# Recent advances in upwelling theory and connections to the Obstacle Problem

### Paul Choboter, Cal Poly, Mathematics Dept.

### Abstract:

Joseph Pedlosky's (1978) dynamical model of upwelling is elegantly simple, yet complex enough to possess rich and subtle dynamics. This model continues to generate new insights into the dynamics of upwelling. We discuss the effect of the bathymetric profile on the structure of velocity and density. When the bathymetric profile has positive curvature, the deep onshore-directed flow is surface-intensified. When the bathymetric profile has negative curvature, such as over a continental shelf break, the deep onshore flow is bottom intensified. For negative curvature of sufficient magnitude, the dynamical model solutions exhibit features of an "obstacle problem", a free-boundary problem that arises in the study of elliptic partial differential equations. These features make it extremely agonizing to solve, either analytically or numerically.