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Laboratoire de Sondages Electromagnétiques de l’Environnement Terrestre (Université de Toulon et du Var) Philippe Fraunié Sabeur BERRABAA Jose Manuel Redondo.

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Presentation on theme: "Laboratoire de Sondages Electromagnétiques de l’Environnement Terrestre (Université de Toulon et du Var) Philippe Fraunié Sabeur BERRABAA Jose Manuel Redondo."— Presentation transcript:

1 Laboratoire de Sondages Electromagnétiques de l’Environnement Terrestre (Université de Toulon et du Var) Philippe Fraunié Sabeur BERRABAA Jose Manuel Redondo et al Stratified turbulent flows in Ocean and Atmosphere : Processes, observations and CFD

2 Observations

3 Basic processes

4 KH instability Kelvin-Helmholtz instability : Richter (1969)

5 Holmboe instability n Ri > ¼ n Su > 2 Sb n Possibility of Holmboe instability

6 Holmboe instability

7 Richardson number

8 Global Richardson number

9 Turbulence scales

10 Measurements in Atmosphere n Profiles of temperature mesured by baloons : weakly and srongly stratified layers (Dalaudier et al., 1994)

11 Measurements in Oceans n Temperature profiles in Malta sea : Contribution of K.-H. instabilities to mixed layers (Woods, 1969) n Korotayev et Panteleyev (1977), Indian and Pacific oceans, Alford et Pinkel (2000) California

12 Measurements in Ocean n Temperature profiles in Japan sea : Contribution of internal waves to mixed layers (Navrotsky, 1999)

13 Laboratory Experiments : the layering effect n Generation of turbulence (grids) in a stratified flow at rest Interaction between Interaction between turbulence and turbulence and stratification stratification

14 Computational Fluid Dynamics n Focused on Kelvin- Helmholtz instability (Palmer et al., 1996) n Only few numerical experiments concerning internal waves (Koudella et Staquet, 1996 ; Bouruet-Aubertot et al., 2001)

15 Navier-Stokes solver n Based on JETLES DNS Code (Versico, Orlandi) adapted to stratified flows :  cartésian coodinates  sreamwise non périodic bc (Ox)  transport equations for salinity and temperature)  LES  Smagorinsky subgrid model

16 LES equations LES equations n Continuity equation : n Momentum equations :

17 Transport of scalar fields Transport of scalar fields n Temperature and Salinity : n State Equation :

18 LES numerical code LES numerical code n Continuity equation : n Momentum equations :

19 Turbulence closure n Smagorinsky model :

20 Discretization n Time marching : three steps Runge- Kutta scheme, third order accurate n Spacial discretization : second order centered finite differences

21 Algorithm

22 Computational domain Taille du domaine: 2 < L x < 4 m ; L y = 0.1 m ; 0.1 < L z < 0.2 m Maillage :  x = 3.9 mm ;  y  mm ;  z = 1 mm Taille de la barre :

23 Boundary conditions En surface et au fond : A la frontière droite : A la frontière gauche : si 0 avec

24 Homogeneous flow : Von Karman streets Champs d’iso-vitesses horizontales, d’iso-vitesses verticales et d’iso-vorticités d’axe (Oy)

25 3D structures low Reynlods number 3D structures low Reynlods number - en rouge et bleu, les surfaces Surfaces d’iso-vorticité : - en vert et noir, les surfaces

26 3D structures larger Reynolds number 3D structures larger Reynolds number Surfaces d’iso-vorticité : - en rouge et bleu, les surfaces - en vert et noir, les surfaces

27 2D du computational domain 2D du computational domain

28 Turbulence collapse (1) Champs d’iso-vorticité d’axe (Oy)

29 Turbulence collapse (2) Transformée de Fourier de l’évolution temporelle des composantes de vitesse dans le sillage proche : - Diminution du nombre de Strouhal dans le sillage proche : - Diminution du nombre de Strouhal avec l’augmentation de la stratification avec l’augmentation de la stratification

