ABSTRACT
Equations ( 12.0. l)-( 12.0.2) are inappropriate to describe free surface flows driven by density gradients. This is the case of estuaries, where the simultaneous presence of fresh light water, together with salt heavy water induces a three-dimensional baroclinic circulation which is not modeled by equations ( 12.0. l)-( 12.0.2). Similarly, most deep lakes in temperate zones present a classical three-dimensional thermocline structure during the summer period. A sharp themocline interface separates the light warm water which floats on the heavy cold water. For these problems, assuming stable stratification, the fluid density is monotonie increasing downward. If density is conserved, as is approximately the case for most geophysical flows, considerable mathematical simplifications follow from considering the three-dimensional governing equations expressed in density p, rather than vertical z coordinate [4,5]. A layered isopycnal model is an ideal fluid system that consists of a finite number of moving layers, stacked one upon another and each having a uniform density. For a system of M layers with densities p { > p2 > · · · > pM > 0, let z = Цк(х, У, t) be the surface of separation between layer k and the layer above k + l . The surfaces z = ηο(χ, у) and z = Лм(х, y, t ) represent the fixed bottom and the free-surface, respectively (see Figure 1).
