In the present report the author calculates the energy releasable from horizontally unstable situations of a wet atmosphere, a sequel to his last paper in which those of a dry atmosphere were treated of, and a modification of the former conclusion in view of the wet adiabatic upward motion of moist air is introduced.
Consider the ini_??_al state of the cold and the saturated warm masses lying side by side. In the final state the cold mass descends dry-adiabatically over the ground and the warm mass ascends over it wet-adiabatically.
Two cases occur according as either the lapserate
a is larger or smaller than the wet adiabatic lapse-rate γ
m. In the former case the entropy decreases upwards and the stratification of ascending mass becomes inverse, therefore the upper half of the warm mass should descend dry-adiabatically and the wet adiabatic motion is possible only in the lower half. In the latter case the whole warm mass ascends, wet-adiabatically with the same stratification.
Margules already treated a similar problem in his famous paper on the energy of storm, assuming the dry adiabatic lapse-rate _??_ in the cold mass and the wet adiabatic lapse-rate in the warm mass, which corresponds to the case of no latent instability as pointed out by Normand.
The energy equation has been derived, assuming the constancy of wet adiabatic lapse-rate and putting γ
m=1/2_??_. The result of numerical evaluation is as follows: horizontal difference of temperature: 10°C.
It is noticeable here that, in case of γ
m<
a<_??_, the available energy of moist air is smaller than that of dry air. This is due to the increase of potential energy by overturning. In case of
a<γ
m, the available energy of moist air is larger than that of dry air, but the difference is rather small.
The present result seems to refute the theory of “feuchtlabile Energie” developed by Refsdal, Normand and others; therefore, as the next problem, the labile energy from the water vapour alone is calculated. Consider the vertical air column of depth
h, in which the upper half subsides dry-adiabatically in overturning and the saturated lower half ascends wet-adiabatically. The available kinetic energy thus releasable is follows:
The result shows that the available energy decreases rapidly with the decrease of lapse-rate and tells us how much the descending motion consumes the energy. The parcel method of energy computation widely applied in the adiabatic chart does not take into account the energy loss due to the descending current and overestimates the “feuchtlabile” energy. Thus it may be concluded that the labile energy from water vapour alone is generally very small in the atmosphere of conditional instability.
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