Dynamics of eddying abyssal mixing layers over rough topography

The abyssal overturning circulation is thought to be primarily driven by small-scale turbulent mixing. Diagnosed watermass transformations are dominated by rough topography "hotspots", where the bottom-enhancement of mixing causes the diffusive buoyancy flux to diverge, driving widespread downwelling in the interior—only to be overwhelmed by an even stronger upwelling in a thin Bottom Boundary Layer (BBL). These watermass transformations are significantly underestimated by one-dimensional sloping boundary layer solutions, suggesting the importance of three-dimensional physics. Here, we use a hierarchy of models to generalize this one-dimensional boundary layer approach to three-dimensional eddying flows over realistically rough topography. When applied to the Mid-Atlantic Ridge in the Brazil Basin, the idealized simulation results are roughly consistent with available observations. Integral buoyancy budgets isolate the physical processes that contribute to realistically strong BBL upwelling. The downwards diffusion of buoyancy is primarily balanced by upwelling along the canyon flanks and the surrounding abyssal hills. These flows are strengthened by the restratifying effects of submesoscale baroclinic eddies on the canyon flanks and by the blocking of along-ridge thermal wind within the canyon. Major topographic sills block along-thalweg flows from restratifying the canyon trough, resulting in the continual erosion of the trough's stratification. We propose simple modifications to the one-dimensional boundary layer model which approximate each of these three-dimensional effects. These results provide \textit{local} dynamical insights into mixing-driven abyssal overturning, but a complete theory will also require the non-local coupling to the basin-scale circulation.

Control of the abyssal ocean overturning circulation by mixing-driven bottom boundary layers

An emerging paradigm posits that the abyssal overturning circulation is driven by bottom-enhanced mixing, which results in vigorous upwelling in the bottom boundary layer (BBL) along the sloping seafloor and downwelling in the stratified mixing layer (SML) above; their residual is the overturning circulation. This boundary-controlled circulation fundamentally alters abyssal tracer distributions, with implications for global climate. Chapter 1 describes how a basin-scale overturning circulation arises from the coupling between the ocean interior and mixing-driven boundary layers over rough topography, such as the sloping flanks of mid-ocean ridges. BBL upwelling is well predicted by boundary layer theory, whereas the compensation by SML downwelling is weakened by the upward increase of the basin-wide stratification, which supports a finite net overturning. These simulated watermass transformations are comparable to best-estimate diagnostics but are sustained by a crude parameterization of boundary layer restratification processes. In Chapter 2, I run a realistic simulation of a fracture zone canyon in the Brazil Basin to decipher the non-linear dynamics of abyssal mixing layers and their interactions with rough topography. Using a hierarchy of progressively idealized simulations, I identify three physical processes that set the stratification of abyssal mixing layers (in addition to the weak buoyancy-driven cross-slope circulation): submesoscale baroclinic eddies on the ridge flanks, enhanced up-canyon flow due to inhibition of the cross-canyon thermal wind, and homogenization of canyon troughs below the level of blocking sills. Combined, these processes maintain a sufficiently large near-boundary stratification for mixing to drive globally significant BBL upwelling. In Chapter 3, simulated Tracer Release Experiments illustrate how passive tracers are mixed, stirred, and advected in abyssal mixing layers. Exact diagnostics reveal that while a tracer’s diapycnal motion is directly proportional to the mean divergence of mixing rates, its diapycnal spreading depends on both the mean mixing rate and an additional non-linear stretching term. These simulations suggest that the theorized boundary-layer control on the abyssal circulation is falsifiable: downwelling in the SML has already been confirmed by the Brazil Basin Tracer Release Experiment, while an upcoming experiment in the Rockall Trough will confirm or deny the existence of upwelling in the BBL.

