Parameter studies of slowly-rotating planets aim to characterise the effect of rotation rate, friction, radiative properties, and other factors to understand the emergence and maintenance of equatorial super-rotation in atmospheres of bodies
similar to Venus and Titan. To analyse and compare the dominant contributions to their circulation in the most general way, it is beneficial to study the properties of different circulation regimes with reference to non-dimensional parameter spaces. The study reported here is especially concerned with the nonlinear responses to the diurnal heating cycle and their impact on the broader circulation. For this study we use a hierarchy of simple GCMs with increasing temporal resolution in thermal forcing (i.e. annually averaged, seasonal cycle, diurnal cycle) using a simple 2-band, semi-gray radiation scheme for a terrestrial-style planetary atmosphere. Our parameter space focuses on varying key parameters such as the thermal Rossby number (planetary rotation rate), the Greenhouse parameter (the ratio between short- and long-wave optical thickness), the thermal inertia of the surface, and atmospheric time-scale. While in many cases the effect of adding diurnal insolation is negligible, the resulting circulations show an increased equatorial super-rotating wind due to the diurnal cycle when the atmosphere is heated at the top.