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A LES-LANGEVIN MODEL

A LES-LANGEVIN MODEL. Colls: R. Dolganov and J-P Laval N. Kevlahan E.-J. Kim F. Hersant J. Mc Williams S. Nazarenko P. Sullivan J. Werne. B. Dubrulle Groupe Instabilite et Turbulence CEA Saclay. IS IT SUFFICIENT TO KNOW BASIC EQUATIONS?. Giant convection cell. Dissipation

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A LES-LANGEVIN MODEL

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  1. A LES-LANGEVIN MODEL Colls: R. Dolganov and J-P Laval N. Kevlahan E.-J. Kim F. Hersant J. Mc Williams S. Nazarenko P. Sullivan J. Werne B. Dubrulle Groupe Instabilite et Turbulence CEA Saclay

  2. IS IT SUFFICIENT TO KNOW BASIC EQUATIONS? Giant convection cell Dissipation scale Solar spot Granule 0.1 km Waste of computational resources Time-scale problem Necessity of small scale parametrization

  3. Influence of decimated scales Typical time at scale l: Decimated scales (small scales) vary very rapidly We may replace them by a noise with short time scale Generalized Langevin equation

  4. Obukhov Model Simplest case No mean flow Large isotropic friction No spatial correlations Gaussian velocities Richardson’s law Kolmogorov’s spectra LES: Langevin

  5. Influence of decimated scales: transport Stochastic computation Turbulent viscosity AKA effect

  6. Refined comparison Additive noise True turbulence Gaussianity Weak intermittency Non-Gaussianité Forte intermittence Iso-vorticity Spectrum PDF of increments LES: Langevin

  7. LOCAL VS NON-LOCAL INTERACTIONS • Navier-Stokes equations : two types of triades NON-LOCAL LOCAL L L l

  8. LOCAL VS NON-LOCAL TURBULENCE

  9. NON-LOCAL TURBULENCE E U  Analogy with MHD equations: small scale grow via « dynamo » effect k Conservation laws In inviscid case

  10. A PRIORI TESTS IN NUMERICAL SIMULATIONS 2D TURBULENCE << Non-local Local small/small scales Local large/ large scales 3D TURBULENCE

  11. DYNAMICAL TESTS IN NUMERICAL SIMULATIONS 2D RDT 2D DNS 3D RDT 3D DNS

  12. THE RDT MODEL Equation for large-scale velocity Linear stochastic inhomogeneous equation (RDT) Reynolds stresses Equation for small scale velocity Forcing (energy cascade) Turbulent viscosity Computed (numerics) or prescribed (analytics)

  13. THE FORCING Iso-vorticity Iso-force PDF of increments Correlations

  14. TURBULENT VISCOSITY SES RDT DNS

  15. k x LANGEVIN EQUATION AND LAGRANGIAN SCHEME Décomposition into wave packets The wave packet moves with the fluid Its wave number is changed by shear Its amplitude depends on forces coupling (cascade) “multiplicative noise” friction “additive noise”

  16. COMPARISON DNS/SES Fast numerical 2D simulation Shear flow Computational time 10 days 2 hours phi_m obs DNS Lagrangian model (Laval, Dubrulle, Nazarenko, 2000) Hersant, Dubrulle, 2002

  17. SES SIMULATIONS SES Experiment Hersant, 2003 DNS

  18. LANGEVIN MODEL: derivation Equation for small scale velocity Turbulent viscosity Forcing Isoforce PDF LES: Langevin

  19. Equation for Reynolds stress with Forcing due To cascade Advection Distorsion By non-local interactions Generalized Langevin equation LES: Langevin

  20. Performances Comparaison DNS: 384*384*384 et LES: 21*21*21 Intermittency Spectrum LES: Langevin

  21. Performances (2) s probability Q vs R LES: Langevin

  22. THE MODEL IN SHEARED GEOMETRY Basic equations RDT equations for fluctuations with stochastic forcing Equation for mean profile

  23. ANALYTICAL PREDICTIONS Mean flow dominates Fluctuations dominates Low Re

  24. TORQUE IN TAYLOR-COUETTE No adjustable parameter Dubrulle and Hersant, 2002

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