The troposphere of Venus, or that region between the surface and the sulphuric acid cloud layer, is characterised by very low horizontal temperature contrasts of less than 10 K. Such low thermal gradients will have a large impact on the tropospheric mean circulation. Using a simplified atmospheric model, we show that the mean circulation might change in strength, and possibly even reverse in direction, on timescales of decades to centuries. The phenomenon is associated with the high surface pressure, and hence long thermal relaxation time scale of the lower atmosphere. Inertial oscillations appear to play a role in any circulation reversals that occur. We note that wind streak data are consistent with a variable Hadley circulation. Our results imply that the Venusian cloud layer could also exhibit significant variability on the same very long timescales, consistent with some observations.