1. Laboratoire de Sondages Electromagnétiques de l’Environnement Terrestre (Université de Toulon et du Var) Philippe Fraunié Non-Homogeneous Turbulence Vilanova y La Geltru june 2008 Stratified turbulent flows in Ocean and Atmosphere : Processes, observations and CFD

2. Observations

4. Basic processes

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

6. Holmboe instability n Ri > ¼ n Su > 2 Sb n Possibility of Holmboe instability

7. Holmboe instability

8. DeSilva, Fernando, Hebert & Eaton, Earth Planetary Sci. Lett., 1996

9. Turbulence scales

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

11. turbulence measurements from high resolution temperature profiles from balloon (MUTSI exp) MU Radar Balloon Thorpe Scale dissipation rate Turbulent Diff structure const (T) Brünt-Vaïsälä frequency (Résolution verticale: 12.8 m) Vertical resolution : 150 m (Gavrilov, Luce, Dalaudier, Crochet, Fukao, Annale Geophys. 2005)

12. Atmosphere n ‘turbulence – waves –stability – shear’ radar reflectance and wind shear Across a front (Luce et al)

13. 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

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

15. The Rhône river plume

16. TSM SPOT image velocity 5 meters deep Secondary flows.

17. The layering effect

18. SAMPOS floating System (JL Devenon) (ADP + DL7 + GPS)

19. CTD and velocity profiles (Arnoux et al, 2005)

20. Settling velocity

21. 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

22. 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)

23. 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

24. LES equations LES equations n Continuity equation : n Momentum equations :

25. Transport of scalar fields Transport of scalar fields n Temperature and Salinity : n State Equation :

26. LES numerical code LES numerical code n Continuity equation : n Momentum equations :

27. Turbulence closure n Smagorinsky model :

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

29. Algorithm

30. 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 :

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

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

33. 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

34. 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

35. 2D du computational domain 2D du computational domain

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

37. 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

38. 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

39. Physical collapse (4) ooo Ri 0 = 0.03 ; ooo Ri 0 = 0.039 L’épaisseur du sillage proche atteint une valeur maximale pour N BV t  2  Ri 0 < 1/9 D ’après Lin et al. (1992)

40. 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 1.5 - 2.5  1/9 < Ri 0 < 1/4 : N BV t varies between 3 and 5  Ri 0 > 1/4 : the wake width is constant

41. 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

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

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

44. Gravity internal wave : strong initial stratification (1)

45. 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) :  

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

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

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

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

50. 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

51. 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

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

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

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

55. Strongly stratified layers ?

56. Stratified layers of another type n Unstable stratification n Convergence of density isolines

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

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

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

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

61. 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

62. Vertical cylinder: computational domain

63. Laboratory experiments n Density profile n Towed vertical cylinder

64. Vertical cylinder n zig-zag instability n Layering effect

65. Zig-Zag Instability, Vortex in stratified flow

66. Energy spectrum

67. Velocity components and gradients

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

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