Data from turbulent flows over steep-sided trapezoidal trenches and a backward-facing step in an open channel were used to assess the performance of three alternative models of turbulence viz. the industry-standardk-ε model, a second-order closure which is linear in the Reynolds stresses and another which is quadratic in the same quantities. The computations were carried out on body-fitted coordinates and were carefully checked for numerical accuracy. It is demonstrated that the mean-flow parameters are predicted equally well by all models but that the details of the turbulence structure are best captured by the second-order closures. The significance of these results to the practical prediction of trench flows is discussed.