Bottom-intensified Mixing Research Articles

Turbulence Generated through Critical Reflection of Internal Waves off the Seafloor due to Nontraditional Effects

Abstract Recent work has shown that, when nontraditional (NT) effects associated with the horizontal component of the Coriolis parameter are taken into account, equatorial waves (EWs) experience critical reflection when they reflect off the seafloor at the latitude where their frequency is equal to the inertial frequency. As a result, the vertical shear associated with the wave is strongly enhanced locally and results in bottom-intensified mixing. Using an off-the-shelf parameterization for mixing, these studies have shown that this process could play an important role in driving diapycnal upwelling in the abyssal ocean, but the specific mechanisms generating the mixing have not been studied yet. In this work, we address this limitation by running two-dimensional, high-resolution, nonhydrostatic simulations of the critical reflection of internal waves modified by NT effects. These simulations can resolve the instabilities triggered when the wave reflects off the bottom, allowing us to characterize the energy cascade to smaller scales and to estimate the mixing it generates. We find that shear instabilities drive elevated turbulent diffusivities between 10−1 and −10−3 m2 s−1 over a critical layer of 100–300 m thick. The shear instabilities result directly from the enhancement of kinetic energy in the reflected wave that is confined against the seafloor during the critical reflection process. Simultaneously, higher harmonics are generated and flux energy upward in the water column. These higher harmonics are unstable to parametric subharmonic instability, which absorbs their energy and drive enhanced dissipation above the critical layer, to a height of O(1000) m off the bottom. We show how these results depend on key elements of the EWs and of the medium and discuss the implementation of a parameterization of these effects in global ocean models.

Circulation Driven by Multihump Turbulent Mixing Over a Seamount in the South China Sea

Turbulent mixing above rough topography is crucial for the vertical motions of deep water and the closure of the meridional overturning circulation. Related to prominent topographic features, turbulent mixing not only exhibits a bottom-intensified vertical structure but also displays substantial lateral variation. How turbulent mixing varies in the upslope direction and its impact on the upwelling of deep water over sloping topography remains poorly understood. In this study, the notable multihump structure of the bottom-intensified turbulent diffusivity in the upslope direction of a seamount in the South China Sea (SCS) is revealed by full-depth fine-resolution microstructure and hydrographic profiles. Numerical experiments indicate that multihump bottom-intensified turbulent mixing around a seamount could lead to multiple cells of locally strengthened circulations consisting of upwelling (downwelling) motions in (above) the bottom boundary layer (BBL) that are induced by bottom convergence (divergence) of the turbulent buoyancy flux. Accompanied by cyclonic (anticyclonic) flow, a three-dimensional spiral circulation manifests around the seamount topography. These findings regarding the turbulent mixing and three-dimensional circulation around a deep seamount provide support for the further interpretation of the abyssal meridional overturning circulation.

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

AbstractRecent 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.

Diapycnal Transport near a Sloping Bottom Boundary

AbstractThe diapycnal motion in the stratified ocean near a sloping bottom boundary is studied using analytical solutions from one-dimensional boundary layer theory. Bottom-intensification of the diapycnal mixing intensity ensures that in the stratified mixing layer (SML), where isopycnals are relatively flat, the diapycnal motion is downward toward denser fluid. In contrast, convergence of the diffusive buoyancy flux near the seafloor drives diapycnal upwelling in what we define as the bottom boundary layer (BBL). Much of the one-dimensional BBL is characterized by a stratification only slightly reduced from that in the SML because the maximum in the buoyancy flux at the top of the BBL, where the diapycnal velocity changes sign, must occur in well-stratified fluid. The diapycnal upwelling in the BBL is determined by variations not only in the magnitude of the buoyancy gradient but also in the curvature of isopycnals. The net diapycnal upwelling is concentrated in the bottom half of the BBL where the magnitude of the buoyancy gradient changes most rapidly. The curvature effect drives upwelling near the seafloor that only makes a significant contribution to the net upwelling for steep slopes. The structure of the diapycnal velocity in this stratified BBL differs from the case of a turbulent well-mixed BBL that has been assumed in some recent theoretical studies on bottom-intensified mixing. This work therefore extends recent theories in a way that should be more applicable to abyssal ocean observations where well-mixed BBLs are not common.

