certainly did not expect to be given the Prandtl Medal, but once being chosen as Medalist I expect a fair and correct reception (including e.g. an invitation to the conference dinner, instead of being asked  to invite and pay myself). I thus expect that the following statement of mine (in bold) will be read at the award ceremony, by myself or by the person presenting my person and work:

The famous Danish physicist Niels Bohr said: “How wonderful that we have met with a paradox. Now we have some hope of making progress.” 

And yes, to give the Prandtl Medal to me is a paradox, or a contradiction, and as such a starting point for making progress. The contradiction is that my work together with Johan Hoffman has shown that Prandtl’s boundary layer theory, Prandtl’s main contribution as the named Father of Modern Fluid Mechanics, is not in accordance with observations and thus incorrect as scientific theory. 

Our evidence consists of computational solutions of the incompressible Navier-Stokes equations as the basic model describing slightly viscous turbulent flow, combined with slip boundary condition as a model of observed small skin friction, which does not generate any no-slip boundary layers, but nevertheless agree with observations of separation, drag and lift for a wide range of problems. 

We conclude that separation, drag and lift  in slightly viscous flow do not originate from thin no-slip boundary layers, in direct contradiction to Father Prandtl. 

Our work breaks the spell of Father Prandtl asking for impossible computational resolution of thin boundary layers beyond the capacity of thinkable computers, and thus opens a wide range of new possibilities for many users of CFD. I will present some of these possibilities in the session Advanced Methods in CFD I following this award ceremony. 

I see no rational reason that this statement by me as chosen Medalist cannot be made at the award ceremony. I further expect that a link to the abstract text I have sent will be put up on the conference web page announcing my talk, together with a link to the following related post on my professional blog:

• Breaking the Spell of Prandtl

I further remind you, for the third time, that I want my first name to be presented as Claes and not the double name Claes-Göran, which still occurs on the talk web page.

Looking forward to seeing you tomorrow.

Best regards,
Claes Johnson

Saturday July 19 11.06 PM 

Dear Professor Johnson, 

the sole intention of ECCOMAS to select you as the awardee of the 2014 Ludwig Prandtl Medal was to acknowledge your outstanding and sustained contribution in the field of Computational Fluid Dynamics.

Your argument "... that Prandtl has had a devastating negative influence on 20th century fluid mechanics" has nothing to do with this intention. The award ceremony would certainly not be the proper forum for publicly voicing your criticism of Prandtl's boundary layer theory, because it would leave no room for instant counter arguments from the auditorium and, thus, would violate a fundamental principle of a fair scientific dispute. 

Therefore, we kindly ask you to withdraw your condition to use the award ceremony for such a criticism. Should you feel unable to do so, we request that you consider not to accept the medal. If you do not respond to this mail we understand that you will not attend the award ceremony on Monday Morning and that you have decided not accepting the medal. 

With best regards, Ekkehard Ramm, Pedro Diez, Ferdinando Auricchio, Josef Eberharsteiner- President, Vicepresidents and Secretary of ECCOMAS Eugenio Oñate, Xavier Oliver, Antonio Huerta - Chairmen of WCCM-ECCM-ECFD 2014


Sunday July 21

To ECCOMAS and Organizers of IACM-ECCOMAS Barcelona 2014

After an extended correspondence with representatives of IACM-ECCOMAS, I have come to the conclusion that I cannot accept to receive the Prandtl Medal given to me. The reason is that I have been denied a fair possibility to present my view as the result of my research the last 20 years, that Prandtl's boundary layer theory is not in correspondence with observations and thus incorrect as scientific theory.

My positive message to the CFD community that computational simulation of slightly viscous flow is today possible without resolution of thin no-slip boundary layers, which is in direct contradiction to Prandtl's legacy as the Father of Modern Fluid Mechanics, has not been allowed to be voiced at the conference, except under unreasonable limitation approaching full suppression. This is a tragedy for CFD, ECCOMAS and IACM and I can only hope that reason finally will win.

If there is tomorrow a glimpse of reason, my above motivation for declining the Medal should be read at the award ceremony.

