1. L ehrstuhl für Modellierung und Simulation UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION Physics of turbulence Lecture 2

2. Experiments of Osborne Reynolds 2 Re_transition=2400 in the pipe flow Reynolds number UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

3. Definition 3 UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION Turbulent motion is the three dimensional unsteady flow motion with chaotical trajectories of fluid particles, with chaotical trajectories of fluid particles, fluctuations of the velocity and fluctuations of the velocity and strong mixing strong mixing arisen at large Re numbers due to unstable vortex dynamics. Difference between vorticity and concentrated vortices Vortex motion Vortex structures

4. Turbulence in free flows 4 UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION Confined jets Diffuser

5. 5 Vortex structures in a free jet close to the nozzle UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

6. 6 Helmholtz Kelvin Instability UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

7. 7 Vortex structures in a free jet in a far field UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

8. 8 Vortex Structures in a free jet with acoustic impact With acoustic waves Free jets UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

9. 9 ResolutionGrid points 31 µm 23 000 000 000 300 µm 23 000 000 LES: Knots number versus resolution 2.72 mm 2.08 mm Resolution 31 µm 90000 points in measur. window 50 mm Resolution 300 µ 2D Vortices in a jet mixer UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

10. 10 Fascinating world of vortices x/D=1 x/D=2 x/D=3 x/D=5 SpatialResolution 31µ. 31µ. UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION Smallest vortices of the flow- kolmogorovvortices PLIF Measurement of the LTT Rostock

11. What vortices are present in the flow? 11 50 mm Resolution 300 µ 2D x/D=3 From scales compared to macrosize of the flow (pipe diameter) ….. to Kolmogorov scales (microns) UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

12. Vortex cascade. Laminar-turbulent transition. 12 UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION One of the possible schemes of the laminar turbulent transition in the boundary layer. One of the possible schemes of the laminar turbulent transition in the boundary layer. Near Wall Turbulence

13. 13 Structure of the turbulent boundary layer. Far from the wall where the viscous stresses are much less compared with turbulent ones UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

14. 14 Structure of the turbulent boundary layer. UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

15. 15 Coherent structures Smoke visualization of streaks in transition under the high- level free-stream turbulence in a boundary layer (from Matsubara & Alfredsson, 2001). UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

16. 16 Coherent structuresStreaks UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

17. 17 UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION From Smith&Walker (1995)Fluid vortices

18. 18 Coherent structures UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION From Smith&Walker (1995)Fluid vortices

19. 19 Coherent structures. Hairpin vortices From Vincent and Meneguzzi (2001) UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

20. 20 Vorticity is solenoidal Vorticity is solenoidal UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

21. 21 Vector algebra. Operator Nabla of Hamilton Exercise. Prove the following expressions NS equations: a mistake is here !!!! Pls correct ! UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

22. 22 Vorticity transport equation NS equations: Vortex stretching Vortex diffusion Vortex convection Rotation and amplification Diffusion (thickening) Source of the turbulence !!! UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

23. 23 Vortex induced velocities UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

24. 24 Vortex cascado. Vortex reconnection UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

25. 25 Sample of the Vortex reconnection. Crow Instability (1971) UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION