  While studies of active nematics in two dimensions have shed light on various
aspects of the flow regimes and topology of active matter, three-dimensional
properties of topological defects and chaotic flows remain unexplored. By
confining a film of active nematics between two parallel plates, we use
continuum simulations and analytical arguments to demonstrate that the
crossover from quasi-2D to 3D chaotic flows is controlled by the morphology of
the disclination lines. For small plate separations, the active nematic behaves
as a quasi-2D material, with straight topological disclination lines spanning
the height of the channel and exhibiting effectively 2D active turbulence. Upon
increasing channel height, we find a crossover to 3D chaotic flows due to the
contortion of disclinations above a critical activity. We further show that
these contortions are engendered by twist perturbations producing a sharp
change in the curvature of disclinations.
