1. Breaking of symmetry in atmospheric flows Enrico Deusebio 1 and Erik Lindborg 2 1 DAMTP, University of Cambridge, Cambridge 2 Linné FLOW Centre, Royal institute of Technology, Stockholm 21th February 2014

2. Symmetry and asymmetry Symmetry often observed in nature and generally thought as a sign of perfection and beauty

3. Symmetry and asymmetry Symmetry often observed in nature and generally thought as a sign of perfection and beauty Used by mathematicians to simplify their systems

4. Symmetry and asymmetry Symmetry often observed in nature and generally thought as a sign of perfection and beauty Used by mathematicians to simplify their systems Also used in numerical simulations in order to reduce the computational cost

5. Asymmetry in atmospheric flows Are atmospheric flows symmetric?

6. Asymmetry in atmospheric flows Are atmospheric flows symmetric?

7. Asymmetry in atmospheric flows Are atmospheric flows symmetric?

8. Asymmetry in atmospheric flows Are atmospheric flows symmetric?

9. Asymmetry in atmospheric flows Are atmospheric flows symmetric? WHY? Can this be observed at small scales? Coriolis terms (not symmetry invariant)

10. Helicity (Moffatt & Tsinober, 1992)

11. Helicity Velocity

12. Helicity (Moffatt & Tsinober, 1992) Vorticity

13. Helicity (Moffatt & Tsinober, 1992) Invariant of the Euler equations, thus conserved apart from viscous effects

14. Helicity (Moffatt & Tsinober, 1992) AS ENERGY

15. Helicity Invariant of the Euler equations, thus conserved apart from viscous effects Both positive and negative values can be attained (Moffatt & Tsinober, 1992) AS ENERGY

16. Helicity Invariant of the Euler equations, thus conserved apart from viscous effects Both positive and negative values can be attained (Moffatt & Tsinober, 1992) AS ENERGY DIFFERENTLY FROM ENERGY

17. Turbulent Ekman boundary layers Recent numerical simulations of turbulent Ekman layers up to Standard numerics using pseudo-spectral codes

18. Budget equations

21. Energy injection Energy dissipation

22. Budget equations Energy injection Energy dissipation

23. Budget equations Helicity injection Energy injection Energy dissipation Helicity dissipation

24. Budget equations Mean field helicityTurbulent helicity Production Dissipation Transport Pressure Rotation

25. Budget equations Mean field helicityTurbulent helicity Conversion from mean to turbulent helicity Production Dissipation Transport Pressure Rotation

26. Budget equations Mean field helicityTurbulent helicity Viscous dissipation of helicity Production Dissipation Transport Pressure Rotation

27. Budget equations Mean field helicityTurbulent helicity Transport of helicity from one place to another Production Dissipation Transport Pressure Rotation

28. Budget equations Mean field helicityTurbulent helicity Transport of helicity due to the pressure terms Production Dissipation Transport Pressure Rotation

29. Budget equations Mean field helicityTurbulent helicity Transport of helicity due to rotation Production Dissipation Transport Pressure Rotation

30. Production Dissipation Transport Pressure Rotation Budget equations

31. Production Dissipation Transport Pressure Rotation

32. The helicity cascade Injection of helicity Helicity dissipation

33. Asymmetry in atmospheric flows Are atmospheric flows symmetric? WHY? Coriolis terms (not symmetry invariant) Can this be observed at small scales?

34. Asymmetry in atmospheric flows Are atmospheric flows symmetric? WHY? Coriolis terms (not symmetry invariant) YES, WE CAN! Can this be observed at small scales?

35. Thank you for the attention!

36. Towards the measurements…

37. Ekman boundary layers Balance between viscous and Coriolis terms Geostrophic Wind far from surface

38. Budget equations In steady conditions the total helicity is determined by a balance between the injection (due to the pressure gradient) and the viscous destruction Total helicity injection

39. Turbulent Ekman boundary layers Recent numerical simulations of turbulent Ekman layers up to Standard numerics using pseudo-spectral codes