Phys. Rev. E 88, 0330133, (2013)

Fluctuations of a passive scalar in a turbulent mixing layer

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
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.