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Appendix B List of symbols
List of Symbols
Only the principal symbols are listed. Symbols formed by adding primes, overbars, or subscripted indices are not listed separately. Boldface type indicates vector quantities. Where symbols have more than one meaning, the section where the second meaning is first used is indicated in the list. a
Radius of the earth; inner radius of a laboratory annulus (Section 10.5)
b
Buoyancy; outer radius of a laboratory annulus (Section 10.5)
c
Phase speed of a wave
Cp
Specific heat of dry air at constant pressure
Cpv
Specific heat of water vapor at constant pressure
cv
Specific heat of dry air at constant volume
Cw
Specific heat of liquid water
493
494
B
LIST OF SYMBOLS
Grid distance Internal energy per unit mass
f
Coriolis parameter (= 2~2 sin 4~) Magnitude of gravity
g
Gravity
g*
Gravitational acceleration
h
Depth of fluid layer; moist static energy (Section 9.5) Square root of minus one Unit vector along the x axis Unit vector along the y axis Unit vector along the z axis Zonal wave number Mixing length; meridional wave number (Section 7.5)
m
Mass element; vertical wave number (Section 7.4); planetary wave number (Section 13.5)
my
Molecular weight of water Distance in direction normal to a parcel trajectory; meridional index for equatorial waves (Section 11.4) Unit vector normal to a parcel trajectory Pressure
ps
Standard constant pressure; surface pressure in cr coordinates (Section 10.3) Quasi-geostrophic potential vorticity; water vapor mixing ratio (Section 9.5)
qs
Saturation mixing ratio Radial distance in spherical coordinates A position vector Generalized vertical coordinate; distance along a parcel trajectory (Section 3.2); entropy (Section 2.7); dry static energy (Section 9.5)
B
LISTOF SYMBOLS
495
Time
Unit vector parallel to a parcel trajectory U*
Friction velocity x component of velocity (eastward) y component of velocity (northward) z component of velocity (upward)
tO*
Vertical motion in log-pressure system
x,y,z
Eastward, northward, and upward distance, respectively
Z*
Vertical coordinate in log-pressure system
A
An arbitrary vector Area Convective available potential energy
Cd
Surface drag coefficient
De
Depth of Ekman layer
E
Evaporation rate
E1
Internal energy
F
A force; EP flux (Section 10.2)
Fr
Frictional force
G
Universal gravitational constant; zonal force (Section 10.2)
H
Scale height Diabatic heating rate
K
Total horizontal wavenumber; kinetic energy (Section 9.3)
Km
Eddy viscosity coefficient
L
A length scale
Zc
Latent heat of condensation
M
Mass; mass convergence in Ekman layer (Section 5.4); absolute zonal momentum (Section 9.3); angular momentum (Section 10.3)
N
Buoyancy frequency
496
B
LIST OF SYMBOLS
P
Ertel potential vorticity; available potential energy (Section 8.3); precipitation rate (Section 11.3)
Q
Q vector
R
Gas constant for dry air; distance from the axis of rotation of the earth to a point on the surface of the earth (Section 1.5); diabatic energy generation rate (Section 10.4)
R
Vector in the equatorial plane directed from the axis of rotation to a point on the surface of the earth
R*
Universal gas constant
s,
--
T
Temperature
U
Horizontal velocity scale
1"
Speed in natural coordinates
81"
Volume increment
U
Three-dimensional velocity vector
V
Horizontal velocity vector
W
Vertical motion scale
X
Zonal turbulent drag force
Z
Geopotential height
T0 In 0/0p, stability parameter in pressure coordinates
Specific volume - df/dy, variation of the Coriolis parameter with latitude; angular direction of the wind (Section 3.3) -
Cp / C u , t h e
ratio of specific heats
Rate of frictional energy dissipation; thermal expansion coefficient of water (Section 10.7) Vertical component of relative vorticity Vertical component of absolute vorticity; weighting function for heating profile (Section 11.3) Potential temperature -
DO/Dt,
vertical motion in isentropic coordinates
B
LIST OF SYMBOLS
0e
497
Equivalent potential temperature R / c p , ratio of gas constant to specific heat at constant pressure; Rayleigh friction coefficient (Section 10.6)
Longitude, positive eastward Dynamic viscosity coefficient Angular frequency; kinematic viscosity (Section 1.4) Density R T0p- l d In 00/dp, standard atmosphere static stability parameter in isobaric coordinates; p i P s , vertical coordinate in tr system (Section 10.3); "Density" in isentropic coordinates (Section 4.6)
rd
Diffusive time scale
~E
Eddy stress Latitude
X
Geopotential tendency; meridional stream function; tracer mixing ratio Horizontal stream function Vertical velocity (--
tO
in isobaric coordinates
Vorticity vector -
1-'d
dp/dt)
-dT/dz,
lapse rate of temperature
Dry adiabatic lapse rate Geopotential
I'I
Exner function
|
Potential temperature deviation Angular speed of rotation of the earth; angular speed of rotation of laboratory annulus (Section 10.7) Angular velocity of the earth
