Geography Reference
In-Depth Information
field by this ageostrophic circulation tends to increase the horizontal temperature
gradient at the surface on the warm side of the jet axis. Temperature advection by the
upper-level secondary circulation, however, tends to concentrate the temperature
gradient on the cold side of the jet axis. As a result, the frontal zone tends to slope
toward the cold air side with height. The differential vertical motion associated
with the ageostrophic circulation tends to weaken the front in the midtroposphere
due to adiabatic temperature changes (adiabatic warming on the cold side of the
front and adiabatic cooling on the warm side). For this reason fronts are most
intense in the lower troposphere and near the tropopause.
The secondary circulation associated with frontogenesis is required to maintain
the thermal wind balance between the along-front flow and the cross-front tem-
perature gradient in the presence of advective processes that tend to destroy this
balance. The concentration of the isotherms by the horizontal advection increases
the cross-stream pressure gradient at upper levels, and thus requires an increase
in the vertical shear of the along-jet flow in order to maintain thermal wind bal-
ance. The required upper-level acceleration of the jet is produced by the Coriolis
force caused by the cross-jet ageostrophic wind, which develops in response to
the increased cross-stream pressure gradient in the jetstream core. As the jet accel-
erates, cyclonic vorticity must be generated on the cold side of the jet axis and
anticyclonic vorticity on the warm side. These vorticity changes require that the
horizontal flow at the jetstream level be convergent on the cold side of the jet
axis and divergent on the warm side of the jet axis. The resulting vertical circu-
lation and low-level secondary ageostrophic motion required by mass continuity
are indicated in Fig. 9.3b.
9.2.2
Semigeostrophic Theory
To analyze the dynamics of the frontogenetic motion fields discussed in the previ-
ous subsection, it is convenient to use the Boussinesq approximation introduced in
Section 7.4, in which density is replaced by a constant reference value ρ
0
except
where it appears in the buoyancy force. This approximation simplifies the equa-
tions of motion without affecting the main features of the results. It is also useful
to replace the total pressure and density fields with deviations from their stan-
dard atmosphere values. Thus, we let (x, y, z, t)
=
(p
−
p
0
)/ρ
0
designate the
pressure deviation normalized by density and
θ
0
designate the potential
temperature deviation where p
0
(z) and θ
0
(z) are the height-dependent standard
atmosphere values of pressure and potential temperature, respectively.
With the above definitions, the horizontal momentum equations, thermodynamic
energy equation, hydrostatic approximation, and continuity equation become
=
θ
−
Du
Dt
−
∂
∂x
=
fv
+
0
(9.2)
