On how walls shape dissipation intermittency

Abstract

Intermittency of energy dissipation has long been studied via high-order moments in homogeneous and isotropic turbulence, but not much where the boundary effects are explicitly included. Here, we derive two fundamental Reynolds number scaling expressions for dissipation moments in wall-bounded flows -- one in the outer region where the boundary effects are weak and the other close to the walls where those effects are strong -- and support these expressions by direct numerical simulations. Dissipation moments in the outer region follow universal power laws with exponents linked to anomalous scaling of velocity structure functions. In contrast, moments near the wall follow a bounded defect law, leading to a finite asymptotic limit without intermittency. For very large Reynolds numbers, the outer proposal predicts vanishing dissipation compared to that on the wall, highlighting the need for solid boundaries in generating Onsager-type singularities.

Figures (4)

• Figure 1: Typical snapshots of the streamwise component of turbulent dissipation rate on (a) the channel centerplane and (b) the wall, normalized by the ensemble-averaged component turbulent dissipation rate $\langle\epsilon_{uu}\rangle$, obtained from direct numerical simulations (DNS) of channel flow in Ref. LM2015 at $Re_\tau=5200$. Spatial domains are nondimensionalized using the Kolmogorov length $\eta$.
• Figure 2: Probability densities of $\epsilon_{uu}/\epsilon_\tau$ at the wall compared with those of $\epsilon_{uu}/\epsilon_o$ at the center (inset). Dashed line represents a slope of $-1/2$, dash-dotted line for slope of $1/2$. Here, $\epsilon_\tau$ is the wall dissipation (defined below Eq. (2)) and $\epsilon_o$ is the scale of outer dissipation (defined just below Eq. (5)). Data for $Re_\tau=180$ and $550$ are ours (see Supplemental Material supply), and for $1000$ and $5200$ are from Ref. LM2015.
• Figure 3: Streamwise dissipation moments. (a) $Re_\tau$-scaling of dissipation moments in the outer flow. Predictions of (\ref{['eq:diss_outer_power']}) are represented by lines, with solid from (\ref{['eq:Sreeni-Yakhot_model']}) and dashed from (\ref{['eq:SL_model']}). For clarity, data at different wall-normal positions are vertically shifted to align with the center values, without affecting the validation of scaling slopes. (b) $Re_\tau$-scaling of dissipation moments at the wall. Dash-dotted lines indicate (\ref{['eq:diss_wall_Townsend']}), while solid lines indicate (\ref{['eq:diss_wall_defect']}). In both panels, colors denote different orders with arrows depicting increasing order for integer $p=1-4$. Gray symbols are data from Ref. Cheng2022_JFM_diss_wall, black symbols are from Refs. Hoyas2008_DNSHoyas2022_DNS, while others are the same as in Fig. \ref{['fig:pdf_diss_uu']}. The parameter values for the theoretical lines are listed in Table \ref{['tab:parameters']}.
• Figure 4: Spanwise dissipation moments. Symbols and lines are the same as in Fig. \ref{['fig:diss_uu_Re']}. There are fewer data points (not reported in the literature) compared to the streamwise components.