1. turbulent open channel flow
Upscale and downscale
energy transfer in
turbulent open channel flow
Salvatore Lovecchio
Università degli Studi di Udine
Dipartimento di Ingegneria Elettrica Gestionale e Meccanica
20 /07/2013

2. Introduction Coexiste Interacte Turbulent flows:
Many different (temporal and spatial) scales which:
Coexiste
Interacte
Leonardo da Vinci

3. Introduction

4. Introduction

5. Introduction
Coexistence of different scales, but how they interact?

6. Introduction Kolmogorov 1941 Kraichnan 1967 DIRECT CASCADE
INVERSE CASCADE
Kolmogorov 1941
Kraichnan 1967

7. Filtered space technique
Spectral energy flux:
Filtered space technique
Rivera et al., PRL 90 (2003)
S. Chen et al., PRL 91 (2003)
Low-pass spatial filter applied to velocity field

8. Filtered space technique
Spectral energy flux:
Filtered space technique
Rivera et al., PRL 90 (2003)
S. Chen et al., PRL 91 (2003)
Low-pass spatial filter applied to velocity field
Equation motion of filtered
Kinetic energy
Energy Flux to scale < r at each space point
Stress tensor induced by eddies at scales < r
Strain tensor
D.H.Kelley,N. T. Ouellette
Phys.Fluids 23 (2011)

9. Filtered space technique
Spectral energy flux:
Filtered space technique
Rivera et al., PRL 90 (2003)
S. Chen et al., PRL 91 (2003)
Low-pass spatial filter applied to velocity field
Equation motion of filtered
Kinetic energy
(Spectral) Energy Flux to scale < r at each space point
Stress tensor induced by eddies at scales < r
Strain tensor
>0 : transfer to smaller structures
FORWARD TRANSFER
<0 : transfer to larger structures
D.H.Kelley,N. T. Ouellette
Phys.Fluids 23 (2011)
INVERSE TRANSFER

10. Filtered space technique
Spectral energy flux:
Filtered space technique
Rivera et al., PRL 90 (2003)
S. Chen et al., PRL 91 (2003)
Low-pass spatial filter applied to velocity field
Equation motion of filtered
Kinetic energy
(Spectral) Energy Flux to scale < r at each space point
Stress tensor induced by eddies at scales < r
Strain tensor
D.H.Kelley,N. T. Ouellette
Phys.Fluids 23 (2011)

11. Energy flux: Literature 2d
S.Chen,R.E.Ecke,G.L.Eyink,M.Rivera,M.Wan,Z.Xiao, PRL 96 (2006)
S.Chen,R.E.Ecke,G.L.Eyink,M.Wan,Z.Xiao, PRL 91 (2003)
Z.Xiao,M.Wan,S.Chen,G.L.Eyink,J.Fluid.Mech (2009)
G.Boffetta, R.E.Ecke, Annu.Rev.Fluid Mech. ( 2012)
G.Boffetta,
“Energy and enstrophy fluxes in the double cascade of two-dimensional
turbulence”, J.Fluid.Mech. 589, (2007)
D.H.Kelley,N.T.Ouelette,
“Spatiotemporal persistence of spectral fluxes in two-dimensional
weak turbulence”, POF 23 (2011)

12. Energy flux: Literature 2d Energy flux Enstrophy flux
G.Boffetta,
“Energy and enstrophy fluxes in the double cascade of two-dimensional
turbulence”, J.Fluid.Mech. 589, (2007)
Energy flux
Enstrophy flux

13. Energy flux: Literature 3d D.Byrne, M.Shats, POF 23 (2011)
H.Xia,D.Byrne,G.Falkovich,M.Shats, Nature physics (2011)
L.Biferale, S.Musacchio,F.Toschi, PRL 108 (2012)
V.K.Natrajan,K.T.Cristensen, POF 18 (2006)
U.Piomelli,W.H.Cabot, P.Moin, S.Lee,
“Subgridscale backscatter in turbulent and transitional flows”, POF 3 (1991)
N.Saikrishnan,E.De Angelis,E.K.Longmire,I.Marusic,C.M.Casciola,
“Reynolds number effects on scale energy balance in wall turbulence”, POF 24 (2012)
N.M.Marati, C.M.Casciola,R.Piva,
“Energy cascade and spatial fluxes in wall turbulence”, J.Fluid.Mech 521 (2004)
Y.Pan,S.Banerjee,
“A numerical study of free-surface turbulence in channel flow”, POF 7 (1995)

14. Energy flux: Literature 3d Y.Pan,S.Banerjee,
“A numerical study of free-surface turbulence in channel flow”, POF 7 (1995)

15. Open channel flow Free-slip wall No-slip wall SHEAR FREE SURFACE:
No surface waves
No-slip wall

16. Open channel flow:
Spectral flux at surface
Gaussian filter

17. 1. Flow at surface: Energy flux

18. 1. Flow at surface
Correlation betweem energy flux and vector flow field

19. 1. Flow at surface
Correlation betweem energy flux and vector flow field

20. 1. Flow at surface
Correlation betweem energy flux and vector flow field

21. Open channel flow: Spectral flux at surface Energy Flux
Surface divergence

22. Open channel flow:
Spectral flux along wall normal

23. Open channel flow: Compressibility
Guido Boffetta, Jahanshah Davoudi, Bruno Eckhardt, Jörg Schumacher , PRL 10 (2004)
John R Cressman, Jahanshah Davoudi, Walter I Goldburg and Jörg Schumacher, New Journal
of Physics (2004)

24. Open channel flow: Compressibility At the surface
Wall-normal behaviour
surface
wall

25. Open channel flow:
Particles at surface

26. Open channel flow:
Particles at surface

27. To think about :
Do particles segregate preferentially in region of downscale cascade energy?
!!! To compute:
Eulerian vs Lagrangian compressibility:
To calculate: compressibility along the trajectories (Jacobian and Lyapunov exponents)

28. Region of upscale and downscale coexiste
Conclusion and future work
Energy flux and compressibility were introduced to characterize the flow
Region of upscale and downscale coexiste
Close to the wall there is an inversion in the average value of energy flux
More quantitative analysis to clarify if sources of velocity field (upwelling) correspond to sink for energy flux (downscale energy)
Other database (wind imposed at surface)