The influence of spatial variations of the oceanic mixed layer depth (OMLD) on tropical cyclones (TCs) is investigated using a coupled atmosphere–ocean model. The model consists of a version of the Naval Research Laboratory limited area weather prediction model coupled to a simple 2½-layer ocean model. Interactions between the TC and the ocean are represented by wind-induced turbulent mixing in the upper ocean and latent and sensible heat fluxes across the air–sea interface. Four numerical experiments are conducted with different spatial variations of the unperturbed OMLD representing idealizations of broad-scale patterns observed in the North Atlantic and North Pacific Oceans during the tropical cyclone season. In each, the coupled model is integrated for 96 h with an atmospheric vortex initially of tropical storm intensity embedded in an easterly mean flow of 5 m s−1 and located over an oceanic mixed layer that is locally 40 m deep. The numerical solutions reveal that the rate of intensification and final intensity of the TC are sensitive to the initial OMLD distribution, but that the tracks and the gross features of the wind and pressure patterns of the disturbances are not. In every experiment, the sea surface temperature exhibits a maximum induced cooling to the right of the path of the disturbance, as found in previous studies, with magnitudes ranging from 1.6° to 4.1°C, depending on the initial distribution of the mixed layer depth. Consistent with earlier studies, storm-induced near-inertial oscillations of the mixed layer current are found in the wake of the storm. In addition, numerical experiments are conducted to examine sensitivity of a coupled-model simulation to variations of horizontal resolution. Results indicate that the intensity and track of tropical cyclones are quantitatively sensitive to such changes.