Polytropic process and tropical Cyclones

We show a parallelism between the expansion and compression of the atmosphere in the secondary cycle of a tropical cyclone with the fast expansion and compression of wet air in a bottle. We present a simple model in order to understand how the system (cyclone) draws energy from the air humidity. In particular we suggest that the upward (downward) expansion (compression) of the warm (cold) moist (dry) air follows a polytropic process, $PV^\beta$= constant. We show both experimentally and analytically that $\beta$ depends on the initial vapor pressure in the air. We propose that the adiabatic stages in the Carnot-cycle model for the tropical cyclone be replaced by two polytropic stages. These polytropic processes can explain how the wind wins energy and how the rain and the dry bands are produced inside the storm.