Landmarks

LANDMARKS Scientific Research Contributions:

1. Egolf, P.W. and Hutter, K. 2020 Nonlinear, Nonlocal and Fractional TurbulenceTable 5.3 The preference for a logarithmic and a power law was alternating over the last hundred years - page 65:
1938 Millikan (1938) Similarity hypothesis favors the logarithmic law phenomena2001 Afzal (2001) Shows that similarity consideration of Millikan can also be applied to confirm a power law

6.1 In a publication of Cipra (1996) in “Science” Chorin is cited:

"The 'law of the wall' was viewed as one of the few certainties in the difficult field of turbulence, and now it has been dethroned". He further continues by writing “Generations of engineers, who learned the law, will have to abandon it.”

Cipra, B. 1996 A new theory of turbulence causes a stir among experts. Science. 272 (5264), page 951. https://science.sciencemag.org/content/272/5264/951.full

6.2 Then at the very beginning of the new millennium Afzal (2001) demonstrated that the Millikan/Izakson/Clauser idea can also be applied to prove consistency with a power law as averaged velocity profile of the overlap region. This work then immediately removed a believed theoretical obstacle for acceptance of a power law.

Noor Afzal 2001 Power and log laws velocity profiles in turbulent boundary layer flows: equivalent relations at large Reynolds numbers. Acta Mechanica, Vol 151, pp.195-216.Noor Afzal 2001 Power and log laws velocity profiles in fully developed turbulent pipe flow: equivalent relations at large Reynolds numbers. Acta Mechanica, Vol 151, pp.171-183.Noor Afzal 1997 Power laws in the wall and wake layers of a turbulent boundary layer. pp 805 - 808 in Proc 7 Asian Congress of Fluid Mechanics at Chennai. Allied Publisher New Delhi. arXiv:2006.02697v2 [physics.flu-dyn] 9 Jun 2020

2. When Prandtl was asked by a colleague about the theoretical derivation of Blasius 1/4 power law , Prandtl answered:

Whoever finds it will become a famous man

(Sie fragen nach der theoretischen Ableitung des Blasiusschen Widerstandsgesetzes fr Rohre. Wer der wird dadurch ein berhmter Mann! Prandtl to Birnbaum, 7 June 1923, MPGA, Abt. III, Rep. 61, Nr. 137), Page 271 footnote 37 in Micheal Eckert, Pipe flow: A gateway to turbulence. Archive for History of Exact Sciences 75(3) pp. 249-282, 2021.

Afzal (2001) has rationally derived the power law velocity and friction factor for all vales of "n" the power law index. Further, the power law velocity and friction factor have the envelope s and a tangent at any point lead to log law velocity log law friction factor, for all values of power law index "n" and all values of Reynolds numbers in the turbulent flow domain.

2i) Prandtl (1935) proposed log law u+ = k^{-1} ln y_+ + B for large Reynolds numbers, and likewise power law of form u+ = C y_+^\al + C*, a very useful formula for smaller Reynolds numbers. [Prandtl, L. 1935 The Mechanics of Viscous Fluids. In: W.F, D. (ed.) Aerodynamic Theory III. Berlin: Springer. Refer page number 135 equations (21.18) and (21.19)

Afzal (2001) has shown that the power law velocity and friction factor have the envelopes and a tangent at any point lead to log law velocity and log law friction factor for all values of power law index "n" and all values of Reynolds numbers in the turbulent flow domain'

3. P. S. Granville [1987, J. Ship Research 31(3), 207] has termed the research work by N.Afzal and R. Narasimha (1976 Journal Fluid Mechanics 74, 113-25) as ”LANDMARK PAPER”, dealing with turbulent flow on axially symmetric cylindrical missile like objects with experimental confirmation of this approach provided by N. Afzal & K.P. Singh (1976, Royal Aeronautical Society, London: Aero. Quart. Vol 27, pp. 217-228). And others have noted it as a widely accepted rational theory: NASA Ames: J.C.Neves, P. Moin & R.D. Moser (1994 Journal Fluid Mechanics 272, 349-381) and R.M. Lueptow (1988 Report NUSC TR 8389, Naval Underwater System Center, New Port R.I., USA).

4. The measurements of N. Afzal and K . P. Singh (1976, Axisymmetric turbulent boundary layers along a circular cylinder, Aeronautical Quarterly: Royal Aeronautical Society London Vol 27, pp 217-228) have for long been.

”the only measurements of turbulent quantities”

in the flow (Denli & Landweber 1979 J. Hydronautics 13, 93) and have been extensively reviewed by Lueptow (1988 Report NUSC Technical Report 8389 Naval Underwater System Center, New Port R.I., USA).

5. Recognizing the nature of an argument in the abstract is often a very big advance, because it illuminates a wide variety of situations earlier thought to be diverse. This of course was the kind of contribution S. Kaplun, P.A. Lagrestrom and Coworker in California Institute of Technology Pasadena California during 1957 made when they invented (or 'abstracted' from Prandtl1s 1904 work on laminar boundary layer) the principles of matched asymptotic expansion, for closed equation, say; laminar motion. In turbulent flow dealing with open equations of motion the contribution made by N. Afzal and R. Narasimha (1976, Journal of Fluid Mechanics) and N. Afzal (1976, Physics of Fluids) when they invented Izakson-Millikan-Kolmogorov hypothesis (or 'abstracted' from Izakson 1937, Millikan 1939 & Kolmogorov 1941 work on the turbulent motion) as the principles of matching in the method of matched asymptotic expansions for instantaneous Navier-Stokes equations for turbulent flow, or the open Reynolds equations of mean turbulent flow and instantaneous turbulent fluctuations.

