Persistence of local anisotropy of passive scalars in wall-bounded flows

Local isotropy of passive scalars in fully developed turbulent channel flow is studied by way of direct numerical simulations. We observe a persistent small-scale anisotropy that (i) persists after the flow has undergone substantial mixing and (ii) is independent of the original large-scale anisotropic initial conditions of the scalar field. This latter observation is in sharp contrast with the persistent local anisotropy observed in homogeneous, isotropic turbulence with imposed mean scalar gradients, for which the small-scale anisotropy is directly correlated to the imposed large-scale anisotropy by way of ramp-cliff structures. The anisotropy observed in the present work is linked to the production of $〈{\varepsilon }_{\theta }〉$ due to the mean velocity gradient. A major implication of the work is that local isotropy of passive scalar fields may never hold in flows in which mean velocity gradients exist, even after mean scalar gradients have been eliminated by the turbulence.

Figure 1

Initial configurations of the concentration field: $I{C}_x$ (a), $I{C}_y$ (b), $I{C}_z$ (c).

Figure 2

Concentration distributions generated at $\tau =7$ by the action of the same fully turbulent channel flow on the initial conditions: $I{C}_x$ (a), $I{C}_y$ (b), and $I{C}_z$ (c).

Figure 3

Time-evolution of the scalar dissipation rate for the three initial conditions: $I{C}_x$ (circles), $I{C}_y$ (squares), $I{C}_z$ (triangles).

Figure 4

Time-evolution of the fractional components of the scalar dissipation rate, $〈{\varepsilon }_{{\theta }_x}〉/〈{\varepsilon }_{\theta }〉$ (circles), $〈{\varepsilon }_{{\theta }_y}〉/〈{\varepsilon }_{\theta }〉$ (squares) and $〈{\varepsilon }_{{\theta }_z}〉/〈{\varepsilon }_{\theta }〉$ (triangles) for the three initial conditions: $I{C}_x$ (a), $I{C}_y$ (b), and $I{C}_z$ (c).

Figure 5

Schematic of the subdivision of the computational domain to investigate small scale anisotropy.

Figure 6

Time evolution of the fractional components of the scalar dissipation rate, $〈{\varepsilon }_{{\theta }_x}〉/〈{\varepsilon }_{\theta }〉$ (circles), $〈{\varepsilon }_{{\theta }_y}〉/〈{\varepsilon }_{\theta }〉$ (squares), and $〈{\varepsilon }_{{\theta }_z}〉/〈{\varepsilon }_{\theta }〉$ (triangles) in Zone 1 (a), (b), (c), Zone 2 (d), (e), (f), and Zone 3 (g), (h), (i) for the three initial conditions $I{C}_x$ (a), (d), (g), $I{C}_y$ (b), (e), (h) and $I{C}_z$ (c), (f), (i).