As discussed in section 1.1.3,
reduced gravity
models are a simple form of isopycnal models. The simplest case,
to be discussed here, is the ``one-active layer'' (also referred to as
1.5 layer) reduced gravity model, in which a top layer of a given
initial thickness (say 300--500m) overlays a layer of infinite
depth in which there are no motions. A peculiarity of these models
is the fact that deviations of the interface between the two
layers (representing excursions of the pycnocline) are multiples
of the free surface elevation, by a factor which is proportional
to the ratio 
, 
being the density and
the density jump
between the two layers (the lower one being heavier, of course).
The derivation of the appropriate equations, from the 3-D
Navier--Stokes equations for incompressible flow on a rotating Earth, will
be given in connection with isopycnal models in a later release of
this case study. Only the equations for the one-active layer model
are given below.
