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3 Reduced Gravity Models

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.