Vorticity Alignment with Local and Nonlocal Strain Rate Eigenvectors in Turbulent Flows

The anomalous alignment of vorticity $\omega_i(\textbf{x})$ with the strain rate eigenvectors in turbulent flows is examined using a decomposition of the strain rate $S_{ij}(\textbf{x})$ into the sum of local $S^R_{ij}(\textbf{x})$ and nonlocal (background) $S^B_{ij}(\textbf{x})$ contributions. Unlike previous work where alignment properties have been examined using the coupled differential transport equations for the vorticity and strain rate, we here consider instead the integro-differential equation for the vorticity that results when the strain rate is represented by a Biot-Savart integral over all vorticity in the flow. The decomposition of the strain rate as $S_{ij}(\textbf{x}) = S^R_{ij}(\textbf{x}) + S^B_{ij}(\textbf{x})$, which is achieved by splitting the integration domain into local $(r \leq R)$ and nonlocal $(r>R)$ domains, clearly distinguishes the linear (nonlocal) and nonlinear (local) contributions to the vorticity dynamics. The calculation of $S^R_{ij}(\textbf{x})$ and $S^B_{ij}(\textbf{x})$, including an operator method involving laplacians of $S_{ij}(\textbf{x})$, is demonstrated. Using data from highly-resolved direct numerical simulations of statistically-stationary homogeneous, isotropic turbulence, we show that while vorticity tends towards anomalous alignment with the intermediate eigenvector of the \textit{combined} strain rate $S_{ij}(\textbf{x})$, it aligns with the most extensional eigenvector of the \textit{background} strain rate $S^B_{ij}(\textbf{x})$, resulting in a significant linear contribution to the vorticity dynamics.