Multifidelity models (MFM) based on Gaussian Processes have shown significant impact when applied to the outer-loop problems, such as uncertainty quantification and predictive surrogate modelling, relying on turbulent flow data [5, 2, 4]. However, significant limitations can be expected when using linear MFMs [1] on data that are poorly correlated, such as when combining data obtained from Direct Numerical Simulations (DNS) and Reynolds-Averaged Navier-Stokes (RANS) simulations of turbulent flows [5]. This (potential) shortcoming has motivated the development of more advanced MFMs. The present study will apply the non-linear MFM proposed in [3] to a set of turbulent flow data. The goal of the non-linear model is to circumvent the concerns of poorly correlated data by replacing the linear scaling factor in a conventional MFM with a covariance matrix of the Gaussian processes describing a lower level of fidelity. We study if and how much the non-linear model can create stronger and more robust correlations between the low- and high-fidelity data. In particular, we assess the improvements in stability and predictive accuracy of the non-linear MFMs considering their extra computational complexities. In the analyses, we use the data collected from the RANS simulations and DNS of the periodic hill problem described in [5, 4] to demonstrate the contrast between the linear and non-linear models. Furthermore, a comparison between the performance of these models and a hierarchical MFM [4] will be presented. The periodic hill shape is controlled by two uncertain parameters varying over a certain range. The objective of the MFMs is to construct a predictive surrogate model over the space of these parameters for the flow quantities of interest.