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

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

Introduction

Introduction

Introduction Coexistence of different scales, but how they interact?

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

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

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)

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

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)

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. 619 (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)

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

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)

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

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

Open channel flow: Spectral flux at surface Gaussian filter

1. Flow at surface: Energy flux

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

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

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

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

Open channel flow: Spectral flux along wall normal

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)

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

Open channel flow: Particles at surface

Open channel flow: Particles at surface

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)

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)