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A variant of the local correlation-based transition model (LCTM) γ is presented to account for the prediction of transition due to stationary crossflow instabilities. The presented T c 1 crossflow criterion is a local approximation of the well-known C1 criterion by Arnal (1984), evaluated locally through auxiliary functions expressed by the solution of the Falkner–Skan–Cooke (FSC) equations. The criterion, originally proposed by Menter and Smirnov (2014), uses the wall-normal directional change of the normalized vorticity as indicator of the crossflow strength. Hereafter, an original calibration FSC-based of Menter & Smirnov criterion is proposed. A local approximation of the sweep angle is included in order to achieve better results on non-wing-like geometries. The capability of this model variant to predict stationary crossflow transition is therefore discussed. A validation study is presented using experimental data on the 6:1 prolate spheroid and the sickle wing. • The study is performed using RANS local transition models. • Falkner–Skan–Cooke equations are used for calibration in default of experiments. • The re–calibration aims to add more physics to the transition correlations. • The sweep angle inclusion widens the range of applications of the Tc1 criterion. • The re–calibrated Tc1 performs very well on non-wing-like geometries. [ABSTRACT FROM AUTHOR]