Sincerely,
Claes Johnson

Breaking the Spell of Prandtl: From Impossible to Possible CFD

When I accepted to receive the Prandtl Medal I stated as a precondition that my views on Prandtl's legacy as the Father of Modern Fluid Mechanics should be made clear when the award is presented at the opening ceremony and then be combined by an open scientific discussion. I will in the mini-session Advanced Methods in CFD I following the opening ceremony present evidence of the unfortunate dominating influence of Prandtl as the Father of Modern Aerodynamics, which has effectively blocked progress for 100 years, under the title:

• Breaking the Spell of Prandtl: From Impossible to Possible CFD (slides)

with the following abstract:

I was surprised of recieving the message that I had been awarded the ECCOMAS 2014 Prandtl Medal, because my work in CFD since 20 years together with Johan Hoffman and his group at KTH gives evidence that Prandtl's main contribution as Father of  Modern Fluid Mechanics, his boundary layer theory initiated in his famous 1904 article On Motion of Fluids Flow with Very Little Viscosity claiming that separation, lift and drag in slightly viscous incompressible bluff body flow (Reynolds number larger than $10^6$) all originate from thin no-slip boundary layers, is not in accordance with observations and thus is incorrect as scientific theory (listen to Prandtl expressing his discovery here with perspectives here and here and here, and comment by Euler here).

The evidence consists of computational solutions of the incompressible Navier-Stokes equations with slip boundary condition, which does not generate any no-slip boundary layers and is motivated by the observation that skin friction is small in slightly viscous flow, do agree with observations with the accuracy increasing with increasing Reynolds number. The evidence shows that separation, lift and drag in slightly viscous flow do not originate from no-slip boundary layers. 

I have thus been awarded the Prandtl Medal while my main contribution contradicts Father Prandtl himself, a somewhat unusual happening.

Our work breaks the spell of Prandtl asking for computational resolution of thin boundary layers which is impossible on any forseeable computer, which has paralyzed CFD since start, by showing that direct computational simulation of turbulent slightly viscous flow is today possible on a supercomputer and tomorrow on a laptop, simply by solving the Navier-Stokes equations with slip boundary conditions using a stabilized finite element method, without any user specified turbulence modeling. This makes CFD of slightly viscous flow possible today for a wide range of users and thus opens many new roads. 

As an example of what can be achieved, we have developed a new theory of flight exhibiting the actual fluid mechanics of flying, which has hitherto been hidden. Another is a characterization of slightly viscous incompressible bluff body flow as potential flow modified by 3d rotational slip separation. 

More complete presentations are listed under Presentations by CJ on this blog.

To get perspective on the Prandtl Medal (including Medals given to Prandtl), I advise to read and contemplate:

• Making of the Prandtl Myth by John D Anderson
• The Dusk of Fluid Mechanics
• Dr Faustus of Modern Physics

The net result is that I can only accept to receive the Prandtl Medal under the condition that my view that Prandtl was wrong, in several respects, is made clear together with the award.

Here is the statement I have asked to be read by me or the person presenting my work at the award ceremony:

The famous Danish physicist Niels Bohr said: “How wonderful that we have met with a paradox. Now we have some hope of making progress.” And yes, to give the Prandtl Medal to me is a paradox, or a contradiction, and as such a starting point for progress.

The contradiction is that my work together with Johan Hoffman has shown that Prandtl’s boundary layer theory, Prandtl’s main contribution as the named Father of Modern Fluid Mechanics, is not in accordance with observations and thus incorrect as scientific theory. Our evidence consists of computational solutions of the incompressible Navier-Stokes equations as the basic model for slightly viscous turbulent flow, combined with slip boundary condition as a model of observed small skin friction, which does not generate any no-slip boundary layers but nevertheless

agree with observation of separation, drag and lift for a wide range of problems.

We conclude that separation, drag and lift  in slightly viscous flow do not originate from thin no-slip boundary layers, in direct contradiction to Father Prandtl. 

Our work breaks the spell of Prandtl asking for impossible computational resolution of thin boundary layers beyond the capacity of thinkable computers, and thus opens a wide range of new possibilities for many users of CFD. I will present some of these possibilities in the session Advanced Methods in CFD I following this award ceremony.  

Perspective on the Prandtl Medal: Model vs Reality

                Prandtl with his model of reality in the form of a little water tank in Göttingen in 1904.

