Presentation on theme: "Subgrid-Scale Models – an Overview"— Presentation transcript:
1 Subgrid-Scale Models – an Overview Sonja WeinbrechtInstitut für Meteorologie und Klimatologie Universität Hannover
2 StructureWhat has to be parameterized ?Eddy diffusion modelsDynamic modelsMixed modelsBackscatter models
3 What has to be parameterized ? Leonard-stressescross-stressesReynolds-stressesLES-Probleme in Bodennähe – SGS-ModelleQuantitativer Vergleich sowohl zur Evaluierung von LES-Modell prinzipiell, als auch (im zweiten Schritt) zur Bewertung verschiedener SGS-Modelle
4 Eddy-diffusion models – The Smagorinsky-model Filtered strain rate tensorCharacteristic filtered rate of straineddy viscosity or turbulent viscositySmagorinsky coefficientProductionterm of kinetic energy
5 The Smagorinsky-model (II) Problems/Disadvantages:Cs is a constant here but actually varies for different types of flowThe Smagorinsky-model is very dissipativeBackscatter of energy from smaller to larger structures can not be consideredThe model is only valid for isotropic turbulenceThe model overestimates the wind shear near the ground
6 The Smagorinsky-model (III) Modification by Deardorff (1980) – implemented in PALM:Turbulent kinetic energyCharacteristic grid spacingWall adjustment factor
7 The Smagorinsky-model (IV)- Deardorff’s modification Prognostic equation for the turbulent kinetic energy has to be solved:C-e-definition is no longer the original Deardorff-model but was modified by Moeng and Wyngaard
8 The Smagorinsky-model (V) Modification by Sullivan et al (1994) – tested in PALM:The so-called two-part eddy viscosity model:Isotropy factoreddy coefficient for inhomogeneous turbulencedenotes average over homogeneous directions
9 Dynamic Models (I) As prototype: model of Germano et al. (1991) Needs filtering twice (grid filter and test filter)u can be split into a resolved part (I), a subgrid-scale part (III), and a part on a scale between and (I)Three stress tensors are defined as shown (Lij can be directly computed from the filtered velocity components)
10 Dynamic Models (II) Smagorinsky-coefficient Csn is no longer constant Advantages:Smagorinsky-coefficient Csn is no longer constantCsn can take negative values, which could be interpreted as backscatter – but which could also cause problems with numerical stability
11 Mixed Models E.g. Bardina et al. (1980) Assumption: the Smagorinsky-parameterization is only made for Cij+ RijThe amount of Lij is explicitly added
12 Backscatter Models (I) E.g. Mason and Thomson (1992), Schumann (1995)Energy transfer from smaller to larger scales is explicitly modeledStochastic stress tensorRandom numberCharacteristic correlation time
13 Backscatter Models (II) γm is a parameter to describe the portion of random stress[kc,nkc] is the wavelength interval, where interaction takes placem is the spectrum slopeFor m=-5/3 and n = 2, γ = 0.9.
14 Comparison of two SGS-models in PALM Dimensionless wind shear: on the left: SGS-model of Deardorff (1980); on the right: SGS-model of Sullivan et al (1994) – dashed line: theoretical solution, solid line: PALM simulation results, dotted line: simulation results with the model of Moeng (1984).