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.