The Prandtl Medal to be given to me (and my coworkers) on July 21 in Barcelona connects to the basic question in science and engineering of model vs reality: As far as I can understand the award expresses a recognition of our work showing that the basic idea of Prandtl of the boundary layer as the origin of lift and drag of an airplane wing, is incorrect.

Our evidence is computed solutions of the Navier-Stokes equations with slip boundary condition, which does not give rise to any boundary layers, but yet fit closely with observations. The agreement improves with increasing Reynolds number beyond $10^5-10^6$, because slip models a turbulent boundary layer. For a jumbojet the Reynolds number is $10^8$ or larger.

More precisely, the computations with slip show somewhat better lift and stall characteristics (higher lift and delayed stall) than experiments.

There are two basic approaches to handle a difference between model and reality: Change the model or change the reality. The second option represents an engineering approach with the goal of constructing a wing so as to realize slip also for moderately large Reynolds numbers (of size $10^5$). One way of doing that is to use rotating cylinders at leading and trailing edge and/or a moving upper wing surface, which indeed shows to improve both lift and stall.

The Prandtl Medal thus invites to redesign of wings according to the model, rather than changing the model to represent existing wings constructed in the spirit of Prandtl as the Father of Modern Aerodynamics.

See also:

• The Spell of Prandtl's Laminar Boundary Layer
• The Spell of Kutta-Zhukovsky Circulation Theory.

The Ludwig Prandtl Medal

Today I received the following message:

Dear Professor Johnson, It is our great pleasure to inform you that you are the winner of the 2014 edition of the ECCOMAS Ludwig Prandtl Medal. The decision has been taken by the ECCOMAS Award Committee in a two-round voting procedure. Please receive our warmest congratulations. 

The Ludwig Prandtl Medal will be delivered at the Opening Session of the WCCM-ECCM-ECFD 2014 Conference in Barcelona, July 21, 2014 (8:30-10:30). We would very much appreciate if you can confirm your participation.

With our best regards and congratulations,

Ekkehard Ramm
ECCOMAS PresidentJosef Eberhardsteiner
ECCOMAS Secretary

Here is my answer:

Dear Profs Ramm and Eberhardsteiner

Thank you for this great honor, which I will be very happy to receive in person at the conference opening. 

The award has an interesting aspect from scientific point of view in that my work (with Johan Hoffman), shows that Prandtl's main idea of the fundamental role of the boundary layer, for both separation and drag and lift, crowning him as the Father of Moden Fluid Mechanics, is incorrect. We show that separation, drag and lift originate from instability of slightly viscous flow and not from a boundary layer. The evidence comes from solving the Navier-Stokes equations with slip boundary condition, which does not give rise to any boundary layer, and we obtain results in full agreement with observations. We conclude that separation, drag and lift in slightly viscous flow do not originate from a boundary layer and thus that Prandtl's main idea is not in agreement with observations.

I would appreciate if this will be made clear to the public at the conference and I would certainly be willing to shortly expose the reasons why Prandtl was wrong. 

The fluid dynamics community will not applaud the award, since 20th century fluid mechanics has followed the Father in search of the origin of separation, drag and lift in the boundary layer. This has had a catastrophic impact on computational fluid mechanics leading to the strong belief that correct results require resolution of boundary layers, which however is impossible even in thinkable future since quadrillions of mesh-points would be required. The result is a dead-lock of rational science. We show that drag and lift of an airplane can today be accurately computed over the entire range of angles of attack including stall, by solving the Navier-Stokes equations with slip using a couple of millions of mesh points. 

The award thus brings a major scientific question to the podium and I hope it can be accompanied by a scientific discussion.
Sincerely, Claes Johnson

Why Prandtl Was Wrong 4

Lift and drag of a NACA0012 wing in computation by Unicorn and experiment.

We have asked if it is possible to check if drag and lift of a body moving through a fluid originate from a thin boundary layer which separates from the body surface into the fluid, as is the mantra of Ludwig Prandtl, the father of modern fluid mechanics, formulated in an 8 page note in 1904.

To check in experiment is cumbersome because the viscosity of a real fluid is never exactly zero and thus it can be argued that no real fluid can satisfy a slip boundary condition with zero skin friction without any boundary layer.

