A Simple Box Model of Stochastically Forced Thermohaline Flow

Abstract A modified Stommel two-box model is considered as a minimal representation of the buoyancy-driven ocean circulation. In the limit of fast temperature relaxation only the salinity evolves in time while the temperature is clamped to the prescribed ambient value. The box model has no intrinsic variability: just two linearly stable and one unstable equilibria. A finite perturbation is needed to shift the system from one stable equilibrium to the other. The minimum amplitude and duration in time of the perturbation are calculated. A stochastic component of the freshwater flux forcing is then added to model the effect of changes in the global hydrological cycle due to the “weather.” The stochastic forcing is a source of extrinsic time dependence. The salinity gradient obeys an equation analogous to the trajectory of a viscous particle in a double-welled potential, subject to Brownian agitation. If the amplitude of the stochastic driving is above a certain threshold, then there is a finite probability o...