Only the principal symbols are listed. Symbols formed by adding primes, overbars, or subscripted indices are not listed separately. Boldface type indicates vector quantities. Where symbols have more than one meaning, the section where the second meaning is first used is indicated in the list. a
Radius of the earth; inner radius of a laboratory annulus (Section 10.5)
b
Buoyancy; outer radius of a laboratory annulus (Section 10.5)
c
Phase speed of a wave
Cp
Specific heat of dry air at constant pressure
Cpv
Specific heat of water vapor at constant pressure
cv
Specific heat of dry air at constant volume
Cw
Specific heat of liquid water
493
494
B
LIST OF SYMBOLS
Grid distance Internal energy per unit mass
f
Coriolis parameter (= 2~2 sin 4~) Magnitude of gravity
g
Gravity
g*
Gravitational acceleration
h
Depth of fluid layer; moist static energy (Section 9.5) Square root of minus one Unit vector along the x axis Unit vector along the y axis Unit vector along the z axis Zonal wave number Mixing length; meridional wave number (Section 7.5)
m
Mass element; vertical wave number (Section 7.4); planetary wave number (Section 13.5)
my
Molecular weight of water Distance in direction normal to a parcel trajectory; meridional index for equatorial waves (Section 11.4) Unit vector normal to a parcel trajectory Pressure
ps
Standard constant pressure; surface pressure in cr coordinates (Section 10.3) Quasi-geostrophic potential vorticity; water vapor mixing ratio (Section 9.5)
qs
Saturation mixing ratio Radial distance in spherical coordinates A position vector Generalized vertical coordinate; distance along a parcel trajectory (Section 3.2); entropy (Section 2.7); dry static energy (Section 9.5)
B
LISTOF SYMBOLS
495
Time
Unit vector parallel to a parcel trajectory U*
Friction velocity x component of velocity (eastward) y component of velocity (northward) z component of velocity (upward)
tO*
Vertical motion in log-pressure system
x,y,z
Eastward, northward, and upward distance, respectively
Z*
Vertical coordinate in log-pressure system
A
An arbitrary vector Area Convective available potential energy
Cd
Surface drag coefficient
De
Depth of Ekman layer
E
Evaporation rate
E1
Internal energy
F
A force; EP flux (Section 10.2)
Fr
Frictional force
G
Universal gravitational constant; zonal force (Section 10.2)
H
Scale height Diabatic heating rate
K
Total horizontal wavenumber; kinetic energy (Section 9.3)
Km
Eddy viscosity coefficient
L
A length scale
Zc
Latent heat of condensation
M
Mass; mass convergence in Ekman layer (Section 5.4); absolute zonal momentum (Section 9.3); angular momentum (Section 10.3)
N
Buoyancy frequency
496
B
LIST OF SYMBOLS
P
Ertel potential vorticity; available potential energy (Section 8.3); precipitation rate (Section 11.3)
Q
Q vector
R
Gas constant for dry air; distance from the axis of rotation of the earth to a point on the surface of the earth (Section 1.5); diabatic energy generation rate (Section 10.4)
R
Vector in the equatorial plane directed from the axis of rotation to a point on the surface of the earth
R*
Universal gas constant
s,
--
T
Temperature
U
Horizontal velocity scale
1"
Speed in natural coordinates
81"
Volume increment
U
Three-dimensional velocity vector
V
Horizontal velocity vector
W
Vertical motion scale
X
Zonal turbulent drag force
Z
Geopotential height
T0 In 0/0p, stability parameter in pressure coordinates
Specific volume - df/dy, variation of the Coriolis parameter with latitude; angular direction of the wind (Section 3.3) -
Cp / C u , t h e
ratio of specific heats
Rate of frictional energy dissipation; thermal expansion coefficient of water (Section 10.7) Vertical component of relative vorticity Vertical component of absolute vorticity; weighting function for heating profile (Section 11.3) Potential temperature -
DO/Dt,
vertical motion in isentropic coordinates
B
LIST OF SYMBOLS
0e
497
Equivalent potential temperature R / c p , ratio of gas constant to specific heat at constant pressure; Rayleigh friction coefficient (Section 10.6)
Longitude, positive eastward Dynamic viscosity coefficient Angular frequency; kinematic viscosity (Section 1.4) Density R T0p- l d In 00/dp, standard atmosphere static stability parameter in isobaric coordinates; p i P s , vertical coordinate in tr system (Section 10.3); "Density" in isentropic coordinates (Section 4.6)
rd
Diffusive time scale
~E
Eddy stress Latitude
X
Geopotential tendency; meridional stream function; tracer mixing ratio Horizontal stream function Vertical velocity (--
tO
in isobaric coordinates
Vorticity vector -
1-'d
dp/dt)
-dT/dz,
lapse rate of temperature
Dry adiabatic lapse rate Geopotential
I'I
Exner function
|
Potential temperature deviation Angular speed of rotation of the earth; angular speed of rotation of laboratory annulus (Section 10.7) Angular velocity of the earth