# American Institute of Mathematical Sciences

May  2002, 2(2): 205-219. doi: 10.3934/dcdsb.2002.2.205

## Dynamics of the thermohaline circulation under wind forcing

 1 Department of Mathematics, Nanjing Normal University, Nanjing 210097, China 2 Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616

Received  June 2001 Revised  August 2001 Published  February 2002

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.
Citation: Hongjun Gao, Jinqiao Duan. Dynamics of the thermohaline circulation under wind forcing. Discrete & Continuous Dynamical Systems - B, 2002, 2 (2) : 205-219. doi: 10.3934/dcdsb.2002.2.205
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