Vortex reconnection under Biot–Savart evolution is investigated geometrically and numerically using a tent model consisting of vortex filaments initially in the form of two tilted hyperbolic branches; the vortices are antiparallel at their points of nearest approach. It is shown that the tips of these vortices approach each other, accelerating as they do so to form a finite-time singularity at the apex of the tent. The minimum separation of the vortices and the maximum velocity and axial strain rate exhibit nearly self-similar Leray scaling, but the exponents of the velocity and strain rate deviate slightly from their respective self-similar values of $-1/2$ and $-1$ ; this deviation is associated with the appearance of distinct minima of curvature leading to cusp structures at the tips. The writhe and twist of each vortex are both zero at all times up to the instant of reconnection. By way of validation of the model, the structure of the eigenvalues and eigenvectors of the rate-of-strain tensor is investigated: it is shown that the second eigenvalue $\unicode[STIX]{x1D706}_{2}$ has dipole structure around the vortex filaments. At the tips, it is observed that $\unicode[STIX]{x1D706}_{2}$ is positive and the corresponding eigenvector is tangent to the filament, implying persistent stretching of the vortex.

This article describes an actuator curve embedding (ACE) concept to model arbitrary lifting lines using body forces within large-eddy simulation (LES). The new method removes some inconsistencies in body-force projection of the actuator line model (ALM) commonly used to represent wind turbine blades in atmospheric boundary-layer simulations. The concept and algorithm of ACE are presented followed by selected results for various blade planform and tip shapes that signify both the predictive capability and the advantages of the ACE concept. Examples include an elliptic wing, the NREL Phase VI rotor in parked and rotating conditions, and the NREL 5-MW turbine.