Setting the Scales of the Ocean Response to Isolated Convection

Abstract

The ocean response to negative buoyancy flux, applied in an isolated region at the surface, is investigated to determine the scales of the equilibrium state, that is, the time to reach equilibrium, the equilibrium density anomaly within the convecting chimney, and, in the case of deep convection, the equilibrium depth of the chimney. Two types of isolated convection, with fundamentally different parameter dependencies, are distinguished based on the importance of the forcing decay region; a region surrounding the isolated forcing region, across which the buoyancy flux decreases to zero. A narrow forcing decay region produces ?internally constrained? convection in which the baroclinic Rossby radius is the dominant horizontal length scale, and the resulting equilibrium scales are those found by Visbeck et al. A wide forcing decay region produces ?externally constrained? convection in which the forcing decay width is the dominant horizontal length scale, and the equilibrium scales are those found by Chapman and Gawarkiewicz. Some simple theoretical ideas are presented that provide an estimate of the transition between the two types of convection, given by where W is the width of the forcing decay region, B0 is the surface buoyancy flux, r0 is the radius of the forcing region, f is the Coriolis parameter, and lrot = (B0/f3)1/2. If W is less (greater) than 3.2(lrot/r0)2/3, then internally (externally) constrained convection results. This estimate is obtained for both shallow convection in which the chimney reaches the bottom almost immediately and deep convection in which the chimney never reaches the bottom. Furthermore, the transition is independent of the ambient stratification and the total water depth. Calculations made with a primitive equation numerical model support the theoretical ideas and show that the transition between the two types of convection is smooth and well behaved. The results suggest that the forcing decay region may be important in ocean convection situations, especially for large forcing regions.