Several sets of equations which can be used to find the
vertical velocity are examined. A distinction is made between
assumptions that are based on physical considerations and those
based on computational necessity. Since the equations are
solved as boundary value problems it is necessary to impose
boundary conditions. These are discussed.
Investigations are made into the use of the overrelaxation
method for solving partial differential equations with either
Dirichlet or Neumann boundary conditions. Emphasis is placed upon
the determination of the optimum overrelaxation factor. A
simple method of calculating this factor for the ω-equation is
tested.
The derivation, meaning and solution of the balance equation
is discussed. New methods of solving this equation are introduced
and are compared with existing methods. The boundary conditions
for the linear balance equation are investigated and this leads
to the derivation of a new boundary condition for the balance
equation.
The geostrophic ω-equation is examined and the elliptic
condition is derived. Appropriate boundary conditions for ω
are discussed and the effects of the form of the static stability
on ω and ϴt are investigated. Simple models of the atmosphere
are used from which several inferences are drawn. These are
tested with case studies. The inconsistency of the usual
boundary conditions for ω and ϴt, is also examined
