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Further steps towards a scale separated turbulence scheme:

Further steps towards a scale separated turbulence scheme:. Aim : General valid (consistent) description of sub grid scale (SGS) processes Problem : Closure assumptions are constraints additional to the only valid first principals General valid closure assumptions can’t exist

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Further steps towards a scale separated turbulence scheme:

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  1. Further steps towards a scale separated turbulence scheme: • Aim: General valid (consistent) description of sub grid scale (SGS) processes • Problem: Closure assumptions are constraints additional to the only valid first principals • General valid closure assumptions can’t exist • SGS turbulence and e.g. convection can’t be described by one set of 2-nd order equations • Solution: Scale separation • A system of closure equations for each scale separated process with specific closure assumptions • wake vortices by SSO (sub grid scale orography) blocking • horizontal shear vortices • surface induced density flow patterns • shallow and deep convection patterns • Complication: Larger scale SGS processes are interacting with turbulence!! • Scale interaction terms • Validation: • Operational verification • Statistical procession with the package TMOS using ACARS turbulence data DWD Matthias Raschendorfer COSMO Rome 2011

  2. Consistent partial solution for turbulence by spectral separation: Turbulenceis that class of sub grid scale structures being inagreementwithturbulence closure assumptions! • Turbulence closure is only valid for scales not larger than • the smallestpeak wave length Lp of inertial sub range spectra from samples in any direction ( ) • the largest (horizontal) dimension Dg of the control volume • Scale separation by • considering budgets with respect to the separation scale Filter is a moving volume average with infinitesimal vertical extension and horizontal dimension L . • averaging these budgets along the whole control volume (double averaging) generalized turbulent budgetsincluding additional scale interaction terms WakeNet workshop Oberpfaffenhofen: 10-11.05.2010 Matthias Raschendorfer

  3. Physical meaning of the scale interaction terms: • Budgets for the non turbulentSGS structures (SGS circulations): source term scale interaction sink The scale interaction term is shifting Co-Variance (e.g. Sub grid scale Kinetic Energy) form the circulation part of the spectrum (CKE) to the turbulent part (TKE) by virtue of shear generated by the non turbulent SGS flow patterns. production terms depend on: singleturbulent length scale and singleturbulent velocity scale (= ) production terms dependent on: specificlength scales and specificvelocity scales (= ) CKE TKE circulation-scale turbulence-scale and other and other statistical moments We need to consider additional length scales besides the turbulent length scale! DWD Matthias Raschendorfer COSMO Rome 2011

  4. Separated semi parameterized TKEequation (neglecting laminar shear and transport): mean (horizontal) shear production of circulations, : with respect to the separation scale L buoyantpartof buoyantandwakepartof : correction factor in case of sloped model layers to be parameterized by a non turbulent approach expressed by turbulent flux gradient solution according Kolmogorov eddy-dissipation rate(EDR) shear production by sub grid scale circulations transport (advection + diffusion) buoyancy production shear production by the mean flow time tendency labil: neutral: stabil: DWD Matthias Raschendorfer COSMO Rome 2011

  5. TKE-production by separated horizontal shear modes: horizontal grid plane • Separated horizontal shear production term: separated horizontal shear effective mixing length of diffusion by horizontal shear eddies velocity scale of the separated horizontal shear mode grid scale isotropic turbulence scaling parameter horizontal shear eddy • Equilibrium of production and scale transfer towards turbulence: scaling parameter additional TKE source term ……….effective scaling parameter DWD Matthias Raschendorfer COSMO Rome 2011

  6. = (dissipation)1/3 out_usa_shs_rlme_a_shsr_0.2 Pot. Temperature [K] out_usa_shs_rlme_a_shsr_1.0 S N frontal zone 06.02.2008 00UTC + 06h -92 E WakeNet workshop Oberpfaffenhofen: 10-11.05.2010 Matthias Raschendorfer

  7. TKE-production by separated wake modes due to SSO: • SSO-term in filtered momentum budget: blocking term • Pressure term in kinetic energy budget: currently Lott und Miller (1997) from inner energy sources of mean kinetic energy MKE sources of sub grid scale kinetic energy SKE expansion production buoyancy production pressure transport Equilibrium of production and loss by scale transfer wake source DWD Matthias Raschendorfer COSMO Rome 2011

