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Appendix B List of Symbols
Appendix
1
B I List of Symbols
Only the principal symbols are listed. Symbols formed by adding primes 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 (1) Radius of the earth; (2) inner radius of a laboratory annulus (Section 10.5) Outer radius of a laboratory annulus Phase speed of a wave Specific heat of dry air at constant pressure Specific heat of water vapor at constant pressure Specific heat of dry air at constant volume Specific heat of liquid water Grid distance (1) Vapor pressure; (2) internal energy per unit mass (Section 2.6) Saturation vapor pressure Coriolis parameter, 2Q sin 4 Magnitude of gravity Gravity Gravitational acceleration 364
B
LIST OF SYMBOLS
365
(1) Depth of fluid layer; (2) moist static energy (Section 12.2.1) 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 (1) Eddy mixing length; (2) meridional wave number (Section 7.5) (1) A mass element; (2) vertical wave number (Section 7.4) Molecular weight of water Distance in direction normal to a parcel trajectory Unit vector normal to a parcel trajectory Pressure (1) Standard constant pressure; (2) surface pressure in a-coordinate system (Section 8.7) (1) quasi-geostrophic potential vorticity; (2) water vapor mixing ratio (Chapter 12) Diabatic heating rate per unit mass Ozone mixing ratio Saturation mixing ratio Radial distance in spherical coordinates A position vector (1) Distance along a parcel trajectory: (2) generalized vertical coordinate (Section 1.6.3); (3) zonal wave number (Section 1 I S ) ; (4) dry static energy (Section 12.2.1); (5) entropy (Section 2.7) Time Unit vector parallel to a parcel trajectory Friction velocity x component of velocity (eastward) y component of velocity (northward) z component of velocity (upward) Vertical motion in log-pressure system Eastward, northward, and upward distance, respectively, in spherical coordinates or on a p plane = - H In(p/p,), vertical coordinate in log-pressure system A An arbitrary vector A Area A,, A , Wave amplitudes A , Eddy mixing coefficient De Depth of Ekman layer E , Internal energy F A force Fr Frictional force
B
366
G H K L M N P R
R R*
S S, T 7;) U V 6V U
V W X Z
m /j
E
i 11
0 0, K
A ,u
v
LIST OF SYMBOLS
(1) Universal gravitational constant; (2) rate of energy generation by diabatic heating (Section 10.2) Scale height (1) Eddy viscosity coefficient; (2) kinetic energy (Section 10.2) A length scale Mass Buoyancy frequency Available potential energy (1) Gas constant for dry air; (2) distance from the axis of rotation of the earth to a point on the surface of the earth (Section 1.5) Vector in the equatorial plane directed from the axis of rotation lo a point on the surface of the earth Universal gas constant = H N Z / R ,stability parameter in log-pressure coordinates = - T i3 In O / a p , stability parameter in pressure coordinates Temperature Standard temperature, constant or dependent only on height Horizontal velocity scale Speed in natural coordinates Volume increment Three-dimensional velocity vector Horizontal velocity vector Vertical motion scale Meridional streamfunction Geopotential height Specific volume (1) = df /dy, variation ofthe Coriolis parameter with latitude; (2) the angular direction of the wind (Section 3.3) = cp/c,, the ratio of the specific heats (1) Rate of frictional energy dissipation; (2) thermal expansion coefficient of water (Section 10.5) Vertical component of relative vorticity (1) Vertical component of absolute vorticity; (2) diabatic heating profile (Section 12.2.6) Potential temperature Equivalent potential temperature = R/c,, ratio of gas constant to specific heat at constant pressure Longitude, positive eastward (1) Dynamic viscosity coefficient; (2) angular momentum per unit mass (Section 10.3) (1) Angular frequency of a wave; (2) kinematic viscosity (Section 1.4.3)
B
LIST OF SYMBOLS
36 7
Dens it y (1) = - a aO/dp, static stability parameter in isobaric coordinates; (2) = p / p , , vertical coordinate in 0 system (Section 8.7) Horizontal frictional stress due to vertical shear Latitude Geopotential tendency Streamfunction Vertical wind component ( d p l d t ) in isobaric coordinates = -dT/dz, Lapse rate of temperature Dry adiabatic lapse rate Geopotential (1) Angular speed of rotation of the earth; (2) angular speed of rotation of laboratory annulus (Section 10.5) Angular velocity of the earth
