External intermittency compensation of dissipation scale distributions in a turbulent boundary layer

The influence of external intermittency on the scaling of the dissipation scale distribution is examined in turbulent boundary layer flow at ${\text{Re}}_{\tau }\approx 1000$. Probability density functions (PDFs) of the dissipative scales are compared with, and without, accounting for the external intermittency using an intermittency detection function. Results showed that accounting for the external intermittency produces better consistency in the shapes of the PDFs at the same wall-normal location at different instances in time. In addition, properly scaling the dissipation scale distribution collapses the probability density functions calculated at different wall-normal locations. This improvement in the scaling of the dissipation scale distribution supports prior observations of universality of the small-scale description of the turbulence for wall-bounded flow.

Figure 1

(a) Portion of instantaneous streamwise velocity measured at $y/\delta =0.66$ by the hot-wire probe, with the dashed line indicating the free-stream velocity. (b) Corresponding detector function $\mathcal{D}\left(t\right)$ with the dashed line indicating the threshold used to identify turbulent-nonturbulent zones. (c) Corresponding binary intermittency signal with $I\left(t\right)=1$ indicating the presence of turbulence and $I\left(t\right)=0$ indicating a nonturbulent state. (d) Profile of average intermittency function, $\gamma$. Solid line indicates Eq. (7) and dashed line indicates the wall-normal location where $\gamma =0.5$, which occurs at $y/\delta \approx 2/3$.

Figure 2

Comparison between the measured PDFs of local dissipation scales when (a) treating the entire time series as turbulent and (b) accounting for the external intermittency. For cases where $\gamma <1$ (i.e., $y/\delta >0.19)$, each wall-normal position has been shifted up by a decade for clarity.

Figure 3

PDFs of $\eta$ for cases with $\gamma <1$ when (a) treating the entire time series as turbulent and (b) accounting for the external intermittency. For (b) the average values of the PDFs at a specific wall-normal position when the flow is intermittent are presented. Corresponding isocontours of $Q(\eta /{\eta }_{\mathcal{L}})$ as a function of $\eta /{\eta }_{\mathcal{L}}$ and $y/\delta$ are shown (c) treating the entire time series as turbulent and (d) accounting for the external intermittency.