 Heat Transport in Simple Models of Meridional Overturning Circulation

Ken Takahashi and Eleanor Frajka Williams

Sandstrom's theorem states that a closed steady circulation can only be
maintained in a fluid body if the heating is applied at a lower level than
the cooling in the absence of mixing.  We investigate meridional
overturning circulation in two simple models, Welander's one-dimensional
loop model and a two-dimensional Boussinesq flow in a box.
Both models have heating and cooling applied at the same level.  We find
that heat transport and circulation intensity depend on the type of
boundary conditions, fixed flux or relaxation, even with negligible
mixing.  In the two-dimensional model, the intensity and geometry of heat
transport--deep or confined to the surface layers--are affected by the
intensity and vertical profile of mixing.  Using these two simple models,
with complex behavior, we draw conclusions about the use of fully
three-dimensional models and the real ocean meridional overturning
circulation.

