Credits[inorderofappearance]:F.Bonaccorso,M.Buzzicotti (Univ.ofRoma‘TorVergata’,Italy),M.Linkmann (Univ.ofMarburg,Germany);A.Alexakis(ENS-Paris,France);P.ClarkdiLeoni (Univ.ofRoma‘TorVergata’,Italy),

Inverseanddirectcascadesinrotatingturbulence

Luca Biferale, Dept. Physics, INFN & CAST University of Roma ‘Tor Vergata’

biferale@roma2.infn.itPARIS 2018

WAVE INTERACTIONS AND TURBULENCE

E(k,t)

k

ENERGYSPECTRUM

TOTALENERGY

t

E(t)

�5/3

3DEVENT

INJECTION

TURBULENCEUNDERROTATION

Rossby =2Rossby =0.8

Rossby =0.2

Rossby =0.1

HOMOGENEOUSANISOTROPIC

2D&3DPHYSICSCHOERENT-STRUCTURES

H.P.GreenspanTheTheoryofRotatingFluids(CambridgeUniv.Press1968);ClarkdiLeoni andP.D.Minnini JFM,809,821(2016);L.M.SmithandWaleffePoF 11,1608(1999);S.Galtier PRE68,015301(2003).S.NazarenkoWaveTurbulence(Springer2011);B.Gallet JFM783,412(2015),L.B.F.Bonaccorso etalPRX6,041036(2016)

(Fast-3D) Iner�al Waves

dispersion rela�on:

This equa�on is sa�s;ed by plane waves of the form:

Inertial waves are intrinsically helical

A rotating flow = 2D3C + 3D helical Slow-2D manifold Fast-3D manifold

“geostrophic” flow “non-geostrophic” flow

eigenvector of the curl operator:

C.Cambon etal.J.FluidMech.,337:303332,1997.A.Sen etalJourAtmos Science68,2757(2011),E.YarometalPoF 25,085105(2013),A.CampagneetalPoF 26,125112(2014),E.Deusebio etalPRE90,023005(2014),A.AlexakisJFM769,46(2015)

H

INFINITEVOLUMELIMIT

P.Contantin andA.Majda CommMatPhys 115,435(1988)F.WaleffePhys FluidsA4,350(1992)

HELICAL-FOURIERDECOMPOSITION

HOMOCHIRAL

HETEROCHIRALHETEROCHIRAL

HETEROCHIRAL

TRIADICINTERACTIONINDECIMATEDHOMOCHIRALNAVIER_STOKESEQS

HOMOCHIRAL

10-5

10-4

10-3

10-2

10-1

100

101

100

101

102

E(k

)

k

k-5/3

t=0

time increasing

L.B.,S.Musacchio &F.ToschiPhys.Rev.Lett.108164501,(2012);JFM730,309(2013)

HOMOCHIRAL3DNAVIERSTOKESEQS.

M.Buzzicotti,H.Aluie,L.B.,M.Linkmann Phys.Rev.Fluids3(3)(2018)034802

FULL3DNAVIERSTOKESEQS.

FULL3DNAVIERSTOKESEQS.+ROTATION:

TOTALFLUX

TOTALFLUX

HOMOCHIRALFLUX

A.AlexakisJFM812,752(2017)

HOMOCHIRALFLUX

FORC

ING

FORC

ING

M.Buzzicotti,H.Aluie,L.B.,M.Linkmann Phys.Rev.Fluids3(3)(2018)034802

FULL3DNAVIERSTOKESEQS.

FULL3DNAVIERSTOKESEQS.+ROTATION:

TOTALFLUX

TOTALFLUX

HOMOCHIRALFLUX

A.AlexakisJFM812,752(2017)

HOMOCHIRALFLUX

FORC

ING

FORC

ING

- ONLY2D3CSLOW-MANIFOLDDYNAMICS(ANDVARIATIONSTHEREOF)[1]

- ONLY3DFAST-MANIFOLD[2,3]

kk

k?

[1]L.B.,MBuzzicotti,MLinkmann PhysicsofFluids29(11),111101(2017)[2]M.Buzzicotti,P.ClarkdiLeoni,L.B.Eur.Phys.J.E41:131(2018)[3]T.LeReun,B.Favier,A.J.Barker,MLeBars.PRL119034502,(2017)

k?

kk

3DFAST-MANIFOLDONLY

kk

k?

Out-of-equilibriumflux-loopcascade

⇧(k) = ⇧HE(k) +⇧HO(k) = 0

⇧HE(k) = �⇧HO(k) 6= 0

M.Buzzicotti,P.ClarkdiLeoni,L.B.Eur.Phys.J.E41:131(2018)

L.B,M.Buzzicotti andM.LinkmannPoF 29,111101(2017)

2D3CSLOW-MANIFOLDONLY

kk

k?

k?

kk

FROM2DTO3DSUPERPOSING2D3CPLANESFROM2DTO3DBYSUPERPOSING2D3CPLANES

FROM2DTO3DBYSUPERPOSING2D3CPLANES UV2DANDIR3D!OPPOSITEOFATHINLAYER!

3PLANES

3PLANES

3PLANES

1PLANE

1PLANE

1PLANE

3PLANES

3PLANES

3PLANES

2PLANES

2PLANES

2PLANES

L.B,M.Buzzicotti andM.LinkmannPoF 29,111101(2017);M.Linkmann,M.Buzzicotti andL.BEPJE(2018)

HOMOCHIRAL FLUX

HETEROCHIRAL FLUX

TOTAL FLUX

CONCLUSIONS

P.ClarkDiLeoni,A.Mazzino,L.B.Inferringflowparametersandturbulentconfigurationwithphysics-informeddata-assimilationandspectralnudging.PhysicalReviewFluids3(10),104604(2018)

- PHASE-SPACEOFROTATINGTURBULENCE ISHIGHLYNON-TRIVIAL(Ro,Re,H,Kforcing ,etc…)- MORETHANONEENERGY-TRANSFERMECHANISMACTINGINTHESYSTEM(FLUXLOOP)- FOURIERvsCONFIGURATIONALSPACEDICHOTOMY:CANWEIDENTIFYTHEDEGREES-OF-FREEDOMTHATDEFINETHETURBULENT BACKBONE?