Locations and Mechanisms of Ocean Ventilation in the High-Latitude North Atlantic in an Eddy-Permitting Ocean Model

AbstractA substantial fraction of the deep ocean is ventilated in the high-latitude North Atlantic. Consequently, the region plays a crucial role in transient climate change through the uptake of carbon dioxide and heat. However, owing to the Lagrangian nature of the process, many aspects of deep Atlantic Ocean ventilation and its representation in climate simulations remain obscure. We investigate the nature of ventilation in the high-latitude North Atlantic in an eddy-permitting numerical ocean circulation model using a comprehensive set of Lagrangian trajectory experiments. Backward-in-time trajectories from a model-defined North Atlantic Deep Water (NADW) reveal the locations of subduction from the surface mixed layer at high spatial resolution. The major fraction of NADW ventilation results from subduction in the Labrador Sea, predominantly within the boundary current (~60% of ventilated NADW volume) and a smaller fraction arising from open ocean deep convection (~25%). Subsurface transformations—due in part to the model’s parameterization of bottom-intensified mixing—facilitate NADW ventilation, such that water subducted in the boundary current ventilates all of NADW, not just the lighter density classes. There is a notable absence of ventilation arising from subduction in the Greenland–Iceland–Norwegian Seas, due to the re-entrainment of those waters as they move southward. Taken together, our results emphasize an important distinction between ventilation and dense water formation in terms of the location where each takes place, and their concurrent sensitivities. These features of NADW ventilation are explored to understand how the representation of high-latitude processes impacts properties of the deep ocean in a state-of-the-science numerical simulation.

Interdependence of Internal Tide and Lee Wave Generation at Abyssal Hills: Global Calculations

AbstractThe generation of internal waves at abyssal hills has been proposed as an important source of bottom-intensified mixing and a sink of geostrophic momentum. Using the theory of Bell, previous authors have calculated either the generation of lee waves by geostrophic flow or the generation of the internal tide by the barotropic tide, but never both together. However, the Bell theory shows that the two are interdependent: that is, the presence of a barotropic tide modifies the generation of lee waves, and the presence of a geostrophic (time mean) flow modifies the generation of the internal tide. Here we extend the theory of Bell to incorporate multiple tidal constituents. Using this extended theory, we recalculate global wave fluxes of energy and momentum using the abyssal-hill spectra, model-derived abyssal ocean stratification and geostrophic flow estimates, and the TPX08 tidal velocities for the eight major constituents. The energy flux into lee waves is suppressed by 13%–19% as a result of the inclusion of tides. The generated wave flux is dominated by the principal lunar semidiurnal tide (M2), and its harmonics and combinations, with the strongest fluxes occurring along midocean ridges. The internal tide generation is strongly asymmetric because of Doppler shifting by the geostrophic abyssal flow, with 55%–63% of the wave energy flux (and stress) directed upstream, against the geostrophic flow. As a consequence, there is a net wave stress associated with generation of the internal tide that reaches magnitudes of 0.01–0.1 N m−2 in the vicinity of midocean ridges.

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

AbstractTo 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.

Restratification of Abyssal Mixing Layers by Submesoscale Baroclinic Eddies

AbstractFor 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.

Dynamics of an Abyssal Circulation Driven by Bottom-Intensified Mixing on Slopes

AbstractThe large-scale circulation of the abyssal ocean is enabled by small-scale diapycnal mixing, which observations suggest is strongly enhanced toward the ocean bottom, where the breaking of internal tides and lee waves is most vigorous. As discussed recently, bottom-intensified mixing induces a pattern of near-bottom up- and downwelling that is quite different from the traditionally assumed widespread upwelling. Here the consequences of bottom-intensified mixing for the horizontal circulation of the abyssal ocean are explored by considering planetary geostrophic dynamics in an idealized “bathtub geometry.” Up- and downwelling layers develop on bottom slopes as expected, and these layers are well described by boundary layer theory. The basin-scale circulation is driven by flows in and out of these boundary layers at the base of the sloping topography, which creates primarily zonal currents in the interior and a net meridional exchange along western boundaries. The rate of the net overturning is controlled by the up- and downslope transports in boundary layers on slopes and can be predicted with boundary layer theory.

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

AbstractLedwell, 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.

