Figure 1

(Color online) DNS data for the approach of the Lagrangian velocity structure function to inertial subrange behavior in a turbulent channel flow with nondimensional height ${hu}_{*}∕\nu \equiv h^{†}=180$, where $\nu$ is the kinematic viscosity and $u_{*}$ is the friction velocity (dashed lines). The lines pass smoothly through data points acquired at $0.032t_{\eta }^E$ intervals. Predictions obtained using a third-order LS model with $C_0=6$ and $a_0=5.5$ are also shown (solid lines). The nondimensional height $y^{+}$ of the origin of the trajectories is indicated. The letter adjacent to the pairs of curves denotes the velocity component.Reuse & Permissions

Figure 2

(Color online) DNS data for the approach of the Lagrangian velocity structure function to inertial subrange behavior in a turbulent shear flow with nondimensional height $h{u}_{*}∕\nu \equiv h^{†}=180$, where $\nu$ is the kinematic viscosity and $u_{*}$ is the friction velocity (dashed lines). The lines pass smoothly through data points acquired at $0.032t_{\eta }^E$ intervals. Predictions obtained using a second-order LS model with $C_0=6$ and nonuniversal anisotropic values of $a_0$ calculated using the Kolmogorov similarity scaling relation $a_0={\sigma }_A^2{ϵ}^{-3∕2}{\nu }^{1∕2}$, and the results of DNS are also shown (lines: streamwise, solid line; vertical, dotted line; cross wind, dashed line). The nondimensional height $y^{†}$ of the origin of the trajectories is indicated. The letter adjacent to the pairs of curves denotes the velocity component.Reuse & Permissions

Figure 3

DNS data (solid lines) and model predictions (second-order model, dotted line; third-order model, dashed line) for the Lagrangian acceleration autocorrelation function ${\rho }_{33}=⟨A_3\left(0\right)A_3\left(t\right)⟩$ (lateral direction). For the second-order model, predictions are shown for $C_0=6$ and nonuniversal anisotropic values of $a_0$ calculated using the Kolmogorov similarity scaling relation $a_0={\sigma }_A^2{ϵ}^{-3∕2}{\nu }^{1∕2},$ and the results of DNS. For the third-order model, predictions are shown for $C_0=6$ and $a_0=5.5$. Time has been nondimensionalized using the friction velocity $u_{\tau }$ and the height of the boundary layer $h$. The nondimensional height $y^{†}$ of the origin of the trajectories is indicated.Reuse & Permissions

Figure 4

Normalized Lagrangian velocity autocorrelation functions $R_{ij}=⟨u_i\left(0\right)u_j\left(s\right)⟩∕{\left({\sigma }_{ii}{\sigma }_{jj}\right)}^{1∕2}$ (no summation; 1, streamwise direction, 2, vertical direction) for homogeneous turbulent shear flow. DNS data (symbols) and model predictions (lines) obtained using first-, second-, and third-order models with $C_0=6$ and $a_0=5.5$.Reuse & Permissions

Figure 5

Lagrangian acceleration autocorrelation functions ${\rho }_{22}=⟨A_2\left(0\right)A_2\left(t\right)⟩$ (1, streamwise direction; 2, vertical direction) for homogeneous turbulent shear flow. DNS data (symbols) and model predictions (lines) obtained using second-(upper) and third- (lower) order models with $C_0=6$ and $a_0=5.5$.Reuse & Permissions