Three-dimensional numerical computations have been carried out for flow past a surface mounted finite height circular cylinder using Open Source Field Operation and Manipulation. Flow field characteristics have been investigated for fixed Reynolds number equal to 300 and varying aspect ratios (AR being the ratio of height to diameter of the cylinder) from 1 to 5. The effect of nonuniform flow (linear shear) with shear intensity (K) ranging from 0 to 0.3 on flow field characteristics has been examined using iso-Q surfaces and streamline plots. Three different flow regimes are reported based on the values of AR and K: steady flow, symmetric mode, and antisymmetric mode of vortex shedding. The formation of critical points (impingement point, source, and spiral node) has been explained using the time-averaged flow field in the longitudinal plane of symmetry. Surface flow topology has been presented with the help of limiting streamlines on the surface of the cylinder. Variation in mean drag coefficient with a change in K has also been reported. Unsteady periodic and aperiodic wake flows have been characterized using the Hilbert spectra of the transverse velocity signal at a point in the wake. The extent of nonlinear interaction in the wake and its influence on frequency distribution have been analyzed using marginal spectra and quantified in terms of degree of stationarity. © 2019 Author(s).