VACILLATING OCEAN GYRES - AN INSTABILITY MECHANISM IN A THERMODYNAMICREDUCED GRAVITY OCEAN MODEL

This paper examines large-scale (in the sense of small Rossby number) wind and buoyancy driven ocean circulation in a thermodynamic single a ctive layer reduced gravity model. It is proved that in a closed domai n bounded by a piecewise orientable boundary there are an infinite num ber of steady state solutions for a given wind stress. Starting with a specific steady solution of the governing adiabatic non-diffusive (wi th respect to temperature) equations, it is shown how a rearrangement of the fluid columns produces an alternative steady-state solution. In the rearrangement process the fluid columns must satisfy (i) the volu me of each fluid column is conserved and (ii) the temperature of each fluid column is conserved. Only one of the steady solutions is stable. The instability mechanism that is present in this type of ocean model arises when the perturbation velocity associated with a perturbation temperature field advects fluid in such a way as to reinforce the init ial perturbation temperature. It is shown that in the inviscid interio r of an ocean gyre the instability condition is satisfied at points wh ere J(h, T) is negative, where h and T are the active layer depth and temperature respectively and J is the Jacobian operator. A subtropical ocean gyre contained in a rectangular domain is found to exhibit vaci llations when the governing prognostic equations are initialised with an unstable solution, and then integrated forwards in time with a surf ace heat flux term which restores the temperature at each point toward s the initial value. In extra-tropical oceans the dominant vacillation period is interannual and is shown to increase (decrease) as (i) the active layer depth increases (decreases) and (ii) the gyre-time scale increases (decreases). Finally an example of a vacillating ocean solut ion is presented using realistic parameters appropriate to the Greenla nd Sea.