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Ulrich Achatz Goethe- Universität Frankfurt am Main

Ulrich Achatz Goethe- Universität Frankfurt am Main. Multiple-scale asymptotics of the interaction between gravity waves and synoptic-scale flow and its implications for soundproof modelling. Gravity waves in the atmosphere. GW radiation : Spontaneous Imbalance. Source: ECMWF.

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Ulrich Achatz Goethe- Universität Frankfurt am Main

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  1. Ulrich Achatz Goethe-Universität Frankfurt am Main Multiple-scale asymptotics of the interaction between gravity waves and synoptic-scale flow and its implications for soundproof modelling

  2. Gravity wavesin theatmosphere

  3. GW radiation: SpontaneousImbalance Source: ECMWF

  4. Gravity Waves in theMiddleAtmosphere Becker und Schmitz (2003)

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

  6. Gravity Waves in the Middle Atmosphere Without GW parameterization Becker und Schmitz (2003)

  7. GWs and Clear-Air Turbulence Koch et al (2008)

  8. Impact GWs on Weather Forecasts Without GWs Analysis Palmer et al (1986)

  9. Impact GWs on Weather Forecasts without GWs with GWs Analysis Palmer et al (1986)

  10. Open Questions

  11. Open Questionsand Research Strategy • Howwell do presentparameterizationsdescribethe GW impact? (theoryneeded!) (e.g. Linzen 1981, Palmer et al 1986, McFarlane 1987, Medvedev andKlaassen 1995, Hines 1997, Lottand Miller 1997, Alexander andDunkerton 1999, Warner andMcIntyre 2001) • Howwell do weunderstand GW breaking? • Howwell do weunderstand GW propagation? • Presentlynoparameterizationofspontaneousimbalance

  12. Open Questions and Research Strategy • Howwell do presentparameterizationsdescribethe GW impact? (theoryneeded!) (e.g. Linzen 1981, Palmer et al 1986, McFarlane 1987, Medvedev andKlaassen 1995, Hines 1997, Lottand Miller 1997, Alexander andDunkerton 1999, Warner andMcIntyre 2001) • Howwell do weunderstand GW breaking? • Howwell do weunderstand GW propagation? • Presentlynoparameterizationofspontaneousimbalance • Approach: DNS(everythingresolved) LES(turbulenceparameterized, GWs resolved) GW parameterization

  13. DNS and LES ofbreaking IGW (Boussinesq) Perturbation IGW by leading transverse SV: snapshot 1152 x 1152 direct numerical simulation 288 x 288 simulation with ALDM (INCA) Fruman, Achatz (GU Frankfurt), RemmlerandHickel (TU München)

  14. DNS and LES of breaking IGW (Boussinesq) Random perturbation IGW Random perturbation NH GW Horizontally averaged vertical spectrum of total energy density vs. wavenumber Fruman, Achatz (GU Frankfurt), RemmlerandHickel (TU München)

  15. GW breaking in the middle atmosphere Rapp et al. (priv. comm.) Conservation Instabilityat large altitudes Momentumdeposition…

  16. GW breaking in themiddleatmosphere Rapp et al. (priv. comm.) • Conservation • Instabilityat large altitudes • Momentumdeposition… • Competitionbetweenwavegrowthanddissipation: • not in Boussinesqtheory

  17. GW breaking in the middle atmosphere Rapp et al. (priv. comm.) • Conservation • Instabilityat large altitudes • Momentumdeposition… • Competitionbetweenwavegrowthanddissipation: • not in Boussinesqtheory • Soundproofcandidates: • Anelastic(Oguraand Philips 1962, Lipps andHemler 1982) • Pseudo-incompressible (Durran 1989)

  18. GW breaking in the middle atmosphere Which soundproof model should be used? Rapp et al. (priv. comm.) • Conservation • Instabilityat large altitudes • Momentumdeposition… • Competitionbetweenwavegrowthanddissipation: • not in Boussinesqtheory • Soundproofcandidates: • Anelastic(Oguraand Philips 1962, Lipps andHemler 1982) • Pseudo-incompressible (Durran 1989)

  19. Interaction between Large-Amplitude GW andMean Flow: Strong Stratification No Rotation Achatz, Klein, and Senf (2010)

  20. Scales: time andspace • forsimplicityfromnow on: 2D • non-hydrostatic GWs: same spatialscale in horizontal andvertical characteristic wave number • time scale set by GW frequency characteristic frequency dispersion relation for Achatz, Klein, and Senf (2010)

