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Scientific Progress and Its Impact on Wind

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Wind Science and Engineering

Part of the book series: Springer Tracts in Civil Engineering ((SPRTRCIENG))

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Abstract

This chapter deals with fluid dynamics, probability theory and automatic computation. Just in the first half of the twentieth century they displayed major improvements, both in general terms and as regards the basic tools for the knowledge of wind that would come to maturity in the second half of the twentieth century. After almost two centuries of trials, fluid dynamics overcame the doubts about D’Alembert’s paradox and the resistance of bodies, formulating the founding principles of the boundary layer, of the vortex wake, and of the transition from laminar to turbulent flows. The probability theory, reorganised on axiomatic grounds, produced a broad range of developments including extreme value theory, principal component analysis, random processes and Monte Carlo methods. The appearance of the electronic computer gave rise to advances firstly addressed to meteorological forecasts, then aimed to solve the increasingly complex problems posed by the renewed culture of the wind.

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Notes

  1. 1.

    Reynolds ’ experiments proved that the transition from laminar to turbulent regime took place in a circular pipe for a R value nearly equal to 2300. In view of the current knowledge, the flow is laminar for R ≤ 2000 and is turbulent for R ≥ 4000. The 2000 ≤ R ≤ 4000 range is defined as the transition domain.

  2. 2.

    Reviewing Boussinesq’s contribution (Sect. 3.6) in the light of Reynolds ’ results, it amounts to expressing Eq. (5.7) in the form:

    $$ \overline{T}_{ij} = - \overline{p}\updelta_{ij} +\upmu_\text{T} \left( {\frac{{\partial \overline{v}_{i} }}{{\partial x_{j} }} + \frac{{\partial \overline{v}_{j} }}{{\partial x_{i} }}} \right)\quad \left( {i,j = 1,2,3} \right) $$

    where μT is the eddy viscosity coefficient. Reynolds ’ demonstration, therefore, expressed in a mathematical form the concept introduced by Boussinesq in physical and phenomenological terms: the μT parameter is strongly dependent on the turbulent agitation of the flow.

  3. 3.

    In his 1894 book, Progress in flying machines, Octave Chanute (Sect. 7.4) wrote: “Science has been awaiting the great physicist, who, like Galilei or Newton, should bring order out of chaos in aerodynamics, and reduce its many anomalies to the rule of harmonious law”. Chanute died in 1910, without making the acquaintance with Prandtl .

  4. 4.

    In 1928, when he was questioned by Goldstein about the succinctness of his famous paper, Prandtl replied that he had no more than 10 min available for the presentation and then he did not believe necessary to write more than what he would have told.

  5. 5.

    In his work presented in 1904 and published in 1905 [9], Prandtl used the “boundary layer” (“Grenzschicht”) term only once; he often resorted, instead, to the “transition layer” (“Übergangsschicht”) term. The “boundary layer” term was extensively used by Blasius in his 1907 doctorate thesis. In 1925 Prandtl judged such term unsatisfactory but resigned himself to its use considering its diffusion.

  6. 6.

    Communication of Prof. Masaru Matsumoto, University of Kyoto, Japan.

  7. 7.

    In his 1908 paper [16] Bénard was the first to call the S quantity in Eq. (5.1) Strouhal number.

  8. 8.

    In the fifth edition of Lamb’s book, Hydrodynamics [3], published in 1924, there was a brief paragraph about the boundary layer, with the following words dedicated to Prandtl : “The calculations are necessarily elaborate, but the results (…) are interesting”. In the sixth edition, published in 1932, a whole chapter was dedicated to the boundary layer, including the equations of motion.

  9. 9.

    Before Karman, other authors obtained expressions of the “velocity-defect law” on empirical and experimental bases. Among them, it is worth noting to cite Henry Philibert Gaspard Darcy (1803–1858) (Recherches expérimentales relatives au mouvement de l’eau dans les tuyaux, 1857) and his assistant, Henry Emile Bazin (1829–1917) (Recherches hydrauliques, 1865).

  10. 10.

    The fact that the exponent of the power law defined by Eq. (5.22) decreases as the Reynolds number increases leads to suppose the existence of an asymptotic profile to which \( \overline{u} \) tends when viscous stresses become evanescent with respect to turbulent ones. Such profile is provided by Eq. (5.35) [33].

