Barotropic-Baroclinic Formulation of the Primitive Equations of the Ocean

In this article, we present an equivalent barotropic-baroclinic formulation of the primitive equations (PEs) of the ocean given in [J.L. Lions, R. Temam and S. Wang (<citeref rid="bib5">1992</citeref>). On the equations of large-scale ocean. Nonlinearity, 5, 1007-1053.]. From the numerical point of view, the main advantage of this new formulation is that the incompressibility condition appearing in the PEs in [J.L. Lions, R. Temam and S. Wang (<citeref rid="bib5">1992</citeref>). On the equations of large-scale ocean. Nonlinearity, 5, 1007-1053.] is automatically satisfied without being explicitly imposed at any stage. Some numerical schemes for the time integration of the PEs are presented and their numerical stability is discussed. These schemes are reminiscent of other schemes that have been used for other equations in particular the Navier-Stokes equations. We end the article by presenting numerical simulations of a wind-driven ocean model using the new formulation. More extensive numerical simulations and physical aspects will be presented elsewhere.

Keywords:

• Primitive Equations
• Barotropic Flow
• Baroclinic Flow
• Lagrange Multiplier