Enhanced Abyssal Mixing in the Equatorial Pacific Associated with Non-Traditional Effects

Recent theoretical work has shown that, when the so-called non-traditional effects are taken into account, the reflection of Equatorially Trapped Waves (ETWs) off the seafloor generates strong vertical shear that results in bottom-intensified mixing at the inertial latitude of the ETW via a mechanism of critical reflection. It has been estimated that this process could play an important role in driving diapycnal upwelling in the Abyssal Meridional Overturning Circulation (AMOC). However, these results were derived under an idealized configuration with a monochromatic ETW propagating through a flat ocean at rest. To test the theory in a flow that is more representative of the ocean, we contrast a set of realistic numerical simulations of the Eastern Equatorial Pacific run using either the hydrostatic or quasi-hydrostatic approximation, the latter of which accounts for non-traditional effects. The simulations are nested into a Pacific-wide hydrostatic parent solution forced with climatological data and realistic bathymetry, resulting in an ETW field and a deep circulation consistent with observations. Using these simulations, we observe enhanced abyssal mixing in the quasi-hydrostatic run, even over smooth topography, that is absent in the hydrostatic run. The mixing is associated with inertial shear that has spatio-temporal properties consistent with the critical reflection mechanism. The enhanced mixing results in a weakening of the abyssal stratification and drives diapycnal upwelling in our simulation, in agreement with the predictions from the idealized simulations. The diapycnal upwelling is on the order of O(10) Sv and thus could play an important role in closing the AMOC.

Mixing-Driven Mean Flows and Submesoscale Eddies over Mid-Ocean Ridge Flanks and Fracture Zone Canyons

To close the abyssal overturning circulation, dense bottom water has to become lighter by mixing with lighter water above. This diapycnal mixing is strongly enhanced over rough topography in abyssal mixing layers, which span the bottom few hundred meters of the water column. In particular, mixing rates are enhanced over mid-ocean ridge systems, which extend for thousands of kilometers in the global ocean and are thought to be key contributors to the required abyssal water mass transformation. To examine how stratification and thus diabatic transformation is maintained in such abyssal mixing layers, this study explores the circulation driven by bottom-intensified mixing over mid-ocean ridge flanks and within ridge-flank canyons. Idealized numerical experiments show that stratification over the ridge flanks is maintained by submesoscale baroclinic eddies and that stratification within ridge-flank canyons is maintained by mixing-driven mean flows. These restratification processes affect how strong a diabatic buoyancy flux into the abyss can be maintained, and they are essential for maintaining the dipole in water mass transformation that has emerged as the hallmark of a diabatic circulation driven by bottom-intensified mixing.

Influence of Abyssal Mixing on the Multilayer Circulation in the South China Sea

By parameterizing the abyssal mixing as the exchange velocity (entrainment/detrainment) between the middle and deep layers of the South China Sea (SCS), its effects on the multilayer circulation are examined. Results indicate that the cyclonic circulation in the deep SCS appears only when the mixing induces an entrainment of at least 0.72 Sv (1 Sv ≡ 106 m3 s−1) from the deep to the middle layer, which is equivalent to a diapycnal diffusivity of 0.65 × 10−3 m2 s−1 or a net input rate of gravitational potential energy (GPE) of 6.89 GW, respectively. It is also found that tidal mixing in the SCS is stronger than the threshold for the generation of the cyclonic abyssal circulation, but the pattern and evolution of the deep circulation and meridional overturning circulation also depend on the spatiotemporal variability of the mixing. Moreover, the abyssal mixing is able to intensify the anticyclonic circulation in the middle layer but weaken the cyclonic circulation in the upper layer. Vorticity analysis suggests that the upward net flux induced by the abyssal mixing leads to vortex stretching (squeezing) and modulates the pressure gradient by redistributing the layer thickness, hence affects the pattern and strength of the circulation in the middle (deep) layer of the SCS, respectively. The depth-integrated effect of the thickness variation can modulate the pressure gradient across all layers and hence influence the upper-layer circulation.

