Free-surface vortices have long been studied to develop an understanding of similar rotating flow phenomena observed in nature and technology. However, a complete description of its turbulent three-dimensional flow field still remains elusive. In contrast, the related Taylor-Couette flow system has been well explicated which classically exhibits successive instability phases manifested in so-called Taylor vortices. In this study, observations made on the turbulent free-surface vortex revealed distinguishable, time-dependent "Taylor-like" vortices in the secondary flow field similar to the Taylor-Couette flow system. The observations were enabled by an original application of 2D ultrasonic Doppler velocity profiling complemented with laser induced fluorescence dye observations. Additional confirmation was provided by three-dimensional numerical simulations. Using Rayleigh's stability criterion, we analytically show that a wall bounded free-surface vortex can indeed become unstable due to a centrifugal driving force in a similar manner to the Taylor-Couette flow. Consequently, it is proposed that the free-surface vortex can be treated analogously to the Taylor-Couette flow permitting advanced conclusions to be drawn on its flow structure and the various states of free-surface vortex flow stability.