Ordinary-cell convective storms - Severe Convective Storms and Tornadoes: Observations and Dynamics - page 135

Figure 3.34. Haboob in Arizona, August 3, 1978. Note how the leading edge (left side) is
wedge shaped (photograph by the author).

current), the cold air mass within the cold pool does not mix with the ambient air
outside the cold pool, and the cold air mass is held at a constant temperature. In
reality, there is vigorous mixing along the interface of the cold, dense air with the
ambient air as a result of the strong vertical shear there and there is some surface
drag. Some of the ambient air does mix in with the cold pool and dilute it some-
what, just as environmental air can be entrained into a cumulus cloud and dilute
its buoyancy, and Kelvin-Helmholtz waves can occur as a result of the vertical
shear and stratification, as Ri ¼ðg= @=@

2

1

4 , where u is the wind
speed ( Figure 3.35 ). The region of turbulent mixing as the waves break can make
for a very bumpy aircraft ride when flying near the top of a gust front.
There are a number of ways of estimating the speed of the density current.
The one presented here is based on the seminal work of T. B. Benjamin published
in 1968; Mitch Moncrieff and his collaborators in the U. K. in the 1970s and early
1980s extended his work to find analytic nonlinear solutions to two-dimensional,
steady-state, squall lines, the simplest possible model of a squall line. Employing
this approach, it is assumed that the gust front is two dimensional and steady
state. In nature, gust fronts do have some three-dimensional structure and do
exhibit a life cycle, but we will neglect any three-dimensional aspects, which are
not usually of primary importance, and consider what happens when a gust front
is mature and quasi-steady. The Boussinesq equations of motion and continuity
are used to find constraints on the ''system'' (both the gust front and its
environment). The ''atmosphere'' of the fluid is not continuously stratified, but
is composed simply of two homogeneous layers: the cold, dense air of density

z Þ=ð@ u =@ z Þ <

1

and the ambient, environmental air of density 0 , neither of which mix with the

other.