A. Attili, F. Bisetti, Fluctuations of a passive scalar in a turbulent mixing layer, Phys. Rev. E 88, 0330133, (2013)

A Attili, F Bisetti

Turbulence, scalar transport, structure functions, spectra, shear turbulence

2013

The turbulent flow originating downstream of the Kelvin-Helmholtz instability in a mixing layer has great

relevance inmany applications, ranging from atmospheric physics to combustion in technical devices. The mixing

of a substance by the turbulent velocity field is usually involved. In this paper, a detailed statistical analysis of

fluctuations of a passive scalar in the fully developed region of a turbulent mixing layer from a direct numerical

simulation is presented. Passive scalar spectra show inertial ranges characterized by scaling exponents −4/3 and

−3/2 in the streamwise and spanwise directions, in agreement with a recent theoretical analysis of passive scalar

scaling in shear flows [Celani et al., J. Fluid Mech. 523, 99 (2005)]. Scaling exponents of high-order structure

functions in the streamwise direction show saturation of intermittency with an asymptotic exponent ζ∞ = 0.4 at

large orders. Saturation of intermittency is confirmed by the self-similarity of the tails of the probability density

functions of the scalar increments at different scales r with the scaling factor r

−ζ∞ and by the analysis of the

cumulative probability of large fluctuations. Conversely, intermittency saturation is not observed for the spanwise

increments and the relative scaling exponents agree with recent results for homogeneous isotropic turbulence with

mean scalar gradient. Probability density functions of the scalar increments in the three directions are compared

to assess anisotropy.

relevance inmany applications, ranging from atmospheric physics to combustion in technical devices. The mixing

of a substance by the turbulent velocity field is usually involved. In this paper, a detailed statistical analysis of

fluctuations of a passive scalar in the fully developed region of a turbulent mixing layer from a direct numerical

simulation is presented. Passive scalar spectra show inertial ranges characterized by scaling exponents −4/3 and

−3/2 in the streamwise and spanwise directions, in agreement with a recent theoretical analysis of passive scalar

scaling in shear flows [Celani et al., J. Fluid Mech. 523, 99 (2005)]. Scaling exponents of high-order structure

functions in the streamwise direction show saturation of intermittency with an asymptotic exponent ζ∞ = 0.4 at

large orders. Saturation of intermittency is confirmed by the self-similarity of the tails of the probability density

functions of the scalar increments at different scales r with the scaling factor r

−ζ∞ and by the analysis of the

cumulative probability of large fluctuations. Conversely, intermittency saturation is not observed for the spanwise

increments and the relative scaling exponents agree with recent results for homogeneous isotropic turbulence with

mean scalar gradient. Probability density functions of the scalar increments in the three directions are compared

to assess anisotropy.