Geography Reference
In-Depth Information
where the shallow water wave speed and the Froude number are now defined using
the local thickness and velocity of the fluid:
c
2
Fr
2
u
2
/c
2
≡
g (h
−
h
M
)
;
≡
From (9.37) it is clear that the flow will accelerate on the upslope side of the ridge
(∂u/∂x > 0 where ∂h
M
/∂x > 0) if the Froude number is less than unity, but will
decelerate if the Froude number is greater than unity.
As a subcritical flow ascends the upslope side of a topographic barrier, Fr will
tend to increase both from the increase in u and the decrease in c.IfFr
1
at the crest, then from (9.37) the flow will become supercritical and continue to
accelerate as it descends the lee side until it adjusts back to the ambient subcritical
conditions in a turbulent hydraulic jump as illustrated in Fig. 9.9c. In this case very
high velocities can occur along the lee slope, as potential energy is converted into
kinetic energy during the entire period that a fluid column traverses the barrier.
Although conditions in the continuously stratified atmosphere are clearly more
complex than in the shallow water hydraulic model, numerical simulations have
demonstrated that the hydraulic model provides a reasonable conceptual model
for the primary processes occurring in downslope windstorms.
=
9.5
CUMULUS CONVECTION
Mesoscale storms associated with cumulus convection represent a large fraction
of all meteorologically important mesoscale circulations. Before considering such
systems it is necessary to examine a few of the essential thermodynamic and
dynamical aspects of individual cumulus clouds. The subject of cumulus convec-
tion is extremely complex to treat theoretically. Much of this difficulty stems from
the fact that cumulus clouds have a complex internal structure. They are generally
composed of a number of short-lived individual rising towers, which are produced
by elements of ascending buoyant air called
thermals
. Rising thermals
entrain
environmental air and thus modify the cloud air through mixing. Thermals are
nonhydrostatic, nonsteady, and highly turbulent. The buoyancy of an individual
thermal (i.e., the difference between its density and the density of the environment)
depends on a number of factors, including the environmental lapse rate, the rate of
dilution by entrainment, and drag by the weight of liquid water in cloud droplets.
A detailed discussion of the dynamics of thermal convection is beyond the scope
of this text. This section utilizes a simple one-dimensional cloud model and focuses
primarily on the thermodynamic aspects of moist convection. Convective storm
dynamics is considered in Section 9.6.
