Definitions

The temperature of an air parcel that has been adjusted for adiabatic heating and the heating due to water vapor content.

Froude number

The Froude number is the ratio of the flow speed to the speed of long gravity waves on the inter face. The Froude number is defined as Fr = U/(g'H) where

U = s peed of the layer,
g' = reduced gravity,
and H = layer depth.

When Fr > 1, the flow is supercritical and information about downstream disturbances cannot propagate upstream. In this regime, analogous to supersonic flight, the flow adjusts abruptly to irregularities in wall of its channel. This adjustment takes the form of hydraulic jumps when the channel narrows and expansion fans when the channel widens. When Fr < 1, the flow is subcritical and receives information about disturbances from downstream.

Flux units

1 Watt/ m^2 = 1 J/s /m^2 = 1 kg m^2 / s^3  for heat flux

Kinematic heat flux = flx/(air_density*specific_heat)   [K m/s]

Gas constant

Rdry = 287.04 Joules/(kg*K) = 287.04 m^2/(s^2*K)

Geopotential height

Height of a pressure surface. For example, a 500 mb map of the geopotenial height shows the various altitudes of the 500 mb pressure surface. Such a map can indicate pressure: high geopotential height of a pressure surface generally corresponds to a high in pressure at a set altitude.

 

850 mb is about 1500 m and can be used to indicate the pressure forcing directly above the boundary layer. 500 mb is about 6000 m, high enough that friction with the earth's surface has negligible effect.
A typical horizontal pressure gradient is 1 mb/100 km.

Joule

Units of work

1 J = N*m = kg*m^2/s^2 =  10^7 erg

Knot

1 knot = .515 m/s = 1.152 mile/hour = 1.689 ft/s

Lifting condensation level

The altitude at which water vapor within a parcel of air begins to condense. Clouds begin to form at this level, and cannot exist below it.

Heat content (equivalent potential temperature) and moisture content (total water mixing ratio) are conserved as an air parcel rises/descends. Mixing between two parcels occurs on a line between their characteristic properties.

• The overall or layer Richardson number determines the stability of the flow such that for Ri >> 1 the flow is stable. The critical value is high because local gradients, which can cause instability, are ignored.

Ri = g d rho h / rho * d U ^2
where d rho and d U are the jumps in density and velocity across a two layer system, h is the depth of the shear layer between the two layers, and rho is the average density of the 2 layers.
• The gradient Richardson number is the ratio of local buoyant to shear forcing. "When a sufficiently large shear is applied across a density interface such that the gradient Ri falls below a critical value of about .25, Kelvin-Helmholtz waves will grow and overturn to produce patches of turbulent mixing." (Turner, 1973)

c = wave speed

f = Coriolis parameter

The Rossby radius defines the region in which the flow is affected by c oastal forcing, about 150 km for the marine atmospheric boundary layer along the west coast.
 

Saturation point

The saturation point of an air parcel is found by dry(moist) adiabatic ascent(descent) to the pressure level where the parel is saturated, giving the saturation level parcel temperature and pressure.   From Betts (1987).

Please send comments or questions to me at kate@coast.ucsd.edu