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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.

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## Breaking of symmetry in atmospheric flows

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**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**Symmetry and asymmetry**Symmetry often observed in nature and generally thought as a sign of perfection and beauty**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**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**Asymmetry in atmospheric flows**Are atmospheric flows symmetric?**Asymmetry in atmospheric flows**Are atmospheric flows symmetric?**Asymmetry in atmospheric flows**Are atmospheric flows symmetric?**Asymmetry in atmospheric flows**Are atmospheric flows symmetric?**Asymmetry in atmospheric flows**Are atmospheric flows symmetric? WHY? Coriolis terms (not symmetry invariant) Can this be observed at small scales?**Helicity**(Moffatt & Tsinober, 1992)**Helicity**Velocity (Moffatt & Tsinober, 1992)**Helicity**Vorticity (Moffatt & Tsinober, 1992)**Helicity**(Moffatt & Tsinober, 1992) Invariant of the Euler equations, thus conserved apart from viscous effects**Helicity**(Moffatt & Tsinober, 1992) Invariant of the Euler equations, thus conserved apart from viscous effects AS ENERGY**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**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**Turbulent Ekman boundary layers**Recent numerical simulations of turbulent Ekman layers up to Standard numerics using pseudo-spectral codes**Budget equations**Energy dissipation Energy injection**Budget equations**Energy dissipation Energy injection**Budget equations**Energy dissipation Energy injection Helicity dissipation Helicity injection**Budget equations**Mean field helicity Turbulent helicity Production Transport Pressure Dissipation Rotation**Budget equations**Mean field helicity Turbulent helicity Production Transport Pressure Dissipation Rotation Conversion from mean to turbulent helicity**Budget equations**Mean field helicity Turbulent helicity Production Transport Pressure Dissipation Rotation Viscous dissipation of helicity**Budget equations**Mean field helicity Turbulent helicity Production Transport Pressure Dissipation Rotation Transport of helicity from one place to another**Budget equations**Mean field helicity Turbulent helicity Production Transport Pressure Dissipation Rotation Transport of helicity due to the pressure terms**Budget equations**Mean field helicity Turbulent helicity Production Transport Pressure Dissipation Rotation Transport of helicity due to rotation**Budget equations**Production Transport Pressure Dissipation Rotation**Budget equations**Production Transport Pressure Dissipation Rotation**The helicity cascade**Injection of helicity Helicity dissipation**Asymmetry in atmospheric flows**Are atmospheric flows symmetric? WHY? Coriolis terms (not symmetry invariant) Can this be observed at small scales?**Asymmetry in atmospheric flows**Are atmospheric flows symmetric? WHY? Coriolis terms (not symmetry invariant) Can this be observed at small scales? YES, WE CAN!**Ekman boundary layers**Balance between viscous and Coriolis terms Geostrophic Wind far from surface**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**Turbulent Ekman boundary layers**Recent numerical simulations of turbulent Ekman layers up to Standard numerics using pseudo-spectral codes

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