Outline of the presentation :

1.Introduction - Illustrative examples from experiments and simulations

2.The baroclinic torque in high Froude number flows, its organization, scale and order of magnitude

3.Transition of the inhomogeneous mixing--layer and the 2D secondary baroclinici instability

4.The strain field of 2D light jets and the question of side-jets

5.Mass segregation in 2D turbulence and the baroclinic instability of massive of vortice

Bretonnet, Loïc

Campagne, Gaëlle

Fontane, Jérôme

Joly, Laurent

Micallef, J.

Reinaud, Jean

Suarez, Juan

English

Open Archive Toulouse Archive Ouverte

University of Alberta – Mech.Eng. Dep. – Seminar on December the 2nd – 2004                            Vortex dynamics in high Froude number variable-density flowsLaurent JolyJ.N. Reinaud, J. Micallef, J. Suarez, L. Bretonnet, J. Fontane, G. CampagneENSICA - Département de Mécanique des Fluides Toulouse - France2Outline of the talk1. Introduction - Illustrative examples from experiments and simulations2. The baroclinic torque in high Froude number flows, its organization, scaleand order of magnitude3. Transition of the inhomogeneous mixing-layer and the 2D secondarybaroclinic instability4. The strain field of 2D light jets and the question of side-jets5. Mass segregation in 2D turbulence  and the baroclinic instability of massive vortices3Stratified medium in a gravity fieldTilted tank experiments : « A method of producing a shear flow in a stratified fluid »S.A. Thorpe JFM32 19684Sheared stratified medium in a gravity field Two-dimensionnal Stratified Mixing Layer (vertical shear)Klaassen and Peltier JFM227 (1991)Re=300Staquet JFM296 (1995)Re=2000 – Ri = 0.1675Sheared stratified medium in a gravity field : Smyth JFM 497 (2003)6Ri=0.06Sheared stratified medium in a gravity field Three-dimensionnal stratified Mixing LayerKlaassen and Peltier JFM227 (1991)Schowalter, Van Atta and Lasheras JFM281 (1994)7Mixing inhomogeneous streams : spreading rateBrown and Roshko, « On density effects and large structure in turbulent mixing layers »,  JFM 64, 19748Mixing inhomogeneous streams : baroclinic instabilityTwo-dimensionnal secondary baroclinic instability : Reinaud, Joly and Chassaing, PoF vol 12(10), pp 2489-2505, 2000homogeneousVariable-densitySpectral Code – Re=3000Material linesVorticity contoursInviscid Vortex-method9S=0,79S=0,47Mixing inhomogeneous streams : absolute instability of light jetsSelf-excited oscillations and mixing in a hot jet : Monkewitz and Bechert, PoF Gallery of fluid motion, 1988101. Introduction - Illustrative examples from experiments and simulations  non-barotropic flows exhibit deviations from theirhomogeneous or barotropic equivalent2. The baroclinic torque in high Froude number flows, its nature, order of magnitude and organization3. Transition of the inhomogeneous mixing-layer and the 2D secondarybaroclinic instability4. The strain field of 2D light jets and the question of side-jets5. Mass segregation in 2D turbulence  and the baroclinic instability of massive vorticesOutline of the talk11Vorticity generation/destruction in non-barotropic flows Focus : Incompressible mixing at infinite Froude numbers12Density contrast versus density ratioCondition :|Cú| < 113The vorticity dynamics : baroclinic torque versus vortex stretching14A prediction of some flow sensitivity to density variations• Fully developped 3D turbulence• Two-dimensional flows : no vortex stretching• Transition flowsNo vortex stretching, baroclinic torque only source/sink of vorticityVortex stretching much larger than baroclinic torque in high Reynolds number turbulenceThe baroclinic torque may bias the transition15t=0t 2Spatial structure of the variable density temporal mixing layerKelvin-Helmholtz instability s=3, Re = Uδ/ν = 1500Vorticity Baroclinic torque468=10216Spatial structure of the variable density mixing layer : length scalesMixing layer s = 1 or 3 , Re = 3000, t=1217Net contribution of the baroclinic torque and the Reynolds numberTemporal mixing layer s=3, Re = Uδ/ν = 500,1500,3000Increasing ReynoldsDiffusive damping18Outline of the talk1. Introduction2. The baroclinic torque• Scales with the bounded density contrast• Inertial nature : accelerated inhomogeneous medium• Competes with vortex stretching in transition flows