A simple approach for vortex core visualization

We propose a method to visualize vortex cores based on manipulation of the pressure field produced by isolated vortices in incompressible flow. Under ideal conditions the function $D=2|\nabla P|/\nabla^2 P$ yields an approximate distance to vortex centerlines. As opposed to local methods to identify coherent structures, isosurfaces of $D$ produce a field of vortex tubes equidistant to the vortex core center which, ideally, are independent of vortex intensity or size. In contrast to other line-vortex identification methods, which typically rely on algorithms to detect vortex core lines and frequently need complex implementations, the proposed method can be computed from the local Eulerian velocity and pressure fields as easily as vortex identification methods such as the $Q$ and $\lambda_2$ criteria. $2|\nabla P|/\nabla^2 P$ results in the exact distance to the core center for a Rankine vortex and is in general valid for the region of a vortex where there is pure rotation, yielding an approximation to the distance farther from the core in other simple one-dimensional vortex models. The methodology performs well in all tests we attempted, though limitations are presented and discussed. The method is demonstrated for a canonical Burgers vortex, a Bodewadt vortex, homogeneous isotropic turbulent flow, the wake of a propeller, a heaving plate, a turning containership and the airwake of a surface combatant. The proposed method helps to better visualize vortical flow fields by displaying vortex cores, complementing methods like $Q$ and $\lambda_2$ which display vortical volumes.