Nonlinear double-diffusive intrusions at the equator

Previous, linear analysis has suggested that observations of interleaving, quasihorizontal layers in the equatorial oceans may be explained by double-diffusive or inertial instability. Here we describe an idealized, two-dimensional, numerical investigation of the nonlinear development of these instabilities, focusing almost exclusively on the double-diffusive case. We consider the mechanisms for equilibration and maintenance of the interleaving intrusions and perform a thorough sensitivity analysis. Nonlinearity arising from changes in diffusive regime is found to be more important than advective nonlinearity in promoting global equilibration. When variations in effective flux ratio are weak, local constraints prevent equilibration until large amplitudes are reached. When variations in flux ratio with density ratio are allowed, small-scale staircase and mesoscale intrusive instabilities coexist, leading to staircase-like intrusions with sharp, steppy interfaces. Solutions are found to equilibrate at between 3 and 13 times the amplitude where mean salinity gradients overturn. Cross-equatorial diffusivities between 20 and 400 m s are found in realistic cases with intrusion lengths of up to 40 km. A modified estimate of the effective cross-equatorial diffusivity based on a balance of lateral advection and vertical diffusion tends to overestimate the sensitivity to the mean horizontal and vertical gradients of salinity and underestimates the sensitivity to the vertical diffusivity but does give values within an order of magnitude of those derived from numerical experiments. For comparison, we give a single example of inertially driven interleaving layers which reach 190 km in length giving cross-equatorial heat fluxes 4 times larger than realistic double-diffusively driven cases. Although the inertial case is not considered in detail, we speculate that observed interleaving is more likely to be created by inertial than double-diffusive instability.