Consider two gas molecules at the dge of the crater. One takes the short route straight across and the other goes the long way down and up. Either we have a pressure difference or the 2nd molecule goes faster, increasing turbelence. This is the process of erosion in pipes.
In looking into theis process I found a report of a related interesting earth-bound process "Wind erosion of Mancos Shale badland ridges by sudden drops in pressure", A. E. Godfrey, Earth Surface Processes and Landforms, 22, 345 - 352, 1998.
For anyone interested ,the abstract reads "One process of erosion of Mancos Shale badlands near Hanksville, Utah, appears to be caused by nearly instantaneous drops in air pressure accompanying gusts of wind. A series of sharp-crested bedrock ridges trend nearly perpendicular to the strong, gusty southwesterly winds that precede cold fronts passing through the area. The Bernoulli effect, resulting from the explosive onset of wind gusts in which the wind over the ridges can accelerate from 7 to 14 m s-1, can cause nearly instantaneous pressure drops of 1·27 mmHg. This provides a unit lifting force of 0·01697 N. Since the average gravitational force acting on a unit area of the crust is only 0·00883 N, this force is sufficient to lift the crust, exposing the underlying weathered shale chips to further wind erosion.
Soils susceptible to this type of erosion consist of polygonally cracked surface crust averaging 1·2 cm thick overlying a porous subsoil of silt-sized shale chips. The arid environment permits complete soil drying between weather fronts, greatly reducing the cohesion that would occur if the soil were moist.
The pressure drops, and the erosion caused by them, were observed on the lee side of bedrock ridges about 10 m high, within 1 m of the ridge crest. Landforms resulting from this process are micro-cirque forms located near the ridge crests. Continued development of micro-cirques eventually forms cliffs on the lee sides of the ridges."
Is Burns Cliff in the lee of the prevailing winds acrss Meridianai Planum?