THE STABILITY OF A ZONALLY AVERAGED THERMOHALINE CIRCULATION MODEL

A combination of analytical and numerical techniques are used to effic iently determine the qualitative and quantitative behaviour of a one-b asin zonally averaged thermohaline circulation ocean model under vario us forcing regimes and over a large region of parameter space. In cont rast to earlier studies which use time stepping to find the steady sol utions, the steady state equations are first solved directly to obtain the multiple equilibria under identical mixed boundary conditions. Th is approach is based on the differentiability of the governing equatio ns and especially the convection scheme. A linear stability analysis i s then performed, in which the normal modes and corresponding eigenval ues are found for the various equilibrium states. Resonant periodic so lutions superimposed on these states are predicted for various types o f forcing. The results are used to gain insight into the solutions obt ained by Mysak, Stocker and Huang in a previous numerical study in whi ch the eddy diffusivities were varied in a randomly forced one-basin z onally averaged model. It is shown that the two-cell symmetric circula tion is generally unstable to anti-symmetric perturbations in the temp erature or salinity (as expected), and that both one-cell (inter-hemis pheric) circulation patterns are generally stable. Resonant stable osc illations with century scale periods are predicted with structures tha t compare favorably with those found in the previous study. In cases w ith large horizontal diffusivities, the two-cell pattern is also stabl e, which parallels cases in the previous study where large vacillation s were seen between the three stable steady states. Further, in cases with large horizontal and large vertical diffusivities, no one-cell pa ttern can be realised and the only asymptotic behaviour found is the t wo-cell pattern. An experiment is also performed to examine the effect of varying the restoring time constants in the relaxation boundary co nditions used at the surface for both salinity and temperature.