Chapter 1. Polytropic potential temperature.
We introduce a new quantity e.g. polytropic potential temperature, _??_, defined by the following formula:
When an air-parcel ascends in polytropic atmosphere of class
k and then the class of polytropic change of state is
k', the rate of decreasing temperature of the air-parcel is equal or not with the lapse-rate of the atmosphere according as
k', is equal or not with
k'. The difference of temperature of the atmosphere and the ascending air parcel at 10km amounts to 8°C and is no more negligible. In our atmosphere the lapserate of temperature is about-0.5°C/100m and this correspond to that of polytropic atmosphere of class . about 7/6. But, this fact does not mean that the. change of state in the atmosphere is polytropic change of class 7/6, therefore, generally, we can not use the polytropic constant 7/6 as that of change of state. However, we may use the constant of change of state in ascending region.
Chapter 2. Relation between lapserates of temperature and potential temperature.We gave a remark on the relation between two lapse-rates of temperature and potential temperature and a numerical table.
Chapter 3. Vertical motion and pseudo-polytropic constant.When an air-parcel ascends in the atmosphere, its volume expands necessarily and does work to the atmosphere. In this case, if heat-excharge of amount
Kin unit time takes place, the pseudopolytropic constant
k is given by where
cp and
cv are specific heats at constant pressure and constant volume respectively. R, g, υ denotes gas-constant, gravity constant and velocity respectively.
Chapter 4. Horizontal motion and pseudo-adiabatic constant.When an air-parcel moves horizontally under the same condition as in chapter 3, the pseudopolytropic constant is given by where
Vn and
V3 denotes velocity components perpendicular and parallel to the isobar and υ is viscosity-coefficient.
View full abstract