But to check in computation is perfectly possible: just set the skin friction to zero in a Navier-Stokes code, that is use a slip boundary condition and see what happpens. Will drag and lift develop in accordance with observation in solutions of the Navier-Stokes equations with slip

without boundary layers?

Yes! Computations without boundary layer give correct drag and lift!

The conclusion is inevitable:

• Prandtl was wrong: Drag and lift do not originate from boundary layers.
• Prandtl's scenario of fluid separation is incorrect.
• The mantra of modern fluid mechanics is incorrect.

For further details see the new article Analysis of Separation in Turbulent Incompressible Flow which exhibits a scenario of fluid separation which is fundamentally different from that of Prandtl and which is supported by mathematical analysis, computation and observation.

Large Boundary Layer Collider: Why Prandtl Was Wrong 3

Part of the Large Boundary Layer Collider at the European Spallation Source in Lund, Sweden.

According to Ludwig Prandtl, named the father of modern fluid mechanics, both drag and lift of a body moving through air or water originate for a thin boundary layer.

This is the fundamental postulate of modern fluid mechanics formulated in 1904, but it is now being questioned. Is modern fluid mechanics based on a postulate which is does not correspond to physical reality?

The answer may be given by the European Spallation Source (ESS) in Lund, Sweden: The world's biggest proton accelerator (see picture).

The idea is to eliminate the boundary layer by bombarding it with high energy protons, and once the boundary layer has been removed completely this way, drag and lift will be measured. If drag and lift remain the same under removal of the boundary layer, then drag and lift do not originate from any boundary layer, and modern fluid mechanics is based on incorrect physics.

But ESS will not be ready to use before 2020, and thus it is natural to ask if there is some other quicker and cheaper way of eliminating a boundary layer? Yes, there is. But what is it?

Follow the thrilling uncovering of one of modern physics most well kept secrets...

PS An alternative to ESS would be to use liquid helium with next to zero viscosity, but to reach a sufficiently large Reynolds number, the dimension of the experiment needs to be 10 times bigger than that of the Large Hadron Collider and thus is out of reach, for the moment at least.

But as UN global warming alarmism is now fading away maybe this experiment could become the next big initiative by the UN backed by EU. DS

Why Prandtl Was Wrong 2

One way of eliminating a butterfly.

Question and Answer 1:

• How can one prove that a butterfly in Brazil cannot cause a tornado in Texas?
• Eliminate the butterfly and notice tornado without butterfly!

Question and Answer 2:

• How can one prove that a boundary layer is not the origin of drag and lift of a body?
• Eliminate the boundary layer and notice drag and lift without boundary layer.

But how to eliminate a butterfly and how to eliminate a boundary layer? Follow the thrilling

continuation of this story...

Why Prandtl Was Wrong 1

Prandtl initating modern fluid mecahnics in 1904: A very satisfactory explanation of the physical process in the boundary layer between a fluid and a solid body could be obtained by the hypothesis of an adhesion of the fluid to the walls, that is, by the hypothesis of a zero relative velocity between fluid and wall (no-slip).

Ludwig Prandtl is named the father of modern fluid mechanics because he discovered the boundary layer of a slightly viscous fluid flowing around a solid body, like air flowing around a moving car or airplane, as a thin layer where the fluid velocity rapidly changes from the free flow velocity away from the body to that of the body surface as an expression of a no-slip boundary condition.

Prandtl claimed that the that turbulent flow in the aft of a body results from separation of turbulent boundary layer away from the body surface into the free flow.

This has become the mantra of modern fluid mechanics: The truth of slightly viscous fluid flow is to be found in thin boundary layers. Both drag and lift of a body moving through a fluid are effects of a no-slip boundary condition creating a thin boundary layer.

In a sequence of posts we shall show that Prandtl was wrong: Drag and lift do not originate from a thin no-slip boundary layer.

But how can one show that Prandtl was wrong? Something to reflect upon a rainy summer day.

Hint 1: Suppose you observe the same drag and lift with the boundary layers eliminated. Can you then be sure that drag and lift do not originate from boundary layers? Yes, you probably say. But how to "eliminate" the boundary layers?

Hint 2: Browse: Dr Faustus of Modern Physics