Bifurcation analysis of 3D ocean flows using a parallel fully-implicit ocean model

To understand the physics and dynamics of the ocean circulation, techniques of numerical bifurcation theory such as continuation methods have proved to be useful. Up to now these techniques have been applied to models with relatively few (O (10⁵)) degrees of freedom such as multi-layer quasi-geostrophic and shallow-water models and relatively low-resolution (e.g., 4° horizontal resolution) primitive equation models. In this paper, we present a new approach in which continuation methods are combined with parallel numerical linear system solvers. With this implementation, we show that it is possible to compute steady states versus parameters (and perform fully implicit time integration) of primitive equation ocean models with up to a few million degrees of freedom.