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Subgrid-Scale Models Universität Hannover Institut für Meteorologie und Klimatologie Sonja Weinbrecht Subgrid-Scale Models – an Overview Sonja Weinbrecht.

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Presentation on theme: "Subgrid-Scale Models Universität Hannover Institut für Meteorologie und Klimatologie Sonja Weinbrecht Subgrid-Scale Models – an Overview Sonja Weinbrecht."— Presentation transcript:

1 Subgrid-Scale Models Universität Hannover Institut für Meteorologie und Klimatologie Sonja Weinbrecht Subgrid-Scale Models – an Overview Sonja Weinbrecht Institut für Meteorologie und Klimatologie Universität Hannover

2 Subgrid-Scale Models Universität Hannover Institut für Meteorologie und Klimatologie Sonja Weinbrecht Structure What has to be parameterized ? Eddy diffusion models Dynamic models Mixed models Backscatter models

3 Subgrid-Scale Models Universität Hannover Institut für Meteorologie und Klimatologie Sonja Weinbrecht What has to be parameterized ? Leonard-stresses cross-stresses Reynolds-stresses

4 Subgrid-Scale Models Universität Hannover Institut für Meteorologie und Klimatologie Sonja Weinbrecht Filtered strain rate tensor Characteristic filtered rate of strain eddy viscosity or turbulent viscosity Smagorinsky coefficient Productionterm of kinetic energy Eddy-diffusion models – The Smagorinsky-model

5 Subgrid-Scale Models Universität Hannover Institut für Meteorologie und Klimatologie Sonja Weinbrecht The Smagorinsky-model (II) C s is a constant here but actually varies for different types of flow The Smagorinsky-model is very dissipative Backscatter of energy from smaller to larger structures can not be considered The model is only valid for isotropic turbulence The model overestimates the wind shear near the ground Problems/Disadvantages:

6 Subgrid-Scale Models Universität Hannover Institut für Meteorologie und Klimatologie Sonja Weinbrecht The Smagorinsky-model (III) Modification by Deardorff (1980) – implemented in PALM: Turbulent kinetic energy Characteristic grid spacing Wall adjustment factor

7 Subgrid-Scale Models Universität Hannover Institut für Meteorologie und Klimatologie Sonja Weinbrecht The Smagorinsky-model (IV)- Deardorffs modification Prognostic equation for the turbulent kinetic energy has to be solved:

8 Subgrid-Scale Models Universität Hannover Institut für Meteorologie und Klimatologie Sonja Weinbrecht The Smagorinsky-model (V) Modification by Sullivan et al (1994) – tested in PALM: The so-called two-part eddy viscosity model: Isotropy factor eddy coefficient for inhomogeneous turbulence denotes average over homogeneous directions

9 Subgrid-Scale Models Universität Hannover Institut für Meteorologie und Klimatologie Sonja Weinbrecht 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 ( L ij can be directly computed from the filtered velocity components)

10 Subgrid-Scale Models Universität Hannover Institut für Meteorologie und Klimatologie Sonja Weinbrecht Dynamic Models (II) Advantages: Smagorinsky-coefficient C sn is no longer constant C sn can take negative values, which could be interpreted as backscatter – but which could also cause problems with numerical stability

11 Subgrid-Scale Models Universität Hannover Institut für Meteorologie und Klimatologie Sonja Weinbrecht Mixed Models E.g. Bardina et al. (1980) Assumption: the Smagorinsky-parameterization is only made for C ij + R ij The amount of L ij is explicitly added

12 Subgrid-Scale Models Universität Hannover Institut für Meteorologie und Klimatologie Sonja Weinbrecht Backscatter Models (I) E.g. Mason and Thomson (1992), Schumann (1995) Energy transfer from smaller to larger scales is explicitly modeled Stochastic stress tensor Random number Characteristic correlation time

13 Subgrid-Scale Models Universität Hannover Institut für Meteorologie und Klimatologie Sonja Weinbrecht Backscatter Models (II) γ m is a parameter to describe the portion of random stress [ k c,nk c ] is the wavelength interval, where interaction takes place m is the spectrum slope For m =-5/3 and n = 2, γ = 0.9.

14 Subgrid-Scale Models Universität Hannover Institut für Meteorologie und Klimatologie Sonja Weinbrecht 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).


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