In our solar system, convective atmospheres are as common as those tha
t are stable, and convective and stable regions sometimes coexist in t
he same atmosphere. There is a need to develop circulation models that
can handle convection and stable-layer flows simultaneously and effic
iently. This paper represents an approach to the construction of such
a model. Taking advantages of the simplicity of implementing implicit
time stepping in spectral models, we solve a non-hydrostatic, fully co
mpressible version of the hydrodynamic equations without the time step
restrictions imposed by acoustic and gravity waves. To simplify the n
onlinear terms and to conserve the total mass and total angular moment
um to round-off accuracy, we introduce a ''stratified'' approximation
which limits the nonlinearity of the equations to quadratic. The linea
r terms remain intact so that all the linear waves are preserved. The
set of assumptions made by the ''stratified'' approximation is a subse
t of those of the anelastic approximation. It offers more generality a
nd accuracy while the computational overhead is relatively low. Tests
are presented to illustrate the capabilities and advantages of the pre
sent model. (C) 1994 Academic Press, Inc.