1. Gravity-wave breaking beyond traditional instability concepts U. Achatz Goethe-Universität Frankfurt am Main, Germany 6.10.2008

2. Gravity Waves in the Middle Atmosphere Becker und Schmitz (2003)

3. Gravity Waves in the Middle Atmosphere Becker und Schmitz (2003)

4. Gravity Waves and Clear-Air Turbulence Koch et al (2008)

5. GW Parameterizations multitude of parameterization approaches (Lindzen 1981, Medvedev und Klaassen 1995, Hines 1997, Alexander and Dunkerton 1999, Warner and McIntyre 2001) too many free parameters reasons : –…–… –insufficent knowledge: conditions of wave breaking basic paradigm: breaking of a single wave –Stability analyses (NMs, SVs) –Direct numerical simulations (DNS)

6. Basic Types of GWs Dispersionsrelation: Trägheitsschwerewellen (TSW): Hochfrequente Schwerewellen (HSW):

7. Basic Types of GWs Dispersion relation: Trägheitsschwerewellen (TSW): Hochfrequente Schwerewellen (HSW):

8. Basic Types of GWs Dispersion relation : Inertia-gravity waves (IGW): Hochfrequente Schwerewellen (HSW):

9. Basic Types of GWs Dispersion relation : Inertia-gravity waves (IGW): High-frequency gravity waves (HGW):

10. GW Signatures in Noctilucent Clouds Parvianien (1989)

11. GW Signatures in Noctilucent Clouds Parvianien (1989)

12. GW Signatures in Noctilucent Clouds Parvianien (1989)

13. Traditional Instability Concepts static (convective) instability: amplitude reference (a>1) dynamic instability limited applicability to HGW breaking

14. Traditional Instability Concepts static (convective) instability: amplitude reference (a>1) dynamic instability limited applicability to HGW breaking

15. Traditional Instability Concepts static (convective) instability: amplitude reference (a>1) dynamic instability BUT: limited applicability to GW breaking

16. GW Instabilities Beyond Traditional Concepts IGW: NM: Exponential energy growth simple shear layer: –Static instability if –Dynamic instability if SV: optimal energy growth over a finite time  (Farrell 1988a,b, Trefethen et al. 1993) HGW: Significant horizontal gradients shear-layer concepts fail

17. GW Instabilities Beyond Traditional Concepts IGW: NM: Exponential energy growth simple shear layer: –Static instability if –Dynamic instability if SV: optimal energy growth over a finite time  (Farrell 1988a,b, Trefethen et al. 1993) HGW: Significant horizontal gradients shear-layer concepts fail (e.g. Lombard and Riley 1996, Achatz 2005)

18. Turbulence in GCMs parameterizations in GCMs: –coarse resolution: all GWs, turbulence –high resolution: small-scale GWs, turbulence central: wave-turbulence interaction basic paradigm: breaking of a single wave methods: –stability analyses (normal modes, singular vectors) –direct numerical simulations (DNS)

19. Modell

20. Stability analysis, 2.5D-DNS

21. Turbulent Dissipation Rates in the Mesosphere

22. Breaking of an IGW by an SV (Ri > ¼): Measured dissipation rates 1…1000 mW/kg (Lübken 1997, Müllemann et al. 2003)

23. NMs of an HGW: Growth Rates  = 70°)

24. HGW amplitude after a perturbation by a NM (DNS):

25. Energetics not the gradients in z matter, but those in  ! instantaneous growth rate:

26. Energetics not the gradients in z matter, but those in  ! instantaneous growth rate:

27. Energetics not the gradients in z matter, but those in  ! instantaneous growth rate:

28. Energetics of a breaking HGW with a 0 > 1 Strong growth perturbation energy: shear instability

29. Breaking HGW with a 0 > 1: Dissipation Rates

30. Energetics of a Breaking HGW with a 0 < 1 Strong growth perturbation energy: buoyancy instability

31. Breaking HGW with a 0 < 1: Wave-Wave Interaction

32. Breaking HGW with a 0 < 1: Dissipation Rates

33. Breaking HGW with a 0 < 1: Dissipation rate Dissipation rate (mW/kg) at ist maximum ( t = 5P ):

34. Turbulent Dissipation Rates in the Mesosphere

35. Singular Vectors: normal modes: Exponential energy growth singular vectors: optimal growth over a finite time  (Farrell 1988, Trefethen et al. 1993) characteristic perturbations in a linear initial value problem:

36. SVs: Turbulent Layers

37. SVs: Turbulent Dissipation Rates

38. Summary the Richardson number is not a good criterion for turbulence from gravity waves! IGWs: Breaking by SVs HGWs: Instabilities due to horizontal gradients References: –Achatz (2005, Phys. Fluids) –Achatz and Schmitz (2006a,b, J.Atmos. Sci.) –Achatz (2007a,b, J. Atmos. Sci.) –Achatz (2007c, Adv. Space Res.) –all PDFs available from my web page (http://www.geo.uni-frankfurt.de/iau/ThMet/english/Publications/index.html)http://www.geo.uni-frankfurt.de/iau/ThMet/english/Publications/index.html see also Fritts et al. (2003, 2006, 2008a,b)