Elsevier

European Journal of Mechanics - B/Fluids

Volume 79, January–February 2020, Pages 1-11
European Journal of Mechanics - B/Fluids

Computers and turbulence

https://doi.org/10.1016/j.euromechflu.2019.06.010Get rights and content

Abstract

This paper briefly reviews the influence that the rapid evolution of computer power in the last decades has had on turbulence research. It is argued that it can be divided into three stages. In the earliest (‘heroic’) one, simulations were expensive and could at most be considered as substitutes for experiments. Later, as computers grew faster and some meaningful simulations could be performed overnight, it became practical to use them as (‘routine’) tools to provide answers to specific theoretical questions. More recently, some turbulence simulations have become trivial, able to run in minutes, and it is possible to think of computers as ‘Monte Carlo’ theory machines, which can be used to systematically pose a wide range of ‘random’ theoretical questions, only to later evaluate which of them are interesting or useful. Although apparently wasteful, it is argued that this procedure has the advantage of being reasonably independent of received wisdom, and thus more able than human researchers to scape established paradigms. The rate of growth of computer power ensures that the interval between consecutive stages is about fifteen years. Rather than offering conclusions, the purpose of the paper is to stimulate discussion on whether machine- and human-generated theories can be considered comparable concepts, and on how the challenges and opportunities created by our new computer ‘colleagues’ can be made to fit into the traditional research process.

Introduction

Although, from its title, this paper may seem to be an appeal for a new and unnecessary journal, it is intended as a review of the role that the rapid development of direct numerical simulations has played over the last decades in the elucidation of turbulence physics, and as a meditation on its possible evolution in the immediate future. It does not address the parallel development of turbulence models and large-eddy simulations, which are the mainstay of industry but which owe less to computational power. As the story unfolds, it should be clear to the reader that many of the themes that we meet in tracing turbulence research can be generalised to the role of computers in other branches of science and technology, some of which have led the way, while others have lagged behind [1], [2], [3], [4]. We may use the former as guides to likely future developments in our field, and the latter as warnings of the pitfalls to be avoided. In addition, and even if a definite answer is well beyond the scope of a paper like the present one, we will briefly discuss what could be the consequences of continuing in the present direction, both for the field and for its practitioners, and leave to the readers the decision on what they think is the right course to follow.

It has become customary to start historical reviews of turbulence with a reference to Leonardo da Vinci. Unfortunately, although he wrote extensively on fluid mechanics and on what later came to be regarded as turbulence, I have been unable to trace any reference to computation or automata applicable to the present review. However, to maintain tradition, I offer a quote which is relevant to the general themes discussed in the paper.

It refers to the relation between theory, experience and data, and can be applied to the hopes of some people, including the author, of what could be expected from computers. It can also be taken as a working definition of a successful theory: “There is nothing in nature without a cause; understand the cause and you will have no need for the experiment” [5, Cod. Atlantico, 147va]. This is clearly a dubious statement, and Leonardo hedges it elsewhere by declaring that: “It is my intention first to cite experience, then to demonstrate through reasoning why experience operates in a given way” [6, Ms E Paris, 55r], or that we should “avoid the teaching of speculators whose judgement is not confirmed by experience” [6, Ms B Paris, 4v]. While aiming for the first of these quotes, this review will try to follow the last two.

The paper is organised in terms of the cost of individual simulations. Section Section 2 deals with simulations which are very expensive, and Section Section 3 discusses the consequences of some simulations becoming inexpensive enough to be considered routine. These two sections can be seen as a short historical survey of the field up to now, but Section Section 4 speculates on how turbulence research might be affected when simulations become cheap enough to be deemed trivial, and offers an example. The paper is intended to promote discussion among researchers, and offers no conclusions, but a summary and a list of possible open questions are collected in Section Section 5.

Section snippets

Turbulence and numerical simulation

Humans must have been aware from very early times that the flow of water is not always smooth, and that crossing a river involves dealing with eddies comparable to the mean drift of the stream. The same applies to the wind, and some of the first recorded uses of the word ‘turbulent’ are applied to the weather. Quantitative study of turbulent flows, even if not recognised as such, must also have been commonplace, because the design of the extensive irrigation canals and aqueducts of antiquity

Overnight simulations and conceptual turbulence

It is a welcome characteristic of fluid mechanics that we know the equations of motion, and that we can simulate the subject of our study to any desired precision. Moreover, we saw in the last section that computers have evolved to the point at which simulations can address what is probably the asymptotically relevant set of parameters in simple flows. It follows that, once computers become fast enough for these simulations to become routine, they can provide answers to any concrete question

Trivial simulations and Monte Carlo research

In the previous section we have given examples of how using computers as ‘universal answering’ machines, performing routine searches and conceptual experiments in no more than a few hours, can advance the study of turbulence. The procedure follows the classical scientific method of designing experiments to address a particular question, with the only difference that they are performed computationally. However, because the time spent in each simulation is short, but not trivial, testing more

Discussion: competitors or colleagues?

As mentioned in the introduction, the goal of this paper is to promote discussion, and it therefore offers no conclusions. However, we can summarise what we have discussed up to now, and highlight some of the questions that, from the point of view of the author, need to be addressed by the community. The paper has been organised in three sections ordered by the increasing capabilities of computers. The first two sections, which deal with computers as expensive experimental apparatus, or as

Acknowledgement

This work was supported by the European Research Council under the Coturb grant ERC-2014.AdG-669505.

References (86)

  • GungorA. et al.

    Scaling and statistics of large-defect adverse pressure gradient turbulent boundary layers

    Int. J. Heat Fluid Flow

    (2016)
  • VinuesaR. et al.