1
B I List of Symbols
Only the principal symbols are listed. Symbols formed by adding primes 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 (1) Radius of the earth; (2) inner radius of a laboratory annulus (Section 10.5) Outer radius of a laboratory annulus Phase speed of a wave Specific heat of dry air at constant pressure Specific heat of water vapor at constant pressure Specific heat of dry air at constant volume Specific heat of liquid water Grid distance (1) Vapor pressure; (2) internal energy per unit mass (Section 2.6) Saturation vapor pressure Coriolis parameter, 2Q sin 4 Magnitude of gravity Gravity Gravitational acceleration 364
B
LIST OF SYMBOLS
365
(1) Depth of fluid layer; (2) moist static energy (Section 12.2.1) 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 (1) Eddy mixing length; (2) meridional wave number (Section 7.5) (1) A mass element; (2) vertical wave number (Section 7.4) Molecular weight of water Distance in direction normal to a parcel trajectory Unit vector normal to a parcel trajectory Pressure (1) Standard constant pressure; (2) surface pressure in a-coordinate system (Section 8.7) (1) quasi-geostrophic potential vorticity; (2) water vapor mixing ratio (Chapter 12) Diabatic heating rate per unit mass Ozone mixing ratio Saturation mixing ratio Radial distance in spherical coordinates A position vector (1) Distance along a parcel trajectory: (2) generalized vertical coordinate (Section 1.6.3); (3) zonal wave number (Section 1 I S ) ; (4) dry static energy (Section 12.2.1); (5) entropy (Section 2.7) Time Unit vector parallel to a parcel trajectory Friction velocity x component of velocity (eastward) y component of velocity (northward) z component of velocity (upward) Vertical motion in log-pressure system Eastward, northward, and upward distance, respectively, in spherical coordinates or on a p plane = - H In(p/p,), vertical coordinate in log-pressure system A An arbitrary vector A Area A,, A , Wave amplitudes A , Eddy mixing coefficient De Depth of Ekman layer E , Internal energy F A force Fr Frictional force
B
366
G H K L M N P R
R R*
S S, T 7;) U V 6V U
V W X Z
m /j
E
i 11
0 0, K
A ,u
v
LIST OF SYMBOLS
(1) Universal gravitational constant; (2) rate of energy generation by diabatic heating (Section 10.2) Scale height (1) Eddy viscosity coefficient; (2) kinetic energy (Section 10.2) A length scale Mass Buoyancy frequency Available potential energy (1) Gas constant for dry air; (2) distance from the axis of rotation of the earth to a point on the surface of the earth (Section 1.5) Vector in the equatorial plane directed from the axis of rotation lo a point on the surface of the earth Universal gas constant = H N Z / R ,stability parameter in log-pressure coordinates = - T i3 In O / a p , stability parameter in pressure coordinates Temperature Standard temperature, constant or dependent only on height Horizontal velocity scale Speed in natural coordinates Volume increment Three-dimensional velocity vector Horizontal velocity vector Vertical motion scale Meridional streamfunction Geopotential height Specific volume (1) = df /dy, variation ofthe Coriolis parameter with latitude; (2) the angular direction of the wind (Section 3.3) = cp/c,, the ratio of the specific heats (1) Rate of frictional energy dissipation; (2) thermal expansion coefficient of water (Section 10.5) Vertical component of relative vorticity (1) Vertical component of absolute vorticity; (2) diabatic heating profile (Section 12.2.6) Potential temperature Equivalent potential temperature = R/c,, ratio of gas constant to specific heat at constant pressure Longitude, positive eastward (1) Dynamic viscosity coefficient; (2) angular momentum per unit mass (Section 10.3) (1) Angular frequency of a wave; (2) kinematic viscosity (Section 1.4.3)
B
LIST OF SYMBOLS
36 7
Dens it y (1) = - a aO/dp, static stability parameter in isobaric coordinates; (2) = p / p , , vertical coordinate in 0 system (Section 8.7) Horizontal frictional stress due to vertical shear Latitude Geopotential tendency Streamfunction Vertical wind component ( d p l d t ) in isobaric coordinates = -dT/dz, Lapse rate of temperature Dry adiabatic lapse rate Geopotential (1) Angular speed of rotation of the earth; (2) angular speed of rotation of laboratory annulus (Section 10.5) Angular velocity of the earth