Abyssal Upwelling and Downwelling Driven by Near-Boundary Mixing

AbstractA buoyancy and volume budget analysis of bottom-intensified mixing in the abyssal ocean reveals simple expressions for the strong upwelling in very thin continental boundary layers and the interior near-boundary downwelling in the stratified ocean interior. For a given amount of Antarctic Bottom Water that is upwelled through neutral density surfaces in the abyssal ocean (between 2000 and 5000 m), up to 5 times this volume flux is upwelled in narrow, turbulent, sloping bottom boundary layers, while up to 4 times the net upward volume transport of Bottom Water flows downward across isopycnals in the near-boundary stratified ocean interior. These ratios are a direct result of a buoyancy budget with respect to buoyancy surfaces, and these ratios are calculated from knowledge of the stratification in the abyss along with the assumed e-folding height that characterizes the decrease of the magnitude of the turbulent diapycnal buoyancy flux away from the seafloor. These strong diapycnal upward and downward volume transports are confined to a few hundred kilometers of the continental boundaries, with no appreciable diapycnal motion in the bulk of the interior ocean.

On a Simple Empirical Parameterization of Topography-Catalyzed Diapycnal Mixing in the Abyssal Ocean

Abstract The global spatial distribution of the turbulent diapycnal diffusivity in the abyssal ocean is reexamined in light of the growing body of microstructure data revealing bottom-intensified turbulent mixing in regions of rough topography. A direct and nontrivial implication of the observed intensification is that the diapycnal diffusivity Kρ, is depth dependent and patchily distributed horizontally across the world’s oceans. Theoretical and observational studies show that bottom-intensified mixing is dependent upon a variety of energy sources and processes whose contributions to mixing are sufficiently complex that their physical parameterization is premature; only rudimentary parameterizations of tidally induced mixing have been attempted, although the tides likely provide no more than half of the mechanical energy available for diapycnal mixing in the abyssal ocean. Here, an empirical (and still rudimentary) parameterization of the spatially variable mean diffusivity Kρ based on a large collection of microstructure data from several oceanic regions, is provided. The parameterization, called the roughness diffusivity model (RDM), depends only on seafloor roughness and height above bottom and has the advantage of tacitly including a broad range of mixing processes catalyzed by the roughness or acuteness of the bottom topography. The study focuses in particular on the vertical structure of Kρ and shows that exponential decay, prominent in current diapycnal mixing parameterizations, does not provide an adequate representation of the mean vertical profile. Instead, an inverse square law decay with a scale height and maximum near-boundary value depending on topographic roughness is shown to provide a more realistic vertical structure. Resulting basin-averaged diffusivities based on the RDM, which increase from ∼3 × 10−5 m2 s−1 at 1-km depth to ∼1.5 × 10−4 m2 s−1 at 4 km, are roughly consistent with spatial averages derived from hydrographic data inversions, supporting the contention that strong, localized mixing plays a major role in maintaining the observed abyssal stratification. The power required to sustain the stratification in the abyssal ocean (defined as 40°S–48°N, 1–4-km depth) is shown to be sensitive to the spatial distribution of the mixing. The power consumption in this domain, given the parameterized bottom-intensified and horizontally heterogeneous diffusivity structure in the RDM, is estimated as approximately 0.37 TW (TW = 1012 W), considerably less than the canonical value of ∼2 TW estimated under the assumption of a uniform diffusivity of ∼10−4 m2 s−1 in the abyssal ocean.

Deep Circulation in the South Atlantic Induced by Bottom-Intensified Mixing over the Midocean Ridge*

Abstract The deep circulation in the South Atlantic is studied through numerical experiments, using an oceanic general circulation model based on z coordinates. The new feature of these numerical experiments is that diapycnal mixing is idealized as strong bottom-intensified mixing on both sides of the midocean ridge; elsewhere diapycnal mixing is set at a low background value. The bottom-intensified diapycnal mixing induces strong equatorward (poleward) flow along the western (eastern) slope of the midocean ridge. In addition, the strong vertical gradient of diapycnal mixing rate induces downwelling in the basin interior and intensifies the upwelling near the axis of the midocean ridge. The strong ridge-following currents induce anticlockwise circulation in both the eastern and western deep basins, and such circulation is opposite to the classical Stommel–Arons circulation. This study indicates that bottom topography, strong mixing over the midocean ridge, and strong localized mixing associated with overf...