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Fig. 16. Vertical (x = 0) and horizontal (left panel: z = 1.6, right panel: z = 0.9) cuts through ALDM results (velocity magnitude) of neutrally and strongly stratified turbulence.

Figure 16 Vertical (x = 0) and horizontal (left panel: z = 1.6, right panel: z = 0.9) cuts through ALDM results (velocity magnitude) of neutrally and strongly stratified turbulence.

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Fig. 1. Ratio of vertical to horizontal kinetic energy in the Taylor-Green vortex (Reo = 1600). 4. Results and discussion
Fig. 1. Ratio of vertical to horizontal kinetic energy in the Taylor-Green vortex (Reo = 1600). 4. Results and discussion
Fig. 2. Visualization of the TGV at t = 10 (DNS 256? cells at Rey = 800). Iso-surfaces at Q = 0.5, colored by the shear rate. The case-dependence of the value for the model constant in the standard Smagorinsky model led to the idea of replacing the con- stant by a dynamic parameter, which automatically adjusts to the flow conditions. Germano et al. (1991) presented a general dy- namic procedure for eddy viscosity models and applied it to the Smagorinsky model. The basic idea is a similarity between the interactions of the smallest resolved scales and unresolved scales compared to the interactions between medium scales and the smallest resolved scales. Transitional flows are a challenging problem for turbulence subgrid-scale models. Their correct prediction is only possible if the subgrid-scale model does not affect the laminar flow and its instability modes. For most eddy-viscosity models, such as the Smagorinsky model without dynamic model-coefficient adaption, this requirement is not fulfilled. We used the transition of the three-dimensional Taylor-Green vortex (TGV) as a test for ALDM in laminar-to-turbulence transition. The velocity field in a triple- periodic box with side length Lp = 27Z is initialized with a set of large scale vortices varying vertically:
Fig. 2. Visualization of the TGV at t = 10 (DNS 256? cells at Rey = 800). Iso-surfaces at Q = 0.5, colored by the shear rate. The case-dependence of the value for the model constant in the standard Smagorinsky model led to the idea of replacing the con- stant by a dynamic parameter, which automatically adjusts to the flow conditions. Germano et al. (1991) presented a general dy- namic procedure for eddy viscosity models and applied it to the Smagorinsky model. The basic idea is a similarity between the interactions of the smallest resolved scales and unresolved scales compared to the interactions between medium scales and the smallest resolved scales. Transitional flows are a challenging problem for turbulence subgrid-scale models. Their correct prediction is only possible if the subgrid-scale model does not affect the laminar flow and its instability modes. For most eddy-viscosity models, such as the Smagorinsky model without dynamic model-coefficient adaption, this requirement is not fulfilled. We used the transition of the three-dimensional Taylor-Green vortex (TGV) as a test for ALDM in laminar-to-turbulence transition. The velocity field in a triple- periodic box with side length Lp = 27Z is initialized with a set of large scale vortices varying vertically:
Fig. 3. Regime diagram (Brethouwer et al., 2007) for the transition of the TGV for different parameters; symbols: DNS, lines: LES with ALDM.
Fig. 3. Regime diagram (Brethouwer et al., 2007) for the transition of the TGV for different parameters; symbols: DNS, lines: LES with ALDM.
Fig. 4. Total energy dissipation rate of the TGV (Rey = 1600).
Fig. 4. Total energy dissipation rate of the TGV (Rey = 1600).
Fig. 6. Contributions to energy dissipation of the TGV (Reo = 1600, Fro = 1).
Fig. 6. Contributions to energy dissipation of the TGV (Reo = 1600, Fro = 1).
Fig. 5. Contributions to energy dissipation of the TGV (Rep = 1600, Fro = 2).
Fig. 5. Contributions to energy dissipation of the TGV (Rep = 1600, Fro = 2).
Fig. 8. Energy budget of the TGV (Reo = 1600, Fro = 1); solid lines: ALDM, dashed lines: SSM. Fig. 7. Contributions to energy dissipation of the TGV (Reo = 1600, Fro = 0.5)
Fig. 8. Energy budget of the TGV (Reo = 1600, Fro = 1); solid lines: ALDM, dashed lines: SSM. Fig. 7. Contributions to energy dissipation of the TGV (Reo = 1600, Fro = 0.5)
Fig. 9. Regime diagram for our simulations of stratified turbulence.
Fig. 9. Regime diagram for our simulations of stratified turbulence.
Fig. 11. DNS of neutrally stratified turbulence (Re = 8440). Iso-surface of Q, color of iso-surface and shading of domain faces by local molecular dissipation rate (normalized by the spatial average). Fig. 10. Ratio of vertical to potential energy in HST as a function of local Froude number.
Fig. 11. DNS of neutrally stratified turbulence (Re = 8440). Iso-surface of Q, color of iso-surface and shading of domain faces by local molecular dissipation rate (normalized by the spatial average). Fig. 10. Ratio of vertical to potential energy in HST as a function of local Froude number.
Fig. 12. DNS of strongly stratified turbulence (Re = 7110, Fr = 0.017). Coloring as in Fig. 11.
Fig. 12. DNS of strongly stratified turbulence (Re = 7110, Fr = 0.017). Coloring as in Fig. 11.
Fig. 13. Vertical (x=0) and horizontal (z= 2.4) cuts through a DNS result of neutrally stratified turbulence. Left panels: velocity magnitude, right panels: molecular dissipation.
Fig. 13. Vertical (x=0) and horizontal (z= 2.4) cuts through a DNS result of neutrally stratified turbulence. Left panels: velocity magnitude, right panels: molecular dissipation.
Fig. 14. Vertical (x = 0) and horizontal (z = 0.1) cuts through a DNS result of strongly stratified turbulence. Left panels: velocity magnitude, right panels: molecular dissipation.
Fig. 14. Vertical (x = 0) and horizontal (z = 0.1) cuts through a DNS result of strongly stratified turbulence. Left panels: velocity magnitude, right panels: molecular dissipation.
Fig. 15. Zoom into the vertical cut through a DNS result of strongly stratified turbulence (molecular dissipation).
Fig. 15. Zoom into the vertical cut through a DNS result of strongly stratified turbulence (molecular dissipation).
Fig. 17. Weakly stratified turbulence kinetic energy spectra (R = 41).
Fig. 17. Weakly stratified turbulence kinetic energy spectra (R = 41).
Fig. 18. Strongly stratified turbulence kinetic energy spectra (R = 6.3).
Fig. 18. Strongly stratified turbulence kinetic energy spectra (R = 6.3).
Related topics:
Turbulence ModellingLarge Eddy SimulationDirect Numerical SimulationTurbulent FlowsStratified FlowsStratified turbulence
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