Tropical cyclones that have nearly circular CDO's are indicative of favorable, low vertical shear environments. A TUTT low is a TUTT that has completely cut-off. TUTTs are different than mid- latitude troughs in that they are maintained by subsidence warming near the tropopause which balances radiational cooling. TUTTs are important for tropical cyclone forecasting as they can force large amounts of harmful vertical wind shear over tropical disturbances and tropical cyclones. For a more detailed discussion on TUTTs see the article by Fitzpatrick et al.
Warm waters are necessary to fuel the heat engine of the tropical cyclone.
An atmosphere which cools fast enough with height such that it is potentially unstable to moist convection. It is the thunderstorm activity which allows the heat stored in the ocean waters to be liberated for the tropical cyclone development. Dry mid levels are not conducive for allowing the continuing development of widespread thunderstorm activity. For tropical cyclogenesis to occur, there is a requirement for non-negligible amounts of the Coriolis force to provide for near gradient wind balance to occur. Without the Coriolis force, the low pressure of the disturbance cannot be maintained.