1 / 39

Breaking of symmetry in atmospheric flows

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. Symmetry and asymmetry.

olin
Download Presentation

Breaking of symmetry in atmospheric flows

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Breaking of symmetry in atmospheric flows Enrico Deusebio1and Erik Lindborg2 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? Coriolis terms (not symmetry invariant) Can this be observed at small scales?

  10. Helicity (Moffatt & Tsinober, 1992)

  11. Helicity Velocity (Moffatt & Tsinober, 1992)

  12. Helicity Vorticity (Moffatt & Tsinober, 1992)

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

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

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

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

  19. Budget equations

  20. Budget equations

  21. Budget equations Energy dissipation Energy injection

  22. Budget equations Energy dissipation Energy injection

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

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

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

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

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

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

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

  30. Budget equations Production Transport Pressure Dissipation Rotation

  31. Budget equations Production Transport Pressure Dissipation 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) Can this be observed at small scales? YES, WE CAN!

  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

More Related