Mountains to climb: on the role of seamounts in upwelling of deep ocean waters

Ocean turbulent mixing exerts an important control on the rate and structure of the overturn- ing circulation. Recent observational evidence suggests, however, that there could be a mismatch between the observed intensity of mixing integrated over basin or global scales, and the net mix- ing required to sustain the overturning’s deep upwelling limb. Here, we investigate the hitherto largely overlooked role of tens of thousands of seamounts in resolving this discrepancy. Dynamical theory indicates that seamounts may stir and mix deep waters by generating lee waves and topo- graphic wake vortices. At low latitudes, this is enhanced by a layered vortex regime in the wakes. 18 We consider three case studies (in the equatorial zone, Southern Ocean and Gulf Stream) that 19 are predicted by theory to be representative of, respectively, a layered vortex, barotropic wake, 20 and hybrid regimes, and corroborate theoretical scalings of mixing in each case with a realistic 21 regional ocean model. We then apply such scalings to a global seamount dataset and an ocean 22 climatology to show that seamount-generated mixing makes a leading-order contribution to the 23 global upwelling of deep waters. Our work thus brings seamounts to the fore of the deep-ocean 24 mixing problem, and urges observational, theoretical and modeling eﬀorts toward incorporating 25 the seamounts’ mixing eﬀects in conceptual and numerical models of the ocean circulation. 26 Turbulence at centimetre scales

boundary current (14)), suggesting that the instabilities may be widely active mixing agents. 48 Yet, as common as these instabilities might be, fresh theoretical advances emphasize the potential prevalence 49 of a largely overlooked, more generic form of mesoscale flow-topography interaction, which encompasses and 50 transcends most scenarios of submesoscale instability development: the generation of topographic wakes. These 51 wakes are produced when the highly-sheared near-boundary flow separates from sloping topography and moves 52 into the oceanic interior (18). Flow separation needs not always be associated with a reversal in the sign of 53 potential vorticity close to the boundary, but may be readily enabled by the boundary's geometry (19) or the 54 background mesoscale strain field (20). Upon escaping the boundary's constraint, the separated, sheared flow 55 undergoes a variety of instabilities, which lead to both elevated turbulent mixing in the wake (17; 21; 22) and 56 the generation of submesoscale vortical filaments (19; 23; 24). These filaments often merge and align to form 57 submesoscale coherent vortices (SCVs) and, ultimately, may result in further mixing via a secondary emission 58 of internal waves. 59 Where, then, might we expect topographic wakes to induce vigorous turbulent mixing in the deep ocean? 60 Although wake generation can potentially occur at any sloping topography, the most common form of such 61 topography is provided by seamounts -of which some tens to hundreds of thousands with heights of hundreds 62 of metres or taller are estimated to exist (25; 26). Thus, in this work, we combine the latest developments in these seamounts are taller than 1 km. Those authors predict that their database likely underestimates the 71 global inventory of seamounts by nearly a factor of two, such that the total number of seamounts may lie in 72 the 40,000-55,000 range. Thus, the KW11 database is conservative, as it includes a significantly lower number 73 of seamounts than earlier predictions. For example, Wessel et al. (25) reported more than 100,000 seamounts 74 with heights exceeding 1 km, and speculated that there are probably 25 million seamounts taller than 100 m. 75 Similarly, Yesson et al.(26) reported ∼140,000 seamounts with peak heights between 500 m and 1 km, and 76 ∼ 33,500 seamounts taller than 1 km. The KW11 data incorporates corrections for the ambiguity in gravity 77 signals due to small seamounts and for the overlap with abyssal hills. As a result, seamounts captured by the 78 KW11 data are distinct from abyssal hills, and correspond instead to active or extinct undersea volcanoes with 79 heights in excess of 100 m. It is worth noting that in the three realistic simulations used in this study, each  Flow Around a Seamount 85 A flow past a seamount generates a turbulent topographic wake with patches of both cyclonic and anticyclonic 86 vorticity, leading to instabilities and formation of SCVs with either sign of vorticity in the wake of the seamount 87 (23; 24; 28; 29). While two-dimensional (2D) wake flow past a cylinder is a classic focal problem in fluid 88 mechanics, the description of 3D seamount wakes in a rotating density-stratified ocean is a recently-attacked, 89 and far more complicated, problem. The impacts on wake dynamics of rotation and stratification can be

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The vertical structure of wake vortices has been found to further depend on the Rossby and Froude numbers 102 too or, specifically, on their ratio, which is expressed by the Burger number Bu = (Ro/F r) 2 = ( N H f D ) 2 . The at a given depth set by the local seamount diameter at that height) (23) -see Fig. 1d In this work, we set aside the lee wave radiation regime (Fig. 1d) which, despite its regional significance, 115 has been investigated within earlier studies of lee wave generation over generalized rough topography (35; 36). 116 We also exclude the influence of tides as we find that the tidal excursion is generally small compared to the 117 horizontal scale of the seamounts, and the tidal flows are thus likely to be secondary to the mean flow in the 118 generation of wake vortices (see Supplementary Information). However, tidal interaction with seamounts may 119 also be important for enhancing mixing (37; 38). Instead, our focus will be on the turbulent mixing induced by 120 vertically-sheared, layered vortices forming in the wake of seamounts across the world ocean. To our knowledge, 121 the basin-scale impacts of this regime of flow-seamount interaction have not been considered to date, yet, as we 122 will see, such impacts are predicted to be of considerable importance to the global ocean circulation.

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In Figure  Antarctic Circumpolar Current (ACC) system, western boundary currents, abyssal channels and passages, etc.

