An integrated two-parameter model has been used, based on the quasi-geostrophic vorticity and thermodynamic equation in which the vertical velocity is taken as a fraction of the divergence of the temperature advection.
The time-dependent variables are the vertically averaged flow and the vertically averaged temperature. Derived quantities are the geopotential height of 1000 mbar and the mean vertical velocity ω.
The initial pattern is a simple purely baroclinic frontless flow with a constant vertically averaged speed and a constant temperature gradient.
A circular barotropic disturbance
with a Gaussian distribution is superposed on the zonal flow at t=0.
The disturbance moves without changing shape with the vertically averaged speed of the basic zonal flow. The mean temperature field is disturbed, leading to the formation of spiraling cold and warm tongues, which also move with the speed of the basic zonal flow.
An analytical solution exists for
the temperature field.
Due to that changing temperature field
meso-alpha scales such as a trough at the rear of the depres-sion, a pressure pattern characteristic for a cold and an occluded front and a cold anticyclone behind the cold front are generated after about 18 hours. The windfield in the
trough at 1000 mbar is typically a low-level jet.
Using certain assumptions, it is possible to estimate the changing slope of the generated frontal surface.
The evolved patterns of mean vertical velocity agree reasonably well with the large-scale cloud pictures of satel-lites.
The validity of the analytical solution is approximately
L.C. Heijboer. Detailstucturen in depressies : een analytisch model
KNMI number: WR-81-05, Year: 1981, Pages: 38