    Turbulent boundary layers around wing sections up to Rec=1,000,000

    Int. J. Heat Fluid Flow

    (2018)
  • BrennerA.E.

    The computing revolution and the physics community

    Phys. Today

    (1996)
  • NormanM.L.

    Probing cosmic mysteries by supercomputer

    Phys. Today

    (1996)
  • MoinP. et al.

    Direct numerical simulation: A tool in turbulence research

    Ann. Rev. Fluid Mech.

    (1998)
  • WuT. et al.

    Toward an AI physicist for unsupervised learning

    (2018)
  • MacCurdyE.

    The Notebooks of Leonardo Da Vinci

    (1939)
  • ZammattioC. et al.

    The Scientist

    (1980)
  • HagenG.H.L.

    Über den Bewegung des Wassers in engen cylindrischen Röhren

    Poggendorfs Ann. Phys. Chem.

    (1839)
  • PoiseuilleJ.M.L.

    Recherches expérimentales sur le mouvement des liquides dans les tubes de très petits diamètres

    Mém. Savants Etrang. Acad. Sci. Paris

    (1846)
  • HagenG.H.L.

    Über den Einfluss der Temperatur auf die Bewegung des Wassers in Röhren

    Math. Abh. Akad. Wiss. Berl.

    (1854)
  • DarcyH.

    Recherches expérimentales rélatives au mouvement de l’eau dans les tuyeaux

    Mém. Savants Etrang. Acad. Sci. Paris

    (1854)
  • BoussinesqJ.

    Essai sur la theorie des eaux courantes

    Mem. Acad. Sci. Paris

    (1877)
  • ReynoldsO.

    An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels

    Phil. Trans. R. Soc.

    (1883)
  • ReynoldsO.

    On the dynamical theory of incompressible viscous fluids and the determination of the criterion

    Proc. R. Soc.

    (1894)
  • RouseH. et al.

    History of Hydraulics

    (1957)
  • LambH.

    Hydrodynamics

    (1895)
  • KolmogorovA.N.

    The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers

    Dokl. Akad. Nauk SSSR

    (1941)
  • RosenheadL.

    The formation of vortices from a surface of discontinuity

    Proc. R. Soc. A

    (1931)
  • KoochesfahaniM.M. et al.

    Mixing and chemical reactions in a turbulent liquid mixing layer

    J. Fluid Mech.

    (1986)
  • RichardsonL.F.

    Weather Prediction By Numerical Process

    (1922)
  • HuntJ.C.R.

    Lewis Fry Richardson and his contributions to mathematics, meteorology, and models of conflict

    Ann. Rev. Fluid Mech.

    (1998)
  • LynchP.

    Richardson’s forecast-factory: the $64, 000 question

    Met. Mag.

    (1993)
  • SeidelR.W.

    From Mars to Minerva: The origins of scientific computing in the AEC labs

    Phys. Today

    (1996)
  • MacraeN.

    John Von Neumann – the Scientific Genius Who Pioneered the Modern Computer

    (1999)
  • CharneyJ.G. et al.

    Numerical integration of the barotropic vorticity equation

    Tellus

    (1950)
  • BellG. et al.

    A look back on 30 years of the Gordon Bell prize

    Int. J. High Speed C.

    (2017)
  • OrszagS.A. et al.

    Numerical simulation of three-dimensional homogeneous isotropic turbulence

    Phys. Rev. Lett.

    (1972)
  • JiménezJ. et al.

    The structure of intense vorticity in isotropic turbulence

    J. Fluid Mech.

    (1993)
  • KanedaY. et al.

    High-resolution direct numerical simulation of turbulence

    J. Turbul.

    (2006)
  • KimJ. et al.

    Turbulence statistics in fully developed channel flow at low Reynolds number

    J. Fluid Mech.

    (1987)
  • HoyasS. et al.

    Scaling of the velocity fluctuations in turbulent channels up to Reτ=2003

    Phys. Fluids

    (2003)
  • LeeM. et al.

    Direct numerical simulation of turbulent channel flow up to Reτ5200

    J. Fluid Mech.

    (2015)
  • TennekesH. et al.

    A First Course in Turbulence

    (1972)
  • JiménezJ.

    Computing high-Reynolds number flows: Will simulations ever substitute experiments?

    J. Turbul.

    (2003)
  • ZimmermanS. et al.

    A comparative study of the velocity and vorticity structure in pipes and boundary layers at friction reynolds numbers up to 104

    J. Fluid Mech.

    (2019)
  • JiménezJ.

    Cascades in wall-bounded turbulence

    Ann. Rev. Fluid Mech.

    (2012)
  • S. Hoyas, M. Oberlack, S. Kraheberger, F. Alcántara-Avila, Turbulent channel flow at Reτ=10000, in: Proc. Div. Fluid...
  • TengH. et al.

    Turbulent drag reduction in plane Couette flow with polymer additives: a direct numerical simulation study

    J. Fluid Mech.

    (2018)
  • PerlmanE. et al.

    Data exploration of turbulence simulations using a database cluster

  • SilleroJ.A. et al.

    Editorial opinion: public dissemination of raw turbulence data

    J. Phys. Conf. Ser.

    (2016)
  • Lozano-DuránA. et al.

    Time-resolved evolution of coherent structures in turbulent channels: characterization of eddies and cascades

    J. Fluid Mech.

    (2014)
  • Vela-MartínA. et al.

    A second-order consistent, low-storage method for time-resolved channel flow simulations

    (2018)
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