Using helicity to investigate scalar transport in wall turbulence

Helicity, defined as the inner product of the velocity and the vorticity vector, is elusive to measure even for laminar flows. Theoretical results for turbulence have shown that flow structures of high helicity are associated with low dissipation of kinetic energy, making them candidates for coherent structures that can persist longer than others in the flow field. As scalar transport in turbulence is enhanced by three-dimensional coherent motions, study of helicity could reveal flow structures that contribute more than others to scalar transport. Direct numerical simulations of turbulent channel flow at ${\mathrm{Re}}_{\tau }=300$ in conjunction with Lagrangian tracking of fluid particles and passive scalar markers for Schmidt numbers 0.7 and 200 are used here. Local helicity along the trajectories of these markers and the fluid particles is calculated. Different levels of helicity are found to relate to the probability that these markers will remain inside a coherent region. The Lagrangian helicity distribution is also presented, indicating a change of the alignment between velocity and vorticity vectors for scalar transport markers.

Figure 1

(a) Mean absolute helicity density $\overline{\left|H\right|}$ and mean absolute relative helicity density $\overline{\left|h\right|}$ in the channel. (b) Contour plot of helicity density $H$ on a y-z plane (the mean flow direction is perpendicular to the y-z plane).

Figure 2

Mean absolute helicity density of markers with different Sc and of fluid particles: (a) location of release at $y_0^{+}=15$ and (b) location of release at $y_0^{+}=5$.

Figure 3

Motion of fluid particles with $|H_0^p|\ge 3$ at (a) $t=0$, (b) $t=10$, (c) $t=20$, and (d) $t=50$. Motion of fluid particles with $|H_0^p|\le 0.15$ at (e) $t=0$, (f) $t=10$, (g) $t=20$, and (h) $t=50$. (Animated videos are available online as Supplemental Material [53].)

Figure 4

Probability density function (PDF) of relative helicity density of markers: (a) $\mathrm{Sc}=0.7$ released at $y_0=5$, (b) fluid particles released at $y_0=5$, (c) $\mathrm{Sc}=0.7$ released at $y_0=15$, and (d) fluid particles released at $y_0=15$.