Instability and multiple steady states in a meridional-plane model of the thermohaline circulation

A meridional-plane model of the thermohaline circulation with a simple friction force and advection and vertical diffusion of the T-S field has been used to demonstrate the instability and existence of multiple steady states associated with “mixed” T-S boundary conditions (specified temperature, flux condition for salinity). With forcing and geometry symmetric to the equator, the symmetric solution was found to be unstable to infinitesimal perturbations, and an asymmetric pole-to-pole circulation was the end-result in all cases. The structure obtained for the meridional-plane stream function and for the poleward heat flux are in qualitative agreement with those obtained by Bryan (1986). Convective overturning caused by static instability was not found to be essential for the transition to the asymmetric steady state. The study suggests that certain aspects of the ocean circulation, in particular those related to the ocean climate, may be profitably explored by use of two-dimensional, zonally averaged models.