The term "Lagrangian coherent structure" (LCS) is normally used to describe numerically detected structures whose properties are similar to those of stable and unstable manifolds of hyperbolic trajectories. The latter structures are invariant curves, i.e., material curves of fluid that serve as transport barriers. In this paper we use the term LCS to describe a different type of structure whose properties are similar to those of invariant tori in certain classes of two-dimensional incompressible flows. Like stable and unstable manifolds, invariant tori are invariant curves that serve as transport barriers. There are many differences, however, between traditional LCSs and invariant-tori-like LCSs. These differences are discussed with an emphasis on numerical techniques that can be used to identify invariant-tori-like LCSs. Structures of this type are often present in geophysical flows where zonal jets are present. A prime example of an invariant-torus-like LCS is the transport barrier near the core of the polar night jet in the Earth's lower and middle stratospheres in the austral winter and early spring; this is the barrier that traps ozone-depleted air inside the ozone hole. This example is investigated using both a simple analytically prescribed flow and a velocity field produced by a general circulation model of the Earth's atmosphere.