A long-time-scale, density-stratified shelf circulation model

Abstract

We describe a computationally efficient, finite-difference numerical model for use in understanding circulation and variability in a density-stratified shelf and slope region on seasonal time scales and longer. The model achieves its efficiency by reducing the horizontal momentum equations to a balance between the Coriolis, pressure gradient and friction terms but leaving the temperature and salinity equations in their full generality. The model uses a sigma coordinate in the vertical, with σ = 0 at the ocean surface and σ = −1 at the ocean bottom. There is no restriction on the form of the parameterizations that can be used for mixing in the temperature, salinity and momentum equations. The most important limitation of the model is the requirement to use a linear parameterization of bottom stress. This can be in terms of either bottom velocity, vertically averaged velocity or bottom geostrophic velocity. The model also lacks information on coastal, baroclinic Kelvin waves. This restricts its use to shelf regions that are wide compared to the internal radius of deformation. Fortunately, many shelf regions (e.g. the Newfoundland/Labrador shelf, the Middle Atlantic Bight, the West Florida shelf and the South Australia shelf) satisfy this requirement. We illustrate the behaviour of the model by describing an experiment showing the development of a shelf-break jet such as the Labrador Current. The model ocean has a uniform depth of 50 m along the western and northern boundaries and has an adjoining shelf and slope region. Initially, the density is everywhere uniform. Lighter water is then flushed in through the northern boundary and allowed to exit through the southern boundary. The inflow water enters the model domain at its shallowest depth, has uniform vertically averaged velocity and has a density which matches the initial value at the eastern boundary and then decreases linearly westwards. As time progresses the flow is increasingly concentrated at the shelf-break. One year into the integration, a well-defined shelf-break jet has developed. At this time, the shelf-break appears as a convergence zone in the bottom level of the model, with offshore Ekman transport on the shelf being opposed by weak upslope flow offshore. Subsequently, the JEBAR term plays a dramatic role in the splitting of the jet, creating a new jet further offshore. After 2000 days, the model exhibits two jets with roughly half the inflow transport feeding directly into the offshore jet. The development of the split jet is sensitive to the parameterization used for the bottom stress.