Abyssal Mixing through Critical Reflection of Equatorially Trapped Waves off Smooth Topography

The inferred diapycnal upwelling in the abyssal meridional overturning circulation (AMOC) is intensified near the equator, but little is known as to why this is so. In this study, it is shown that the reflection of equatorially trapped waves (ETWs) off the bottom leads to seafloor-intensified mixing and substantial diapycnal upwelling near the equator when the full Coriolis force and the so-called nontraditional effects are taken into account. Using idealized simulations run with the MITgcm of downward-propagating ETWs of various types (i.e., inertia–gravity, Yanai, Kelvin, and Rossby waves) accounting for nontraditional effects, it is demonstrated that the reflection of ETWs off a flat seafloor generates beams of short inertia–gravity waves with strong vertical shear and low Richardson numbers that result in bottom-intensified, persistent, zonally invariant mixing at the inertial latitude of the ETW through the mechanism of critical reflection. The beams are more intense with weaker stratification and, for a given wave type, are stronger for waves with shorter periods and longer vertical wavelengths. The intensity of the beams also differs between wave types because their distinct meridional structures modulate the amount of energy fluxed to the bottom at the inertial latitude. As a result, equatorial inertia–gravity, Rossby, and eastward-propagating Yanai waves yield stronger mixing than Kelvin and westward-propagating Yanai waves in the simulations. It is estimated that this process can result in order 10 Sv (1 Sv ≡ 106 m3 s−1) of diapycnal upwelling per wavelength of ETW in the abyss and thus could play an important role in closing the AMOC.

Restratification of Abyssal Mixing Layers by Submesoscale Baroclinic Eddies

For small-scale turbulence to achieve water mass transformation and thus affect the large-scale overturning circulation, it must occur in stratified water. Observations show that abyssal turbulence is strongly enhanced in the bottom few hundred meters in regions with rough topography, and it is thought that these abyssal mixing layers are crucial for closing and shaping the overturning circulation. If it were left unopposed, however, bottom-intensified turbulence would mix away the observed mixing-layer stratification over the course of a few years. It is proposed here that the homogenizing tendency of mixing may be balanced by baroclinic restratification. It is shown that bottom-intensified mixing, if it occurs on a large-scale topographic slope such as a midocean ridge flank, not only erodes stratification but also tilts isopycnals in the bottom few hundred meters. This tilting of isopycnals generates a reservoir of potential energy that can be tapped into by submesoscale baroclinic eddies. The eddies slide dense water under light water and thus restratify the mixing layer, similar to what happens in the surface mixed layer. This restratification is shown to be effective enough to balance the homogenizing tendency of mixing and to maintain the observed mixing-layer stratification. This suggests that submesoscale baroclinic eddies may play a crucial role in providing the stratification mixing can act on, thus allowing sustained water mass transformation. Through their restratification of abyssal mixing layers, submesoscale eddies may therefore directly affect the strength and structure of the abyssal overturning circulation.

Reply to “Comment on ‘Abyssal Upwelling and Downwelling Driven by Near-Boundary Mixing’”

Ledwell, in a comment on McDougall and Ferrari, discusses the dianeutral upwelling and downwelling that occurs near isolated topographic features, by performing a buoyancy budget analysis that integrates the diffusive buoyancy fluxes only out to a set horizontal distance from the topography. The consequence of this choice of control volume is that the magnitude of the area-integrated diffusive buoyancy flux decreases to zero at the base of a topographic feature resulting in a net dianeutral upwelling of water. Based on this result, Ledwell argues that isolated topographic features are preferential locations for the upwelling of waters from the abyss. However the assumptions behind Ledwell’s analysis may or may not be typical of abyssal mixing in the ocean. McDougall and Ferrari developed general expressions for the balance between area-integrated dianeutral advection and diffusion, and then illustrated these general expressions using the very simple assumption that the magnitude of the buoyancy flux per unit area at the top of the turbulent boundary layer was constant. In these pedagogical illustrations, McDougall and Ferrari concentrated on the region near the top (rather than near the base) of isolated topographic features, and they found net sinking of abyssal waters. Here we show that McDougall and Ferrari’s conclusion that isolated topographic features cause dianeutral downwelling is in fact a result that applies for general geometries and for all forms of bottom-intensified mixing profiles at heights above the base of such topographic features.