It is generally understood that small-scale mixing, such as is caused by breaking internal waves, drives upwelling of the densest ocean waters that sink to the ocean bottom at high latitudes. However, the observational evidence that the strong turbulent fluxes generated by small-scale mixing in the stratified ocean interior are more vigorous close to the ocean bottom boundary than above implies that small-scale mixing converts light waters into denser ones, thus driving a net sinking of abyssal waters. Using a combination of theoretical ideas and numerical models, it is argued that abyssal waters upwell along weakly stratified boundary layers, where small-scale mixing of density decreases to zero to satisfy the no density flux condition at the ocean bottom. The abyssal ocean meridional overturning circulation is the small residual of a large net sinking of waters, driven by small-scale mixing in the stratified interior above the bottom boundary layers, and a slightly larger net upwelling, driven by the decay of small-scale mixing in the boundary layers. The crucial importance of upwelling along boundary layers in closing the abyssal overturning circulation is the main finding of this work.

Turbulent mixing produced by breaking of internal waves plays an important role in setting the patterns of downwelling and upwelling of deep dense waters and thereby helps sustain the global deep ocean overturning circulation. A key parameter used to characterize turbulent mixing is its efficiency, defined here as the fraction of the energy available to turbulence that is invested in mixing. Efficiency is conventionally approximated by a constant value near one sixth. Here we show that efficiency varies significantly in the abyssal ocean and can be as large as approximately one third in density stratified regions near topographic features. Our results indicate that variations in efficiency exert a first‐order control over the rate of overturning of the lower branch of the meridional overturning circulation.

We study the competition between various secondary instabilities that co-exist in a preturbulent stratified parallel flow subject to Kelvin–Helmholtz instability. In particular, we investigate whether a secondary braid instability might emerge prior to the overturning of the statically unstable regions that develop in the cores of the primary Kelvin–Helmholtz billows. We identify two groups of instabilities on the braid. One group is a shear instability which extracts its energy from the background shear and is suppressed by the straining contribution of the background flow. The other group, which seems to have no precedent in the literature, includes phase-locked modes which grow at the stagnation point on the braid and are almost entirely driven by the straining contributions of the background flow. For the latter group, the braid shear has a negative influence on the growth rate. Our analysis demonstrates that the probability of finite-amplitude growth of both braid instabilities is enhanced with increasing Reynolds number and Richardson number. We also show that the possibility of emergence of braid instabilities decreases with the Prandtl number for the shear modes and increases for the stagnation point instabilities. Through detailed non-separable linear stability analysis, we show that both braid instabilities are fundamentally three dimensional with the shear modes being of small wavenumbers and the stagnation point modes dominating at large wavenumber.

Motivated by the importance of small-scale turbulent diapycnal mixing to the closure of the large-scale meridional overturning circulation (MOC) of the oceans, we focus on a model problem which allows us to address the fundamental fluid mechanics that is expected to be characteristic of the oceanographic regime. Our model problem is one in which the initial conditions consist of a stably stratified parallel shear flow which evolves into the turbulent regime through the growth of a Kelvin-Helmholtz wave to finite amplitude followed by transition to turbulence. Through both linear stability analysis and direct numerical simulations (DNS), we investigate the secondary instabilities and the turbulent mixing at a fixed high Reynolds number and for a range of Prandtl numbers. We demonstrate that the oceanographically expected high value of the Prandtl number has a profound influence on the nature of the secondary instabilities that govern the transition process. Specifically through non-separable linear stability analysis, we discover new characteristics for the shear-aligned convective instability such that it is modified into a mixed mode that is driven both by static instability and by shear. The growth rate and ultimate strength of this mode are both strongly enhanced at higher Pr while the growth rate and ultimate strength of the stagnation point instability (SPI), which may compete for control of the transition process, are simultaneously impeded. Of equal importance is the fact that, for higher Pr, the characteristic length scales associated with the dominant mixed mode of instability decrease and therefore there ceases to be a strong scale selectivity. In the limit of much higher Pr, we conjecture that a wide range of spatial scales become equally unstable so as to support an 'ultraviolet catastrophe', in which a direct injection of energy occurs into a broad range of scales simultaneously. We further establish the validity of these analytical results through a series of computationally challenging DNS analyses, and provide a detailed analysis of the efficiency of the turbulent mixing of the density field that occurs subsequent to transition and of the entrainment of fluid into the mixing layer from the high-speed flanks of the shear flow. We show that the mixing efficiency decreases monotonically with increase of the molecular value of the Prandtl number and the expansion of the shear layer is reduced as such entrainment diminishes.

It is an open question whether turbulent mixing across density surfaces is sufficiently large to play a dominant role in closing the deep branch of the ocean meridional overturning circulation. The diapycnal and isopycnal mixing experiment in the Southern Ocean found the turbulent diffusivity inferred from the vertical spreading of a tracer to be an order of magnitude larger than that inferred from the microstructure profiles at the mean tracer depth of 1,500 m in the Drake Passage. Using a high-resolution ocean model, it is shown that the fast vertical spreading of tracer occurs when it comes in contact with mixing hotspots over rough topography. The sparsity of such hotspots is made up for by enhanced tracer residence time in their vicinity due to diffusion toward weak bottom flows. The increased tracer residence time may explain the large vertical fluxes of heat and salt required to close the abyssal circulation.