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The corresponding estimate of Bu is displayed in Figure 1e, illustrating that, overall, seamount wakes are 130 expected to be more layered around the equator due to the inverse dependence of Bu on f . At high latitudes 131 (e.g., in the ACC region) flow impingement on seamounts is instead mostly predicted to generate barotropic 132 vortices. Note however that substantial regional departures from this general pattern do occur, linked primarily 133 to the seamount aspect ratio H/D.  Next, we will show that the preceding theoretical framework, which was developed within highly idealized Bu ∼ 100 − 10, 000. These correspond squarely to the layered wake vortex regime (Fig. 1d), and thereby 167 indicate that the area should have a rich field of layered topographic vortices (33) -as indeed it is found to do.

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The simulation further lends support to the scaling relation for the diapycnal diffusivity produced by idealized 169 numerical experiments (Eq. 1). Specifically, the vertically sheared layers in the simulation give rise to critical 170 Richardson number values that, in turn, yield high diffusivities of as much as O(10 −3 − 10 −2 ) in the wakes 171 of seamounts (Figs. 2f,g). These diffusivities exceed those away from topography by typically one to two 172 orders of magnitude below 1500 m depth (Fig. 2d), and are in the range of (though, on average, slightly larger 173 than) diffusivities predicted by the theoretical scaling (Fig. 2c) and lee waves. This prediction is tested here with a dynamically-downscaled regional simulation (Fig. 3a,b),  The seamount shown in Fig. 4d has a shape similar to that of the idealized seamount studied by Perfect Burger number Bu ∼ 2. The vortical wake structure is thus expected to be more vertically coherent than in 205 the equatorial case, as confirmed by the simulation (Fig. 4b and supplementary animation).

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The vortical wake is associated with an enhancement of turbulent mixing, again by one to two orders of 207 magnitude relative to typical levels at the same depth away from the seamounts (Fig. 4d). In this case, the 208 elevated diffusivities are localized predominantly on the anticyclonic side of the wake, as is characteristic of 209 centrifugal instability in the near wake for extratropical cases with Ro < 1 (33). The diffusivities exceed again 210 those predicted by the theoretical scaling (Fig. 4c), as further described in the Supplementary Materials. shear in between the layered wake vortices (Bu > 1), which is absent from representation of ocean turbulence 215 in climate models (and hence is the novelty of this work), and not the mixing associated with seamountradiated internal lee waves or wave-vortex interactions which can have overlaps with existing mixing estimates.

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The outcome is shown in Fig. 5a - and lee waves on an illustrative deep-ocean density level. Seamount-generated mixing is found to be intense 220 compared to the most energetic tidal and lee wave mixing, specially at lower latitudes, although strong tidal 221 mixing is substantially more widely spread. The map in panel a is entirely absent from mixing parameterizations 222 in ocean and climate general circulation models. Our decision to exclude the tidal or lee wave mixing induced 223 by seamounts ensures that there is no overlap between panels a and c,d.

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The impact on deep-ocean upwelling of seamount-generated mixing is assessed by quantifying the rate 225 of water mass transformation effected by this and other (i.e., internal tides and lee waves) mixing agents.

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The characteristic distribution of the diapycnal velocity induced by the three mixing agents considered may 227 be illustrated with an example from a deep isopycnal in the Pacific Ocean (Fig. 5e) where the selected isopycnal approaches the seafloor. When integrated globally (Fig. 5f) or across the Pacific 232 (Fig. 5h), as much as tens of Sverdrups (1 Sv ≡ 10 −6 m 3 s −1 ) of deep waters down-or upwell across isopycnals,

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We emphasize that our estimates are conservative due to four factors: (I) the seamount count of KW11 242 is likely very conservative; for example all three of our regional examples included many seamounts missing 243 from KW11, (II) we only accounted for high Bu tall seamounts (e.g., compare Fig 5a with Fig 1b); other 244 seamounts also contribute to mixing, (III) we only accounted for shear-induced turbulence in between layered 245 vortical wakes; seamounts generate mixing due to wave generation, wave-vortex interactions, near boundary 246 instabilities, and tide-seamount interactions, none of which were accounted for here, and (IV) the formula used to 247 infer mixing from the seamount dataset seems to underpredict mixing compared to our regional high-resolution 248 model outputs.

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We have demonstrated that theoretical descriptions of the turbulent mixing generated by flow impingement 251 on seamounts, which were developed for highly idealized scenarios, hold broadly for realistic flow and topogra-252 phy configurations. By conservatively applying these theoretical ideas to global seamount and oceanographic 253 datasets, we have shown that turbulence associated with seamount-generated layered vortices makes a leading-254 order contribution to deep-ocean mixing and upwelling -comparable to contributions from other, much more 255 extensively studied sources of turbulence. We conclude that seamount-induced turbulence may be a significant, The data used to produce figures 1 and 5, along with the scripts used for the analyses, will be made available 273 upon acceptance of this article. Data from simulations described in figures 2,3 and 4 will be available from Ali 274 Mashayek and Jonathan Gula upon request.    Figure 5: (a) Distribution of seamounts that are expected to give rise to shear-induced turbulence due to baroclinic vortex decoupling in their wakes (Bu > 1). Seamounts with Ro > 1 (too close to the equator and not accounted for in Eq. (1)), F r > 1 (for which flow goes primarily above them rather than around them), and H<100m (fully or partially within the bottom turbulent boundary layer) are all discarded from the map shown in Figure 1. The colour coding implies the effective turbulent diffusivity that represents the mixing around and over the height of seamounts as per Eq.