ABSTRACT - DRUM - University of Maryland

overshooting air and the amount of environmental air. Assuming the fraction of
detraining air in the mixture is dr, the potential temperature of the mixture is
θ
m
= dr ⋅θ
a
+ ( 1−
dr)
⋅θ
(1)
The potential temperature difference between the mixture and the environment is
( dr ⋅θ
+ ( 1−
dr ⋅θ
) −θ
dθ
= θ
m
−θ
=
a
)
(2)
If we rearrange this equation for dr,
dθ
Q ⋅ dt
dr = =
(3)
θ −θ
θ −θ
a
a
where Q is the cooling rate, which we measured to be about –7 K/day.
For the usual values of potential temperatures (θ a = 355 K at LNB and θ = 375 K
at 100 hPa), the fraction of detraining air in the mixture that is needed to generate the
-7 K/day cooling is
dr
dt
Q − 7K
/ day
= =
θ
a
−θ
355K
− 375K
= 0.35 (1/day) (4)
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