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

2. Observations

3. Basic processes

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

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

6. Holmboe instability

7. Richardson number

8. Global Richardson number

9. Turbulence scales

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

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

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

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

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

15. Navier-Stokes solver
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
Continuity equation :
Momentum equations :

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

18. LES numerical code
Continuity equation :
Momentum equations :

19. Turbulence closure
Smagorinsky model :

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

21. Algorithm

22. Computational domain Taille du domaine:
2 < Lx < 4 m ; Ly = 0.1 m ; 0.1 < Lz < 0.2 m
Taille de la barre :
Maillage :
dx = 3.9 mm ; dy = 3.1 mm ; dz = 1 mm

23. Boundary conditions En surface et au fond : A la frontière droite :
A la frontière gauche : si
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
Surfaces d’iso-vorticité :
- en rouge et bleu, les surfaces
- en vert et noir, les surfaces

26. 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

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
avec l’augmentation de la stratification

30. Turbulence collapse (3) : physical process
Temporal evolution of the near wake width for Richardson numbers less than 1/4 :
the wake grows following a t1/3 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) L’épaisseur du sillage proche atteint une valeur
ooo Ri0 = 0.03 ; ooo Ri0 = 0.039
D ’après Lin et al. (1992)
L’épaisseur du sillage proche atteint une valeur
maximale pour NBVt  2  Ri0 < 1/9

32. Physical collapse (5)
NBVt (maximum wake width) depends on Ri0 (Xu et al., 1995) :
Ri0 < 1/9 : NBVt varies in the range
1/9 < Ri0 < 1/4 : NBVt varies between 3 and 5
Ri0 > 1/4 : the wake width is constant

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

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

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

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

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

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

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

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

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

44. Mixing Processes in the far wake : strong initial stratification (2)
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 »
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
Unstable stratification
Convergence of density isolines

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

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

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

52. Successive infinitesimal perturbation (2)
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
Density profile
Towed vertical cylinder

56. Vertical cylinder
zig-zag instability
Layering effect

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

58. Perspectives CFD improvements : subgrid models (Babiano et al)
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
Evolution temporelle d’un profil vertical de densité dans les cas de faible et de forte stratification