Table Of ContentERCOFTAC Series
Mikhael Gorokhovski
Fabien S. Godeferd Editors
Turbulent
Cascades II
Proceedings of the Euromech-ERCOFTAC
Colloquium 589
ERCOFTAC Series
Volume 26
Series Editors
Bernard Geurts, Faculty of Mathematical Sciences, University of Twente,
Enschede, The Netherlands
Maria Vittoria Salvetti, Dipartimento di Ingegneria Civile e Industriale, Pisa
University, Pisa, Italy
Aims and Scope of the Series
ERCOFTAC (European Research Community on Flow, Turbulence and
Combustion) was founded as an international association with scientific objectives
in 1988. ERCOFTAC strongly promotes joint efforts of European research
institutes and industries that are active in the field of flow, turbulence and
combustion, in order to enhance the exchange of technical and scientific
information on fundamental and applied research and design. Each year,
ERCOFTAC organizes several meetings in the form of workshops, conferences
and summerschools, where ERCOFTAC members and other researchers meet and
exchange information.
The ERCOFTAC Series will publish the proceedings of ERCOFTAC meetings,
whichcoverallaspectsoffluidmechanics.Theserieswillcompriseproceedingsof
conferences and workshops, and of textbooks presenting the material taught at
summerschools.
The series covers the entire domain offluid mechanics, which includes physical
modelling, computational fluid dynamics including grid generation and turbulence
modelling, measuring-techniques, flow visualization as applied to industrial flows,
aerodynamics, combustion, geophysical and environmental flows, hydraulics,
multiphaseflows,non-Newtonianflows,astrophysicalflows,laminar,turbulentand
transitional flows.
More information about this series at http://www.springer.com/series/5934
Mikhael Gorokhovski Fabien S. Godeferd
(cid:129)
Editors
Turbulent Cascades II
Proceedings of the Euromech-ERCOFTAC
Colloquium 589
123
Editors
Mikhael Gorokhovski FabienS. Godeferd
Laboratoire deMécaniquedes Fluides et Laboratoire deMécaniquedes Fluides et
d’Acoustique CNRS d’Acoustique CNRS
UniversitédeLyon,École centrale deLyon UniversitédeLyon,École centrale deLyon
Écully,France Écully,France
ISSN 1382-4309 ISSN 2215-1826 (electronic)
ERCOFTAC Series
ISBN978-3-030-12546-2 ISBN978-3-030-12547-9 (eBook)
https://doi.org/10.1007/978-3-030-12547-9
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Organization
TheColloquiumEC589wasorganizedbytheLaboratoryofFluidMechanicsand
Acoustics(LMFA),whichisajointlaboratoryofCNRS,UniversityofLyon,École
Centrale de Lyon (ECL), Université Claude Bernard Lyon I (UCBL), and Institut
National des Sciences Appliquées de Lyon (INSA), under the auspices of
Euromech and ERCOFTAC.
Executive Committee
Colloquium Chairs Mikhael Gorokhovski (LMFA, ECL, FR)
Bernard Geurts (University of Twente, NL)
Joachim Peinke (University of Oldenburg, GE)
Organizing Chair Fabien S. Godeferd (LMFA, CNRS, FR)
Organizing Committee
Colloquium Chair Mikhael Gorokhovski (LMFA, ECL, FR)
Wouter Bos (LMFA, CNRS, FR)
Mikhael Bourgoin (LP-ENSL, CNRS, FR)
Anne Cadiou (LMFA, CNRS, FR)
Claude Cambon (LMFA, CNRS, FR)
Alexandre Delache (LMFA, U. St-Étienne, FR)
Fabien S. Godeferd (LMFA, CNRS, FR)
Raffaele Marino (LMFA, CNRS, FR)
Nicolas Mordant (LEGI, CNRS, FR)
v
vi Organization
Sponsoring Institutions
European Mechanics Society (Euromech), EU
EuropeanResearchCommunityonFlow,TurbulenceAndCombustion(ERCOFTAC),
EU
Office of Naval Research (ONR), USA
Laboratory of Fluid Mechanics and Acoustics (LMFA), FR
École Centrale de Lyon (ECL), FR
Laboratory of Physics, École Normale Supérieure de Lyon (LP-ENSL), FR
Laboratory of Geophysical and Industrial Flows (LEGI), FR
Engineering Federation of Lyon-Saint-Étienne (IngéLySE), FR
European Research Council (ERC), EU
National Research Agency (ANR), FR
Preface
This book contains papers presented at the Euromech-ERCOFTAC Colloquium
“TurbulentCascades II,”held onDecember 5–7, 2017,at LMFA laboratory inthe
Ecole Centrale, Lyon, France.