  11. 11.

    A Markov chain is defined as simple if the probability of the result of the (n + 1)-th experiment only depends on the result of the n-th experiment; if, conversely, it depends on the results of the previous k experiments, it is called a composite Markov chain of the k-th order.

  12. 12.

    The paper by Benjamin Peirce (1809–1880), Criterion for the rejection of doubtful observations (1852), and the posthumous treatise by William Chauvenet (1820–1870), A manual of spherical and practical astronomy (1878), are especially significant.

  13. 13.

    Thomas Joannes Stieltjes (1856–1894) was a Dutch mathematician known for his studies about integrals.

  14. 14.

    Using Lebesgue’s decomposition theorem, any distribution function may be written as \( F(x) = a_{1} F_{1} (x) + a_{2} F_{2} (x) + a_{3} F_{3} (x) \), being \( a_{i} \ge 0\,(i = 1,2,3) \), \( a_{1} + a_{2} + a_{3} = 1 \); F1 is an absolutely continuous function (anywhere continuous and differentiable for almost any x), F2 is a step function with a finite or infinitely enumerable number of steps, F3 is a singular function (continuous, with a null derivative almost everywhere). In case of probability distributions, F1 and F2 respectively correspond to continuous and discrete random variables. In the case of power spectral distributions, F1 and F2 respectively refer to continuous and discrete harmonic contents. In both cases, F3 corresponds to pathological conditions that are unlikely to be present in real problems.

  15. 15.

    Erik Ivar Fredholm (1866–1927) was a Swedish mathematician known for his contributions to integral equations. Equation (5.63) was discussed in a paper, Sur une classe d’equations fonctionnelles, which appeared on Acta Mathematica in 1903.

  16. 16.

    In the 1950s, RAND Corporation produced a table with 1,000,000 random numbers. After the correction of an error, the table was published in 1955.

  17. 17.

    Starting from the researches carried out by Harry Nyquist (1889–1976) about the transmission of information (Certain topics in telegraph transmission theory, 1928), in 1949 Shannon formulated the modern version of the sampling theorem (Communication in the presence of noise). It, now known as the Nyquist-Shannon’s theorem, defines the sampling frequency of a signal to avoid distortion. Given a f(t) signal with finite band amplitude (with an harmonic content limited by the ns frequency), and being known the minimum signal sampling frequency (n = 1/Δt, being Δt the sampling time), it must be at least equal to twice the maximum frequency of the signal (n ≥ 2ns).

  18. 18.

    ENIAC was presented to the press on 14 February 1946, creating sensation: the neon lamps indicating the status of the computation units were covered with ping-pong balls cut in half and turned on and off creating suggestive lighting effects. The term “electronic brain” came into existence with ENIAC. It was definitively turned off at 11:45 on 2 October 1955.

  19. 19.

    John von Neumann, Leo Szilard (1898–1964), Edward Teller (1908–2003) and Eugene Wigner (1902–1995), formed the so-called Hungarian clan, the core of the group that developed the atomic bomb Manhattan Project in Los Alamos. Besides being Hungarian, they also shared the same Jewish origins and the need to seek refuge from Nazi persecution in the U.S. It is said that Enrico Fermi (1901–1954), one of the prominent figures of the Manhattan Project, was sceptical about the existence of extra-terrestrial beings; one day Szilard told him: “they are already here, and you call them Hungarians”. Neumann came from a different planet. When he was 10, he fluently spoke four languages. During the gymnasium he was flanked by a university tutor who followed him with mathematics. At the age of 22 he graduated in chemical engineering in Zurich and in mathematics in Budapest, associating with Karman, Einstein and David Hilbert (1862–1943). In Los Alamos, the challenges among Richard Feynman (1918–1988), Fermi and Neumann on the most complex mathematical problems were famous: the first used a mechanical calculator, the second wrote on paper scraps, the third solved them in his mind.

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  1. Department of Civil, Chemical and Environmental Engineering, Polytechnic School, University of Genoa, Genoa, Italy

    Giovanni Solari

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Solari, G. (2019). Scientific Progress and Its Impact on Wind. In: Wind Science and Engineering. Springer Tracts in Civil Engineering . Springer, Cham. https://doi.org/10.1007/978-3-030-18815-3_5

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