Linear wave analysis of the QB equations
Before going on to discuss further simplifications that can be made based on scaling arguments, it is instructive to consider the properties of infinitesimal wave solutions to the QB set. Linearizing the QB equations about an atmosphere at rest with constant static stability ; assuming two-dimensionality in the sense that
, and attaching tracer parameters , , and (whose value may be either either or ) to certain terms gives:
The significance of the terms to which tracer parameters have been assigned will become clear later.
We now look for wave solutions for which:
and
in eqs. (15) to (19) giving: