S.Di Savino, M.Iovieno, L.Ducasse, D.Tordella. EPDFC2011, August Politecnico di Torino, Dipartimento di Ingegneria Aeronautica e Spaziale

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1 Mean Dimensionality S.Di Savino, M.Iovieno, L.Ducasse, D.Tordella Politecnico di Torino, Dipartimento di Ingegneria Aeronautica e Spaziale EPDFC2, August 2

2 Passive Basic phenomenology Mean A passive is a contaminant present in so low concentration that it has no dynamical effect on the fluid motion, Turbulence s the by making particles follow chaotic trajectories and disperses the concentration if exists concentration gradient. Fluctuations reach the smaller scales.

3 Turbulent shearless mixing Mean General flow configuration: Turbulent kinetic energy E(x,t) E E 2 High energy turbulence Mixing layer Low energy turbulence periodic boundary condition 2 mixing layers

4 Main features of mixing layers Mean Shearless mixing layers shows the following properties: no gradient of mean velocity, thus no kinetic energy production the mixing is generated by the inhomogeneity in the turbulent kinetic energy and integral scale the mixing layer becomes very intermittent at both large and small scales the presence of a gradient of energy is a sufficient condition for the onset of intermittency [Tordella and iovieno (26); Tordella et al. (28)] 2D and 3D mixings: different asymptotic layer thickness growth exponent

5 Passive Mean We solve the passive advection-diffusion equation ϑ t + u ϑ j = ( )n+ x j Re Sc 2n ϑ for the shearless mixing configuration. DNS simulations have been performed at Re λ = in 3D turbulence (6 2 2 grid points, n = ) and Re λ = 6 in 2D turbulence (24 2 grid points, n = 2). Assume Schmidt number Sc =

6 Visualizations of the mixing layer Mean 2D mixing = = = 3D mixing

7 Mean Diffusion Mean 3D Mixing 2D Mixing θ θ (x x c )/L (x x c )/L Energy ratio E /E 2 = 6.7

8 mixing layer thickness 3D Mixing 2D Mixing Mean θ/l, E/l 2 kinetic energy with E /E 2 = with E /E 2 = ±. θ/l, E/l kinetic energy with E /E 2 = with E /E 2 = 6.6 kinetic energy, lab.exp., lab.exp..46 ± layer thickness: ϑ = x ϑ=.7 x ϑ=.2 3D mixing: ϑ t.4, 2D mixing: ϑ t.7

9 variance 3D Mixing 2D Mixing Mean θ θ (x-x c )/Δ θ Self-similar distribution, peak shifted toward the high kinetic energy region

10 skewness Mean 3D Mixing D Mixing 2 S θ S θ energy flow flow energy flow flow Strong non-gaussian statistic at the mixing layer border 2D: intermittency penetrates more in the direction opposite to the energy gradient.

11 kurtosis 3D Mixing 2D Mixing Mean Kθ energy flow flow Kθ energy flow flow D: higher asymmetry, wider intermittent region Intermittency gradually reduces as the mixing procedes

12 No energy gradient 2D mixing - numerical validation Mean variance skewness 2 θ 2. S θ No energy gradient no asymmetry

13 flux Mean 3D Mixing.2 flow direction.2 flow direction 2D Mixing u θ energy flow direction u θ energy flow direction u ϑ / ϑ (t)

14 Spectra in the mixing layer Mean 3D Mixing Eθ(k) k E u k 3, = 2 3 k Eθ(k)k / D Mixing E u k /3, = k 2 3 Compensated and velocity one-dimensional spectra in the same position

15 Mean 2D/3D Passive diffusion across an energy step: all profiles are skewed towards the higher kinetic energy region self-similar profiles of first and second order large intermittency and non-gaussian behaviour on both sides of the mixing, even where the flux is small. larger asymmetry in moment distributions in 2D mixing 2D: no stretching, inverse cascade, long-range interaction which penetrate more against the energy gradient

16 Scheme of the flow Passive Mean 3D Mixing 2D Mixing (6 2 2 grid) (24 2 grid) 4 Δx 4 Δx Passive Run 3D Movie Run 2D Movie