The long-time development of an isolated wing-tip turbulent vortex has been studied by Reynolds-averaged Navier-Stokes computations. The vortex is assumed to extend to infinity and to be axisymmetric and homogeneous in the axial direction, and the axial velocity is assumed to be negligible. The validity of different turbulence models, ranging from Reynolds stress transport models to eddy-viscosity K-ε models, has been assessed and qualitative comparisons with field measurements are made. Reynolds stress transport models correctly predict strong suppression of the turbulence in the rotation-dominated vortex core and a reasonable decay rate of the vortex. Outside of the core, the different Reynolds stress models differ significantly. The standard eddy-viscosity K-ε model is insensitive to rotation and, thus, overpredicts the vortex decay rate. Computations using explicit algebraic Reynolds stress models that are strictly based on Reynolds stress transport models show that the algebraic form compares reasonably well with the full transport form. It is, however, important that the curved flow algebraic assumption is invoked when deriving the explicit algebraic model.