In the present work we approach the hydrodynamic problem of discriminating the state of the turbulent fluid region as a function of the distance from the axis of a turbulent jet axis. More specifically, we analyzed temperature fluctuations in vertical turbulent heated jets where temperature time series were recorded along a horizontal line through the jet axis. We employed data from different sets of experiments with various initial conditions out of circular and elliptical shaped nozzles in order to identify time series taken at the jet axis, and discriminate them from those taken near the boundary with ambient fluid using nonconventional hydrodynamics methods. For each temperature time series measured at a different distance from jet axis, we estimated mainly nonlinear measures such as mutual information combined with descriptive statistics measures, as well as some linear and nonlinear dynamic detectors such as Hurst exponent, detrended fluctuation analysis, and Hjorth parameters. The results obtained in all cases have shown that the proposed methodology allows us to distinguish the flow regime around the jet axis and identify the time series corresponding to the jet axis in agreement with the conventional statistical hydrodynamic method. Furthermore, in order to reject the null hypothesis that the time series originate from a stochastic process, we applied the surrogate data method.