  8. = (dissipation)1/3 Increased due to separated wake terms out_usa_rlme_sso out_usa_rlme_tkesso moderate light S N MIN = 0.00104324 MAX = 10.3641 AVE = 0.126079 SIG = 0.604423 MIN = 0. 00109619 MAX = 10.3689 AVE = 0.127089 SIG = 0.804444 out_usa_rlme_tkesso – out_usa_rlme_sso mountain ridge SSO-effect in TKE budget 06.02.2008 00UTC + 06h -77 E MIN = -0.10315 MAX = 0.391851 AVE = 0.00100152 SIG = 0.00946089 DWD Matthias Raschendorfer COSMO Rome 2011

  9. 10X10 GP above Appalachian mountains out_usa_shs_rlme_a_shsr_0.2 out_usa_shs_rlme_sso COSMO user seminar Matthias Raschendorfer Offenbach: 09-11.03.2009

  10. TKE-Production by convection (thermal circulations): • Circulation scale 2-nd order budgets with proper approximations valid for thermals: circulation scale temperature variance ~ circulation scale buoyant heat flux circulation term vertical velocity scale of circulation virtual potential temperature of ascending air convectivethermals can be derived directly form current mass flux convection scheme virtual potential temperature of descending air Equilibrium of production and loss by scale transfer DWD Matthias Raschendorfer COSMO Rome 2011

  11. DWD Matthias Raschendorfer COSMO Rome 2011

  12. including horizontal shear – and SSO-production reference pot. temperature [K] including horizontal shear –, SSO- and convective production DWD Matthias Raschendorfer COSMO Rome 2011

  13. Turbulence index = 1 (light) Turbulence index = 4 (moderate) Turbulence index = 5 (severe) Colours for measurement height in [m] DWD Matthias Raschendorfer COSMO Rome 2011

  14. DWD Matthias Raschendorfer COSMO Rome 2011

  15. Distribution between Model- and ARCAS-EDR: • Prediction-pedictor correlation: 0.44 DWD Matthias Raschendorfer COSMO Rome 2011

  16. Final distribution after successive regression: • 21 predictors • most effective besides edr: p, dt_tke_(con, sso, hsh) • Successive cubic regression of residuals • Prediction-pedictor correlation: 0.627 • Variance reduction: 39.9 % DWD Matthias Raschendorfer COSMO Rome 2011

  17. Conclusion: • A double filter approach formally generates a system of 2-nd order equations valid for turbulence closure approximations • It differs form the usual single filter approach (according to the grid scale) only by additional scale interaction terms • They describe the source of turbulent 2nd order moments by the action of shear from non turbulent(larger scale)sub grid scale flow structures • Those are • Horizontal shear eddies • Wake eddies by SSO • Convective vertical flow circulations • For them exist specific closure assumptions and they generate their own larger scale diffusion (e.g. by coherent mass flux transport) • Scale interaction is able to generate a needed larger amount of EDR compared to measurements • However, the used ACARS EDR data seem to be biased by • The domination of either low-level or high level measurements • The avoiding of strong turbulence events except in low levels near air ports • The influence of aircrafts ahead during the low level flights • Uncertainties of altitude registration • Flight activities • Thus for the time being, simply pressure or altitude is a significant predictor for EDR DWD Matthias Raschendorfer COSMO Rome 2011

  18. Next steps: • Correction of ACARS data and considering other data sources including LES-data • Some revisions concerning the solution of TKE equation and implicit formulation of vertical diffusion • Reformulation of the surface induced density flow term (original circulation term) in the current scheme to become a thermal SSO production dependent on SSO parameters • Investigation of adoptions regarding the turbulent length scale above the boundary layer • Generating a consistent ensemble of sub grid scale parameterizations by expressing the non turbulent ones scale dependent, containing the scale interaction terms as sink terms. • A revised formulation ofmass flux convectionhas already started (talk in Moskow) • Adoption of the sub grid scale cloud description in the framework of scale separation • Expression of sub grid scale transportby SSO eddies and horizontal shear eddies DWD Matthias Raschendorfer COSMO Rome 2011

  19. Aircraft measurements of EDR (from ACARS data base): turbulent peak wavelength turbulence CKE TKE Circulation Turbulent aircraft velocity with respect to mean wind ln [wave number k] Kinetic Energy model resolution frequency of aircraft oscillations spectrum of vertical oscillations attenuation function and velocity of the aircraft inertial sub range spectrum of atmosphere EDR by regression of the Kolmogorov spectrum WakeNet workshop Matthias Raschendorfer Oberpfaffenhofen: 10-11.05.2010

  20. Effect of the density flow driven circulation term for stabile stratification: turbulent buoyancy flux circulation buoyancy flux horizontal scale of a grid box • Even for vanishing mean wind and negative turbulent buoyancy there remains a positive definite source term TKE will not vanish Solution even for strong stability DWD Matthias Raschendorfer CLM-Training Course

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