30 Turbulence collapse (3) : physical process Turbulence collapse (3) : physical process n Temporal evolution of the near wake width for Richardson numbers less than 1/4 :  the wake grows following a t 1/3 law as for homogeneous flow  coolapse occurs when the wake width is maximum  the wake widh decreases up to an constant value

31 Physical collapse (4) ooo Ri 0 = 0.03 ; ooo Ri 0 = L’épaisseur du sillage proche atteint une valeur maximale pour N BV t  2  Ri 0 < 1/9 D ’après Lin et al. (1992)

32 Physical collapse (5) n N BV t (maximum wake width) depends on Ri 0 (Xu et al., 1995) :  Ri 0 < 1/9 : N BV t varies in the range  1/9 < Ri 0 < 1/4 : N BV t varies between 3 and 5  Ri 0 > 1/4 : the wake width is constant

33 Physical collapse (6) : La taille de la zone perturbée dans le cas La taille de la zone perturbée dans le cas n’évolue pas contrairement au cas n’évolue pas contrairement au cas

34 Gravity internal wave : weak initial stratification (1) n Iso-density fields for différent Richardson numbers :  Ondulation occurs at the starting point

35 Gravity internal wave : weak initial stratification (2) n Profiles of local Richardson number :  Waves occur for Ri > 1 : stratification dominates turbulence

36 Gravity internal wave : strong initial stratification (1)

37 Gravity internal wave : strong initial stratification (2) n Iso-density and d’iso-vorticity - transverse axis (Oy)  ondulatory motion imposed by internal waves n Remember Lee waves (Atkinson) :  

38 Mixing Processes in the near wake : weak initial stratification (1) n Iso-vorticity - transverse axis (Oy) in the near wake  Shear instability overturning

39 Mixing Processes in the near wake : weak initial stratification (2) n Overturning : time evolution of two density surfaces  Roll up

40 Mixing Processes in the near wake : weak initial stratification (3) Unstable situation Overturning Local convective instability

41 Mixing Processes in the near wake : strong initial stratification (1) n Time evolution of two density surfaces  Breaking internal waves

42 Mixing Processes in the far wake : weak initial stratification n Iso-density field in the far wake  Mushroom type structures collapse due to stratification Sillage lointain

43 Mixing Processes in the far wake : strong initial stratification (1) n Iso-density field in the far wake  Mixed fluid inside the elliptic zones Sillage lointain

44 Mixing Processes in the far wake : strong initial stratification (2) n Iso-density fields at different times  interaction betyween shifted internal waves : Breaking

45 Layering effect : computational domain Succession de passages d’une ou de plusieurs barres

46 « sheets & layers » n Density profiles for weak and strong initial stratification  Layering effect weakly depends on initial stratification

47 Strongly stratified layers ?

48 Stratified layers of another type n Unstable stratification n Convergence of density isolines

49 Successive wakes n Density profiles and gradients after each cylinder tow  Sratification increases after each towing

50 Successive wakes n Time evolution of the density gradient  The maximum value increases  Damped oscillations

51 Infinitesimal perturbation (1) Infinitesimal perturbation (1) Champ de densité après trois passages de la perturbation

52 Successive infinitesimal perturbation (2) n Density profiles and gradients after 4 tows  Growth of the perturbation after each towing

53 Time evolution of the density and velocity gradients  Oscillation is damped  The stratification is evolving following three steps  The layering increase is due to the initial state before new perturbation

54 Vertical cylinder: computational domain

55 Laboratory experiments n Density profile n Towed vertical cylinder

56 Vertical cylinder n zig-zag instability n Layering effect

57 Conclusion n Caractéristics of stratified flows :  turbulence collapse  internal waves occuring n Mixing processes :  overturning collapse  breaking internal waves n Layering effect :  sheets & layers  reorganizing layers

58 Perspectives n CFD improvements :  boundary conditions (open problem)  long time computation : statistics and budgets  subgrid models (Babiano et al)

59 Energy spectrum

60 Velocity components and gradients

61 Processus de mélange dans le sillage proche : zones mélangées n Evolution temporelle d’un profil vertical de densité dans les cas de faible et de forte stratification


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