  21. Scales: time andspace • forsimplicityfromnow on: 2D • non-hydrostatic GWs: same spatialscale in horizontal andvertical characteristic length scale • time scale set by GW frequency characteristic frequency dispersion relation for Achatz, Klein, and Senf (2010)

  22. Scales: time andspace • forsimplicityfromnow on: 2D • non-hydrostatic GWs: same spatialscale in horizontal andvertical characteristic length scale • time scalesetby GW frequency characteristic time scale dispersion relation for Achatz, Klein, and Senf (2010)

  23. Scales: time andspace • forsimplicityfromnow on: 2D • non-hydrostatic GWs: same spatialscale in horizontal andvertical characteristic length scale • time scalesetby GW frequency characteristic time scale linear dispersionrelationfor Achatz, Klein, and Senf (2010)

  24. Scales: velocities • windsdeterminedby linear polarizationrelations: what is ? • most interesting dynamics when GWs are close to breaking, i.e. locally Achatz, Klein, and Senf (2010)

  25. Scales: velocities • windsdeterminedby linear polarizationrelations: what is ? • mostinterestingdynamicswhen GWs areclosetobreaking, i.e. locally Achatz, Klein, and Senf (2010)

  26. Non-dimensional Euler equations • using: yields Achatz, Klein, and Senf (2010)

  27. Non-dimensional Euler equations • using: yields isothermal potential-temperaturescaleheight Achatz, Klein, and Senf (2010)

  28. Scales: thermodynamicwavefields • potential temperature: Achatz, Klein, and Senf (2010)

  29. Scales: thermodynamicwavefields • potential temperature: • Exner pressure: Achatz, Klein, and Senf (2010)

  30. Multi-ScaleAsymptotics • Additional verticalscaleneeded: • andhaveverticalscale • scaleofwavegrowthis Therefore: Multi-scale-asymptotic ansatz also assumed: Achatz, Klein, and Senf (2010)

  31. Multi-ScaleAsymptotics • Additional verticalscaleneeded: • andhaveverticalscale • scaleofwavegrowthis Therefore: Multi-scale-asymptotic ansatz also assumed: Achatz, Klein, and Senf (2010)

  32. Multi-ScaleAsymptotics • Additional verticalscaleneeded: • andhaveverticalscale • scaleofwavegrowthis • hereassumed: Achatz, Klein, and Senf (2010)

  33. Large-amplitude WKBb Achatz, Klein, and Senf (2010)

  34. Large-amplitude WKB Achatz, Klein, and Senf (2010)

  35. Large-amplitude WKB Achatz, Klein, and Senf (2010)

  36. Large-amplitude WKB Meanflowwithonly large-scaledependence Achatz, Klein, and Senf (2010)

  37. Large-amplitude WKB • Wavepacketwith • large-scaleamplitude • wavenumberandfrequencywith large-scaledependence Achatz, Klein, and Senf (2010)

  38. Large-amplitude WKB Achatz, Klein, and Senf (2010)

  39. Large-amplitude WKB Next-order meanflow Achatz, Klein, and Senf (2010)

  40. Large-amplitude WKB Harmonicsofthewavepacket due tononlinearinteractions Achatz, Klein, and Senf (2010)

  41. Large-amplitude WKB • collectequalpowers in • collectequalpowers in • nolinearization! Achatz, Klein, and Senf (2010)

  42. Large-amplitude WKB: leadingorder Achatz, Klein, and Senf (2010)

  43. Large-amplitude WKB: leading order dispersionrelationandstructureasfromBoussinesq Achatz, Klein, and Senf (2010)

  44. Large-amplitude WKB: 1st order Achatz, Klein, and Senf (2010)

  45. Large-amplitude WKB: 1st order Solvabilityconditionleadstowave-action conservation (Bretherton 1966, Grimshaw 1975, Müller 1976) Achatz, Klein, and Senf (2010)

  46. Large-amplitude WKB: 1st order Same resultfrom pseudo-incompressibleandfromanelastictheory (Klein 2011) Solvabilityconditionleadstowave-action conservation (Bretherton 1966, Grimshaw 1975, Müller 1976) Achatz, Klein, and Senf (2010)

  47. Large-amplitude WKB: 1st order, 2nd harmonics Achatz, Klein, and Senf (2010)

  48. Large-amplitude WKB: 1st order, 2nd harmonics Achatz, Klein, and Senf (2010)

  49. Large-amplitude WKB: 1st order, 2nd harmonics 2nd harmonics are slaved Achatz, Klein, and Senf (2010)v

  50. Large-amplitude WKB: 1st order, higherharmonics Achatz, Klein, and Senf (2010)

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