In1941intheframeworkof–5/3powerlaw,KolmogorovandObukhov(KO-41)
formulated the Richardson idea of the energy cascade along with fragmentation of
turbulent eddies. Considering the turbulence at very high Reynolds number, the
main assumption in KO-41 is that statistical characteristics of turbulence on small
scales are unaffected by the structure of large-scale turbulence; i.e., adopting the
largetime-varyingenergyflux,handeddownfromlargescales,thehigh-frequency
fluctuations on small scales attain quickly a universal statistically homogeneous
state, referred toasequilibriumstate. Thereby, themean fluxof transferredenergy
becomes in KO-41 the only dimensional parameter, supposed to be homogeneous,
andintheconditionofequilibrium,itisequaltothelocalmeanviscousdissipation
rate. The KO-41 cascade model has yielded different approaches to the closure
problem of averaged Navier–Stokes equations, and consequently, the efficient
solutions were found in many practical applications (the drag reduction for cars,
trains, planes, ships, etc., is an example). However, there are some difficulties in
interpretationofturbulenceintermsofKO-41.Ontheonehand,evenfromformal
consideration of purely kinematic coupling constraints it turns out that small- and
large-scale motions, i.e., local and non-local interactions, are statistically interde-
pendent. The evidence of non-local interactions in the high Reynolds number tur-
bulence is provided by direct numerical simulations and experiments. On smallest
turbulentscales,thesestudiesrevealedthehighlyenergetic,stablevorticalfilaments
whichmaypersistonlargetimesandmayinteractdirectlywithotherstructures.The
intersectionofsuchfilamentsmayleadtotheviolentgradientsofvelocitygivingrise
to long-range correlations. In this situation, the assumption that mean viscous dis-
sipationistheonlyonecontrollingparameterofturbulentcharacteristicsappearsto
bequestionable.Ontheotherhand,the–5/3lawofKO-41isalwaysconfirmed,and
itisconfirmedbymoststudiesnotonlyinawiderangeofhydrodynamicflows,but
also inastrophysicsand biological systems.This raises thefollowingquestion:Do
wehaveanothermechanismofthekineticenergytransferbetweendifferentlength
vii
viii Preface
scales which works differently from the KO-41 cascade picture and which
nonethelessprovidesthecelebrated–5/3law?Thisquestionwasaddressedalready
in the first edition of the “Turbulent Cascades” colloquium, held in Lille in
December 2015. Two years later in Lyon, we decided to continue our discussions.
Apartofthisdiscussioncanbefoundinthisbook.Atthesametime,thescopeofour
colloquium in Lyon was enlarged beyond the turbulent cascade in simplest flows;
manydiscussionsconcernedthephysicsofturbulenceincomplexconditions.Inthis
book, one can find papers on the turbulence modulation through the finite size of
dispersed inertial particles or bubbles, as well as through wavy structures of the
gas/liquid interface and its surface tension. Some papers are devoted to effects of
compressibility, of shear, of body forces (Coriolis and Lorentz forces, buoyancy
effects). After our colloquium in Lyon, the number of open questions about turbu-
lence in complex conditions was not decreased but increased. So much the better.
This motivates for the future work and for future meetings. Look below at the
photographofBasilicaofNotre-DamedeFourviereinLyon.Anabsolutelystunning
picture!Lookatthestableboundarybetweenhorizontalstreaksandlargestructures,
and look at the vertical persisting small-scale structures. How is working such a
whole machineof turbulence in thecomplexconditions?
There are people to whom the theme of turbulent cascade appears as a “literary
genre” and who are rather skeptical to bring together scientists for the umpteenth
timefordiscussionsonturbulenceandframesofKO-41.Webelievethatamajority
of people think otherwise.
PicturecourtesyofPhilippeBleicher
Écully, France Mikhael Gorokhovski
Fabien S. Godeferd
Contents
Part I Multi-scales Interactions and Non-stationary Cascades:
Physics, Models and Tools
Infrared Dynamics and Decay of Helicity in Homogeneous
Isotropic Turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Antoine Briard and Thomas Gomez
Dual Cascades in Axisymmetric Turbulence . . . . . . . . . . . . . . . . . . . . . 11
Bo Qu, A. Naso and Wouter J. T. Bos
A Rigorous Entropy Law for the Turbulent Cascade. . . . . . . . . . . . . . . 17
André Fuchs, Nico Reinke, Daniel Nickelsen and Joachim Peinke
Evolution of Local Structure of Turbulent Flow Along Pathlines. . . . . . 27
Joseph Mathew
Renormalized Equations in Turbulent Immiscible Gas-Liquid
Flows—The Target on LES-Formulation . . . . . . . . . . . . . . . . . . . . . . . . 37
M. A. Gorokhovski and V. L. Saveliev
The Turbulence Cascade in Physical Space . . . . . . . . . . . . . . . . . . . . . . 45
Javier Jiménez, José I. Cardesa and Adrián Lozano-Durán
Effects of Regenerating Cycle on Lagrangian Acceleration
in Homogeneous Shear Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
A. Barge and M. A. Gorokhovski
Part II Compressibility , Turbulence; Turbulence , Atomization
Energy Transfer and Spectra in Simulations of Two-Dimensional
Compressible Turbulence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
Alexei G. Kritsuk
ix
