Inertial flow in the Gulf Stream

This paper departs from previous studies of steady, laminar, purely inertial models of the Gulf Stream in that it considers two moving layers of different density and with different vertically uniform flow velocities instead of only one such layer. The flow takes place over a resting layer of denser water. Numerical methods are used where analytical results cannot be obtained. Instead of yielding a refined description that fits the observed Gulf Stream better than do the one-layer models, the two-layer models show anomalous features that seem physically unreasonable and that seem to prevent any correspondence with the observed Gulf Stream. Two types of anomalies occur. 1. If an overall density gradient is modelled by splitting the one-layer model into two equally thick layers where the lower layer has a density intermediate between that of the upper layer and the fluid at rest below, the inertial-dynamical solution is invalidated by discontinuities at latitudes near the middle of the range where the observed Gulf Stream seems steady and well-behaved, and where the one-layer models seem to give an adequate description of the flow. 2. If the interface between the lower layer and the fluid at rest below is made nearly horizontal in the interior of the ocean to the east of the Gulf Stream, so as to correspond to the observed 6°C isotherm, then no dynamical solution exists. This is because conservation of potential vorticity for transport of water over large ranges of latitude is incompatible with the small geostrophic velocities required in the lower layer by the nearly horizontal lower interface. Such difficulties lead to the tentative conclusion that steady, purely inertial models are inadequate to describe even the lower latitude growth region of the Gulf Stream.