Founder of mesolayer (intermediate layer): In a turbulent shear flow the mesolayer (Afzal 1982-1985) is around the peak of Reynolds shear stress domain, being the geometric mean of inner wall layer and outer wake layer of a turbulent shear flow -- after 1930's classical discovery of inner and outer layers by Ludwig Prandtl and Theodore Von Karman. The mesolayer length scale is the order of the Taylor micro length scale. The mesolayer time scale is of the order of the Taylor micro time scale; having turbulent energy bursting time process phenomena.

Noor Afzal's Invention of an Intermediate layer (mesolayer) of a turbulent shear flow in space and time variables (Afzal 1982 Ingenieur-Archiv Vol 52, pp. 355-377 Springer Verlag, Berlin) being geometric mean of inner layer and outer layer.scales in a turbulent pipe, channel and boundary layer flows; after Prandtl & Karman 1930's proposals of inner wall layer and outer layer : Review of four decades research, Technical Report No 5 of 14 July 2022 AMU Aligarh. Perspectives of world wide plagiarism by researchers in advance Counties, Submitted to Journal of Fluid Mechanics with a letter to Colm-cille P. Caulfield Editor, Journal of Fluid Mechanics

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6. Part of work in Afzal (1983 Analysis of a turbulent boundary layer subjected to a strong adverse pressure gradient Int. J. Engineering Sciences Vol 21, pp. 563-576) was presented by Noor Afzal (1980) and published in the Proceedings of the First Asian Congress of Fluid Mechanics (ACFM) Bangalore. The ACFM Bangalore Organizer, Professor Roddam Narasimha, sent the manuscript or review to Professor Akiva Moiseevich Yaglom, Moscow and his comments. Yaglom in a letter dated 6 December 1979 addressed to the Chairman ACFM wrote, a part of which is quoted below:

(Quote begins) " The most exciting statement of Afzal's paper from my point of view is the proof of the half-power law with the non-constant coefficients A(L) and C(LRp). Unfortunately, I must confess that I do not understand this proof. In fact, we tried hard to obtain theoretically, the half-power law with A(L) when working at the power with Kader*. At least twice we had the feeling that we have found the proof, but after that, we found deficiencies in our arguments. Now my feeling is that this law can not be proved logically but I 'II be happy if I am not right and you are right ---- I think that the topic is very exciting and I hope you will continue the work --"(Quote ends).

*Kader B. A. Yaglom, A.M. 1978 Similarity treatment of moving-equilibrium turbulent boundary layers in adverse pressure gradients, Journal of Fluid Mechanics 89(02):305 - 342

7. M. H. Buschmann, and M. Gad-el-Hak 2007 Recent developments in scaling of wall-bounded flows, Progress in Aerospace Sciences, Vol. 42 , pp. 419-467.

50 citations of Afzal's recent work-See Section 6. Power laws by N. Afzal and W. Nunner pages 446 - 4526.1 The open functional equation by N.Afzal page 446 6.2 The power law by W. Nunner page 4486.3 Experimental evidence of Afzal’s and Nunner’s power laws page 450

8. Year 2007 Citations of Dr Afzal’s research work: 50 citations of Afzal’s recent work in a paper by Matthias H. Buschmann, and M. Gad-el-Hak 2007 Recent developments in scaling of wall-bounded flows, Progress in Aerospace Sciences, Vol. 42 (2007) pp. 419-467.

9. M.H. Buschmann and M. Gad-el-Haq (2003 AIAA J. 41(1),page 40) have termed that ”Afzal (2001 Acta Mechanica, v 151, pp171-183 and pp195-216) rigorously demonstrated the equivalence of the log and power laws at very large Reynolds numbers”, and on page 47 have termed that ”the second order theory was originally derived by Afzal (1976, Physics of Fluids 19, 600-602) and third order theory developed by Afzal & Bush (1985, Proc Ind. Acad Sci A: 94, 135-48)”.

10. M. H. Buschmann and M. Gad-el-Haq (2002 IUTAM Symposium Princeton Uni) on first page stated that ”Alternative Reynolds number dependent power laws (George & Castillo 1997, Barenblatt etal 2000, Afzal 2001) have been advanced”.

11. The summary report by Eaton, J. K. & Nagib, H. M. (2004) on the ’Second International Workshop on wall bounded turbulent flows’ by Nagib, H. M. & Smits A, J. held on 2-5 Nov 2004 at the Abdus Salam International Center of Theoretical Physics, Trieste on page 3 stated that ” Noor Afzal highlighted a number of limitations in the asymptotic analysis leading to the power law for the boundary layer theory by George et al (1996-2003). (see also Paper No AIAA-2005-0109 by Afzal).

12. N. Afzal & A. Bushra (2011, 2006, 2002) J. Hydraulic Research provided rational theory to the outstanding flow problem in the Structure of turbulent hydraulic jump for rough and smooth bed open channels, after 175 years of Belanger (1928) hydraulic jump conditions (see review by W.H. Hager 1990 Schweizer Ingenieur & Architect No 25 pp 728-735).

Mesolayer theory

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