Normal convection takes place below an Inversion which acts as a cap preventing air from rising further, it has to go somewhere so it moves horizontally until it cools and sinks back towards the surface. This motion in the inversion layer results in turbulence which ceases as you climb above the inversion layer.
But is that really the inversion causing the turbulence? To me the cause is the convection with the inversion just exacerbating it.