Many coastal regions in the world ocean are characterized by well-mixed conditions to shelf depth in the density field during the winter season. In these situations it is appropriate to construct a model based on the assumption that the shelf is vertically well mixed. Such a model has been constructed assuming that (i) vertical mixing of momentum is stronger than either horizontal mixing or inertial effects; (ii) the density field is also vertically well mixed, i.e., varies only in horizontal at zero order in the expansion in the vertical Peclet number, (iii) the cross-shelf scale is small compared to the alongshelf scale; (iv) depth varies only in cross-shelf direction. The transport streamfunction equation and the advective density equation can then be combined into a single model equation by noting that in the vertically well-mixed flow, density is conserved as it is advected along streamlines.
This model is used to study two different configurations quite common for shelf circulations in the world ocean. The first configuration considers the effect of a deep baroclinic ocean in driving the shelf circulation. Past studies show that a barotropic deep-ocean pressure gradient cannot drive significant shelf flow and that the continental slope effectively “insulates”the shelf from the deep ocean. Thus, the basic question we want to answer is: how does the baroclinic structure of a deep ocean flow affect its ability to penetrate the shelf and determine its circulation? The second configuration to which the model is applied is that of a coastal current driven by an alongshore buoyancy source, such as a river discharge or an alongshore jet.
In all model applications studied, the basic mechanism by which the flow is able to cross topography is bottom friction. In the first situation the flow is driven by prescribing the velocity and density at the outer edge of the shelf. Three types of shelf forcing by the deep ocean are studied: a wide inflow, a narrow inflow and forcing by a Gulf Stream ring. A specific application is made to the northern Adriatic coastal shelf forced by a dense water pool formed in wintertime in the Adriatic interior. In all cases, the main conclusion for the baroclinic deep-ocean inflow onto the well-mixed shelf is that, like in the barotropic case, the tendency for the flow to follow isobaths is much stronger than the degree to which bottom friction allows cross-isobath motion. The deep ocean inflow forces a horizontal boundary layer against the shelf edge. The width of this boundary layer, and therefore the shelf penetration, is larger if the drag coefficient is higher, the latitude lower or the bottom slope weaker. Also, surface-intensified deep ocean flows penetrate the shelf few strongly than bottom intensified flows.
In the two examples studied of flow entering the shelf region near shore, i.e. a coastal river outflow and a coastal jet, it is again shown that the vertical shear of the shore inflow again determines the overall flow pattern. Because of bottom friction, a light alongshore jet or a low density river, i.e., surface intensified flow, expands across the topography more slowly than a bottom intensified flow, such as a high density river or a heavy jet.