Atmospheric Vortex Engine

Table 1       SYMBOLS
P Pressure (kPa)
T Temperature (K)
U Relative humidity (%), U=100 rv/rs
r Mixing ratio total water content (g/kg)
rl Mixing ratio water in liquid phase (g/kg)
rv Mixing ratio water in vapor phase (g/kg)
rs Saturation mixing ratio (g/kg)
Tv Virtual temperature (K)
D Tv Virtual temperature excess of the updraft (K)
h Enthalpy (kJ/kg)
s Entropy (J K-1kg-1)
e Fractional entrainment
m Mass of updraft as a ratio of its mass near the surface
f Fraction ambient air entrained in mixture
g Fractional detrainment
d Updraft diameter (m)
v Updraft upward velocity (m/s)
vt Updraft terminal velocity (m/s)
Cpa Specific heat at constant pressure of air
Ra Gas constant of air
Rv Gas constant of vapor
Fd Drag force (N)
Fb Buoyancy force (N)
r Density (kg m-3)
b Buoyancy
Cd Drag Coefficient
F Darcy friction factor
L Length (m)
Subscripts
e Environment
u Updraft
c Combined updraft after mixing
a Updraft with no entrainment, a=0
Model Constants
a Entrainment coefficient
b Entrainment exponent
c Detrainment coefficient
i Interval (kPa)

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