Even if the expansion is adiabatic, in the sense that it takes place inside a non-conducting enclosure and no heat is supplied from external sources, it will not be isentropic, since the heat supplied by internal friction must be included in reckoning the change of entropy.
If the tube is a perfect non-conductor, and if there are no eddies or frictional dissipation, the state of the substance at any point of the tube as to E, p, and v, is represented by the adiabatic or isentropic path, dE= -pdv.
It is noted that both the initial states have interior reversals in the sign of the latitudinal gradient of PV on isentropic surfaces.
I have investigated the modulation by the quasi-biennial oscillation of the tropical winds of the isentropic mixing in the tropics and subtropics.