& Tornado Alley Two-Layer (Five-Level) Model of the Atmosphere
The governing equations for the model, which are derived
elsewhere, are where V1, V2 and V3 are the wind velocity vectors
at levels 1, 2 and 3, respectively, and are determined from the
stream function ψ at those two levels. ω2 is the vertical
pressure velocity at level 2. The relationships to the levels is
shown below. It is assumed that V2=(V1+V2)/2. Rather than
replacing V2 by this relationship it is more convenient to
express the 1 and 3 levels of the variables in terms of the
level 2 variables and the difference between level 1 and level 3
values. But first it is necessary to obtain the linearized form
of the equations. It is assumed that the stream function ψ is of
the form This notation will be later replaced by a notation in
which ψi(x,y,t) means ψ(x,y,pi,t). Under the assumption
concerning the stream function then In the linearization process
the only parts of the wind velocity vectors that can survive in
the momentum equations are the ba