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Dynamics of the thermohaline circulation under wind forcing
The ocean thermohaline circulation, also called meridional overturning
circulation, is caused by water density contrasts. This circulation has
large capacity of carrying heat around the globe and it thus affects the energy
budget and further affects the climate. We consider a thermohaline circulation
model in the meridional plane under external wind forcing. We show that,
when there is no wind forcing, the stream function and the density fluctuation
(under appropriate metrics) tend to zero exponentially fast as time goes to
infinity. With rapidly oscillating wind forcing, we obtain an averaging principle
for the thermohaline circulation model. This averaging principle provides
convergence results and comparison estimates between the original thermohaline
circulation and the averaged thermohaline circulation, where the wind
forcing is replaced by its time average. This establishes the validity for using
the averaged thermohaline circulation model for numerical simulations at long
time scales.