ON THE FORCED FLOW OF SALTY WATER IN A LOOP

The buoyancy-driven flow of salty water in a loop is computed. This pr oblem belongs to the general class of the convective behavior of solut al fluids, a specific example of which is the oceanic thermohaline cir culation. The two cases of freshwater flux forcing and so-called virtu al salt flux forcing are compared and contrasted. The former is an exa ct statement of the saline forcing of the ocean by the atmosphere, whi le the latter is an approximation used in many climate models. Analyti cal solutions appropriate to both cases are presented for broad parame ter ranges and ultimately encapsulated in the form of bifurcation maps . These allow for comparisons between the behaviors predicted for the two cases. Furthermore, the solutions are supported by means of numeri cal experimentation. It is found that a simple loop model, forced by a steady flux, can possess multiple solutions, either stationary soluti ons and limit cycles or distinctly different limit cycles. This result is closely related to climate models. In addition, this study transce nds climate applications and applies to the more general classical pro blem of convection in a loop. The novel aspect here is the application of freshwater flux to a salty fluid. The effect on density of this fo rcing is different from that due to the application of heat to a therm ally sensitive fluid. Surprising and counter-intuitive behaviors have been found which reflect these differences. As an example, in the limi t where diffusion is weak relative to freshwater flux, a delta-functio n-like salinity profile appears if freshwater flux conditions are used . Models using a virtual salt flux approximation, or a relaxation cond ition, yield a low mode solution for these parameters. In contrast, th e virtual salt flux equations can be obtained from the freshwater-forc ed equations by a systematic expansion in one limit where diffusion do minates freshwater flux. Numerical experiments are used to examine the comparisons between virtual salt flux and freshwater-forced solutions , with the result that virtual salt flux generally yields accurate res ults when diffusion is strong. (C) 1996 American Institute of Physics.