Nonlinear double-diffusive intrusions at the equator

Abstract

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 2 s −1 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.

Extended deep equatorial layering as a possible imprint of inertial instability

“…Typical Atlantic Turner angle profiles within 3° of the equator (Figure 3a) displays values such that the flow is either stable (between −45° and 45°) or marginally unstable (close to −45° or 45°) to double diffusive instability, especially between 600 and 2000 m. This suggests that this mechanism is not responsible for the large‐scale Atlantic deep layering. Let us furthermore mention that double diffusion is not able to generate extended layers in upper‐layer Pacific interleaving, as shown fairly convincingly by Edwards and Richards [2004].…”

Characterizing Thermohaline Intrusions in the North Pacific Subtropical Frontal Zone

“…A number of field observations, however, have reported slopes and scales for the intrusive features that are inconsistent with the ''active'' theories (Kuzmina et al 2005;Beal 2007). Moreover, it is uncertain whether the classical DD instabilities exist in the presence of typical oceanic levels of turbulent mixing (Zhurbas and Oh 2001;Edwards and Richards 2004). ''Passive'' theories ascribe intrusions to differential stirring of preexisting thermohaline gradients by mesoscale eddies (Ferrari and Polzin 2005;Smith and Ferrari 2009) or through inertial instability (Edwards and Richards 2004).…”

Direct Measurements of Turbulence in the Upper Western Pacific North Equatorial Current over a 25-h Period

“…Previous studies suggest the important contribution of double-diffusive mixing processes to vertical mixing in the tropical western Pacific Ocean [ 36 , 37 ]. Lee et al (2014) [ 38 ] first quantified the estimated flux and associated vertical diffusivity due to double diffusion in the western equatorial Pacific by using oceanic microstructure measurements in the upper 300 m, which are approximately one order of magnitude higher for temperature and density and two orders of magnitude higher for salinity compared to values calculated from a turbulence model.…”