The paper presents a numerical investigation of buet ¯ows using various turbulence models, including linear and non-linear low-Re eddy-viscosity models (EVM). The accuracy of the models is assessed against experimental data for transonic ¯ows around the NACA-0012 aerofoil. The study shows that non-linear two-equation models in conjunction with functional c l coecient for the calculation of the eddy-viscosity (henceforth labelled NL-c l ), provide satisfactory results for transonic buet ¯ows. The computations also reveal that the Spalart±Allmaras one-equation model provides comparable results to the NL-c l models, while larger inaccuracies are introduced by linear and non-linear models based on constant c l coecient. Moreover, the buet onset boundaries are similarly predicted by the one-equation and NL-c l models. The study has been performed using a second-order time accurate implicit-unfactored method which solves in a coupled fashion the Navier±Stokes and turbulence transport equations. The spatial discretisation of the equations is obtained by a Riemann solver in combination with a third-order upwind scheme.