Stratified turbulent flows in Ocean and Atmosphere : Processes, observations and CFD

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

2. Observations

4. Basic processes

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

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

7. Holmboe instability

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

9. Turbulence scales

10. Measurements in Atmosphere • 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) Vertical resolution : 150 m (Résolution verticale: 12.8 m) MU Radar Balloon Thorpe Scale dissipation rate Turbulent Diff structure const (T) Brünt-Vaïsälä frequency (Gavrilov, Luce, Dalaudier, Crochet, Fukao, Annale Geophys. 2005)

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

13. 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

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

15. The Rhône river plume

16. velocity 5 meters deep TSM SPOT image 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 • Generation of turbulence (grids) in a stratified flow at rest Interaction between turbulence and stratification

22. 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)

23. 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

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

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

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

27. Turbulence closure • Smagorinsky model :

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

29. Algorithm

30. 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

31. si 0 si Boundary conditions En surface et au fond : A la frontière droite : A la frontière gauche : 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 Surfaces d’iso-vorticité : - en rouge et bleu, les surfaces - en vert et noir, les surfaces

34. 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

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 avec l’augmentation de la stratification

38. 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

39. Physical collapse (4) oooRi0 = 0.03 ;oooRi0 = 0.039 D ’après Lin et al. (1992) L’épaisseur du sillage proche atteint une valeur maximale pour NBVt  2  Ri0 < 1/9

40. Physical collapse (5) • NBVt (maximum wake width) depends on Ri0 (Xu et al., 1995) : • Ri0 < 1/9 : NBVt varies in the range 1.5 - 2.5 • 1/9 < Ri0 < 1/4 : NBVt varies between 3 and 5 • Ri0 > 1/4 : the wake width is constant

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

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

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

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

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

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

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

50. 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