and 2D flows• Enstrophy source at high wavenumbers/small scales• Intense local source/sink of vorticity but a weak net effect• Significantly damped by diffusion, enhanced by isopycnal stretching3. Transition of the inhomogeneous mixing-layer and the 2D secondary baroclinicinstability19Spatial structure of the variable density mixing layerNormalized vorticity along the central material line20The model of a stretched vorticity/density-gradient sheetThe stretched density-gradient and vorticity filament,Reinaud, Joly et Chassaing, Physics of Fluids (2002)21A nice breakup into smaller scale vorticesDensityVorticityHigh-density fluidLow-density fluid22The secondary instability : scale invariance ?• A specific transition mecanism of the inhomogeneous shear flow;• Twodimensional secondary mode;• The vorticity pattern is repeated in second generation structures, and so on untillviscous length scales are produced and baroclinic vorticity generation is prevented.23The secondary instability in the spatially developping flowForced spatially developing mixing-layer (simulations with a variable density vortex method)contergradienthomogeneouscogradient243. The 2D mixing-layer in the nonlinear regime and the secondary baroclinic instability• The non-linear stage ends in a rather asymmetric vorticity distribution due to alternate positive and negative baroclinic contributions;• From the vorticity field the structure is not a standard KH smooth roller; • A secondary baroclinic instability developes on the light side of the KH billow;• Not observed so far at Reynolds numbers up to 3000 nor in experimentalrealizations of high Reynolds number flows;• Provides a 2D bypass route to turbulence under high Reynolds numberconditions.4. The strain field of 2D light jets and the question of side-jets5. Mass segregation in 2D turbulence  and the baroclinic instability of massive vorticesOutline of the talk25Sides ejetions in the helium jet : illustrationgravitynozzle26Transition of the turbulent helium jetRe = 750 Re = 1000 Re = 2600Influence of the Reynolds number27The mechanism of side ejectionsBrancher, Chomaz & Huerre (1994)Lambda2 probe of coherent structures in a DNS of a homogeneous 3D temporal jet with a 3-lobe corrugation of the initial vorticity tube. Paradigm of secondary 3D mode yielding counter-rotative vortices lying between adjacent distorted ringsSide jets induced by pairs of counter-rotative streamwise aligned vortices28The baroclinic torque in infinite Froude number jets29A measure of the strain rate in the mixing layerThe strain rate and the shear rate are measured along some relevant line« Variable density fluid turbulence » 2003Chassaing, Antonia, Anselmet, Joly and Sarkar, Kluwer30t = 4,5 Light jetThe strain field along material linesTemporal jet s=1/3, Re = UD/ν = 2500Red : positive γ (stretching) – Blue : negative γ (compression) – Shaded : above same positive levelPassive scalar31Summary on side jets1. The jet is absolutely unstable under a critical density ratio s<0.7,2. SJ aknowledged within some range of Reynolds number,3. A shorter route to the mixing transition and a large increase of the mixing rate,4. SJ recovered in a pulsed homogeneous jet by Monkewitz and Pfizenmaier (1991)5. From undergoing experiments : i. Intemmittent ejection,ii. Unsteady number and azymuthal positon,iii. Reynolds sensitive azimuthal wavenumber,iv. Quasi-steady streamwise position,v. Life time of several Primary Mode periodsvi. How to control SJ and promote mixingFisrt observation by Monkewitz & Bechert (Album of Fluid Motion - 1988)Side ejections on Re = 1000 helium jets from Hermouche, Institut de Mécanique des Fluides de Toulouse (1996)323. The 2D mixing-layer in the nonlinear regime and the secondary baroclinic instability4. The strain field of 2D low-density jets and the question of side-jets• The strain fields of low-density jets present a folded layered structure,• Much higher strain rates may be produced in the baroclinically modified roll-up,• High strain rates are to be expected « inside » the low-density jet and close to favored leg of the vorticity braid.