A steady state two-dimensional model for the maintenance of shelf break fronts

Abstract

A two-dimensional inviscid steady state shelf break frontal model is described in this paper. The model has three immissible, incompressible, homogeneous layers, the lowest of which is assumed to be motionless. In the upper layer, created by freshwater runoff for example, all the fluid is assumed to originate over the shelf. Within both active layers the cross-shelf momentum balance is assumed to be geostrophic and the potential vorticity is assumed to be uniform. In the upper layer the potential vorticity value is set at the coast, while in the intermediate layer it is defined by the potential vorticity value far offshore. Provided that the cross-sectional area of the upper layer together with its depth and along-shore velocity at the coast are specified, the model determines the interfacial displacements and the net longshore transport in each layer. Increasing the coastal depth, keeping all other parameters fixed, leads to offshore movement of the surface outcrop point of the front, while the bottom frontal anchor point moves towards the coast. The anchor point where the interface between the lower two layers intersects the slope is found to be weakly dependent on coastal depth changes. As coastal depth increases the frontal shape evolves from an inclined, almost linear profile, to an S-shaped profile (with associated local maximum and minimum upper layer depths). In the latter case the upper layer velocity attains a local maximum and minimum over the slope, whereas in the former case it can either monotonically increase the magnitude over the slope or attain a local maximum. For the near linear frontal regime, if the coastal velocity is negative (right bounded) it is possible for the upper layer velocity to change sign over the slope. As the volume of upper layer fluid increases, a situation is reached where the anchor point of the interface between the lower two layers becomes constant. Over the shelf and slope the interfaces inshore of this anchor point become invariant as the volume of upper layer fluid is increased above this critical limit and the interfaces adopt a “self-similar” structure as a result of potential vorticity conservation in both active layers.