2013/07/22 by P. C. Valente, Valente, P. C., J. C. Vassilicos +1 · 1 citation
Physics and Astronomy · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.1307.5901
submitted
arxiv created 2014/02/23 · arxiv updated 2014/02/25
We investigate non-equilibrium turbulence where the non-dimensionalised dissipation coefficient Cε scales as Cε ∼ ReMm/Reℓn with m≈ 1 ≈ n (ReM and Reℓ are global/inlet and local Reynolds numbers respectively) by measuring the downstream evolution of the scale-by-scale energy transfer, dissipation, advection, production and transport in the lee of a square-mesh grid and compare with a region of equilibrium turbulence (i.e. where Cε≈ constant). These are the main terms of the inhomogeneous, anisotropic version of the von Kármán-Howarth-Monin equation. It is shown in the grid-generated turbulence studied here that, even in the presence of non-negligible turbulence production and transport, production and transport are large-scale phenomena that do not contribute to the scale-by-scale balance for scales smaller than about a third of the integral-length scale, ℓ, and therefore do not affect the energy transfer to the small-scales. In both the non-equilibrium and the equilibrium decay regions, the peak of the scale-by-scale energy transfer scales as (u2)3/2/ℓ (u2 is the variance of the longitudinal fluctuating velocity). In the non-equilibrium case this scaling implies an imbalance between the energy transfer to the small scales and the dissipation. This imbalance is reflected on the small-scale advection which becomes larger in proportion to the maximum energy transfer as the turbulence decays whereas it stays proportionally constant in the further downstream equilibrium region where Cε ≈ constant even though Reℓ is lower.