• Spontaneous side jets in absolutely unstable low-density jets,• If understood may help mixing,5. Mass segregation in 2D turbulence  and the baroclinic instability of massive vorticesOutline of the talk33Mass segregation in 2D turbulenceDécroissance de turbulence bidimensionnelle34Mass segregation in 2D turbulencePassive scalar 2D turbulence Inhomogeneous 2D turbulenceInspection of an isolated vortex …35Looking for a variable-density vortex being an Euler equilibrium solution A barotropic vortex is a vortex where the pressure depends on density only,The axisymmetric vortex with circular isodensity lines (globally advection invariant) is the only barotropic vortex (we found) that is also a steady solution of the Euler (inviscid) equations,Since            pressure and density gradients are aligned and the barotropic vortex exhibits no baroclinic vorticity sources,p(ú)The circular barotropic vortex spreads as a barotropic vortex in the diffusive context,We study the stability of barotropic vortices with gaussian vorticity and density distributions.The axisymmetric barotropic vortex36The baroclinic instability mechanism of a perturbated barotropic vortex AxisymmetrizationStable caseMass ejectionUnstable case37Linear stability analysis of variable-density gaussian vorticesΩ(r, ò) =ùî2Γexp(àî2r2)Definiton of the base stateR = úb + (úc à úb) exp(àî2úr2)Density contrast in à 1, 1[ ] Radius ratio in 0,∞[ [ε =îúîCú =úc + úbúc à úbLinearized Euler equations and normal mode analysisuêr , uêò , pê , úê[ ] (r, ò, t) = iur(r), uò(r), p(r), ú(r)[ ] exp i mò à ωt( )[ ]m Positive integer azimuthal wavenumberω Complex disturbance phase speed38Linear stability analysis : main resultsm = 2 m = 3Amplification rate in the (density contrast – radius ratio) plane39Linear stability analysis : main resultsFirst modes sensitivity to density contrast and radius ratioModerate density constrast Moderate radius ratio Cú = 0.5 or úc/úb = 3 ε = 2 or î = 2îú40Numerical simulation pf the non-linear development of the instability Eigen mode perturbation m=3, Cρ = 0.5, ε = 241Numerical simulation of the non-linear development of the instability Density radius large amplitude déformation m=3, Cρ = 0.8, ε = 1423. The 2D mixing-layer in the nonlinear regime and the secondary baroclinic instability4. The strain field of 2D light jets the question of side-jets5. Mass segregation in 2D turbulence  and the baroclinic instability of massive vortices• Light vortex stable, heavy vortex unstable,• Patches of low-density fluid are robust to vortex interaction : anti-mixing effect on low-density samples• Patches of high-density fluid are ejected from vortex cores and strained lumps of high-density fluid are efficiently smeared out by molecular diffusion : mixing of high-density samples is promoted• Mass segregation by vorticity in 2D inhomogeneous turbulence andasymmetric relaxation of the density pdf.Outline of the talkThank you for your attention…43Transition slide44Inviscid incompressible inhomogeneous flowsA unified view on baroclinic vorticity generation45Baroclinic streamwise vorticity generationScheme of the vorticity generation on the model flow of unstrained counter-rotating vortices46A first glance at baroclinic streamwise vorticity generation :vorticity Baroclinic torquevorticity• Shift of the vortex centers toward the light side• Asymmetric entrainment• A trend expected to be enhanced by the underlynig stretching in braid area47• Vorticity of the gaussian vortex :• Orthoradial velocity and centripetal acceleration :• Density field on an elleptic patch :• Density gradient vector :• Baroclinic torque :Baroclinic distribution for an elliptic density patch on a circular vortex48Normalization of variable density effectsA set of scales49The structure of the 2D low-density jet (with pairing)Temporal jet s=1/3, Re = UD/ν = 2500Baroclinic TorqueLow-densityHigh-densityVorticityKyle et Sreenivasan JFM 249 (1993)Passive scalar50The strain field according to the Caulfield and Kerswell’s analysisTemporal jet s=1/3, Re = UD/ν = 2500Passive scalar Light jett = 4,551Vortex lourd trois lobes52The axisymmetrization of the low-density vortex53The breakdown of a massive vortex+ Film with s=10

Vortex dynamics in high Froude number variable-density flows

http://oatao.univ-toulouse.fr/2365/1/Joly_2365.pdf

Vortex dynamics in high Froude number variable-density flows

Abstract

Similar works

Full text

Available Versions

Open Archive Toulouse Archive Ouverte