Ordinary-cell convective storms - Severe Convective Storms and Tornadoes: Observations and Dynamics - page 136

Figure 3.35. Idealized representation of features in an atmospheric density current associated
with a gust front in a convective storm, as seen in a vertical cross section and the corresponding
changes in meteorological parameters at the surface, where WS is the wind shift and PJ(NH) is
the nonhydrostatic pressure jump at the leading edge, PJ(H) is the hydrostatic pressure jump at
the leading edge, TD is the temperature drop behind the leading edge, and PM is the pressure
minimum (NH, non-hydrostatic) under the turbulent wake (from Droegemeier and Wilhelm-
son, 1987).

Consider a density current h length units deep 3 embedded in an environment
H length units deep (H h).
In two dimensions, the Boussinesq equation of continuity (2.35) in the x-z-
plane is

@ u =@ x þ@ w =@ z ¼ 0 ð 3 : 9 Þ

We integrate (3.9) over the domain shown in Figure 3.37 , so that
ðð

ðð

@ u =@ xdxdz þ @ w =@ zdxdz ¼ 0 ð 3 : 10 Þ

3 In nature, the top of the cold pool is not necessarily level; in fact, the leading edge of a gust
front often has a deeper ''head'' or nose ( Figure 3.35 ) and the depth of the cold air increases
with distance behind the leading edge and so the gust front assumes a wedge shape; Figure 3.36
illustrates the way in which, since the hydrostatic pressure excess behind the density current
decreases with height, the cold side/warm side-directed pressure gradient force decreases with
height, so that a layer of vertical shear caused by baroclinically generated horizontal vorticity
(in terms of

x) at the leading edge is advected up and over the leading edge, leading to a
rise and suppression of the height of the cold air mass.

@ B =@