Prevailing hypotheses for secondary eyewall formation are examined using data sets from two high-resolution mesoscale numerical model simulations of the long-time evolution of an idealized hurricane vortex in a quiescent tropical environment with constant background rotation. The modeled hurricanes each undergo a secondary eyewall cycle, casting doubt on a number of other authors' hypotheses for secondary eyewall formation due to idealizations present in the simulation formulations. A new hypothesis for secondary eyewall formation is proposed here and is shown to be supported by these high-resolution numerical simulations. The hypothesis requires the existence of a region with moderate horizontal strain deformation and a sufficient low-level radial potential vorticity gradient associated with the primary swirling flow, moist convective potential, and a wind-moisture feedback process at the air-sea interface to form the secondary eyewall. The crux of the formation process is the generation of a finite-amplitude lower-tropospheric cyclonic jet outside the primary eyewall with a jet width on the order of a local effective beta scale determined by the mean low-level radial potential vorticity gradient and the root-mean square eddy velocity. This jet is hypothesized to be generated by the anisotropic upscale cascade and axisymmetrization of convectively generated vorticity anomalies through horizontal shear turbulence and sheared vortex Rossby waves as well as by the convergence of system-scale cyclonic vorticity by the low-level radial inflow associated with the increased convection. Possible application to the problem of forecasting secondary eyewall events is briefly considered.