Investigating microscale patchiness of motile microbes driven by the interaction of turbulence and gyrotaxis in a 3D simulated convective mixed layer.

Microbes play a primary role in aquatic ecosystems and biogeochemical cycles. Spatial patchiness is a critical factor underlying these activities, influencing biological productivity, nutrient cycling and dynamics across trophic levels. Incorporating spatial dynamics into microbial models is a long-standing challenge, particularly where small-scale turbulence is involved. Here, we combine a fully 3D direct numerical simulation of convective mixed layer turbulence, with an individual-based microbial model to test the key hypothesis that the coupling of gyrotactic motility and turbulence drives intense microscale patchiness. The fluid model simulates turbulent convection caused by heat loss through the fluid surface, for example during the night, during autumnal or winter cooling or during a cold-air outbreak. We find that under such conditions, turbulence-driven patchiness is depth-structured and requires high motility: Near the fluid surface, intense convective turbulence overpowers motility, homogenising motile and non-motile microbes approximately equally. At greater depth, in conditions analogous to a thermocline, highly motile microbes can be over twice as patch-concentrated as non-motile microbes, and can substantially amplify their swimming velocity by efficiently exploiting fast-moving packets of fluid. Our results substantiate the predictions of earlier studies, and demonstrate that turbulence-driven patchiness is not a ubiquitous consequence of motility but rather a delicate balance of motility and turbulent intensity. Understanding how spatial patchiness in aquatic microbes develops at different scales is crucial for understanding their interactions, their population dynamics, and their role in the wider ecosystem. Patchiness in microbial populations at very small scales is hard to measure or model, particularly where turbulence is involved, and patch formation mechanisms remain poorly understood. In this study, we simulate both swimming and passive microbes in a realistic model of small-scale turbulence at an unprecedented resolution. We find that patchiness is triggered far below the surface and only among highly agile swimmers. This demonstrates that microbial patchiness can develop at sub-metre scales within realistic turbulent flows, albeit under restricted conditions. Our simulations are directly relevant to real world conditions in, for example, the upper ocean at night or during cold weather. In such conditions, we propose that strong turbulence near the ocean surface inhibits patch formation, and that patchiness is triggered primarily in deeper waters near the thermocline – a region of transition between warm surface waters and cooler waters at greater depth. Our findings illustrate the sensitive balance of conditions needed to trigger patchiness in realistic flows, and demonstrate how small differences in individual behaviour can produce substantially different outcomes in a population as a whole.


Introduction
and sensory abilities to exploit patches [21], or because of increased viral transmission 22 rates in patch-dwelling microbes [22,23]. Furthermore, patchiness at the smallest 23 (< 1 m) scales has its own particular suite of consequences, intensifying competition for 24 nutrients within microbe patches [9], colonising disproportionately high-growth 25 micro-habitats [20] and establishing a basis for the formation of patches of other 26 organisms of higher trophic levels [24]. The effects of patchiness on microbial 27 populations can ultimately impact the dynamics of the wider ecosystem. For example, 28 temporal or spatial separation of phytoplankton and zooplankton patches can increase 29 primary productivity several-fold relative to a homogeneous environment [25], the 30 aggregation of diatom detritus can increase bacterial species richness and abundance 31 [26], and strong patchiness in competing plankton species has even been proposed as an 32 explanation for Hutchison's long standing "paradox of the plankton" [27,28]. 33 Spatial dynamics and microbial patchiness are thus critical to understanding aquatic 34 ecosystems. However, measuring and modelling their influence is difficult due to the state-of-the-art technologies such as high-resolution fluorometry [17,30]  and fluid dynamics has begun to present candidate mechanisms [32][33][34]. 44 In this paper, we address the hypothesis that gyrotactic microbial motility interacts 45 with microscale turbulence to trigger intense patchiness, increasing local microbe 46 concentrations by an order of magnitude or more [32,[35][36][37]. The aggregation effect has 47 been hypothesised to be driven by a coupling between fluid shear (which acts to 48 overturn or 'disorient' gyrotactic swimmers) and motility (by which the swimmers 49 attempt to re-orient towards the vertical); when a suitable balance is achieved between 50 the overturning effect of shear, and the swimmers' inherent stabilising torque, intense 51 patchiness results [32]. So far however, this hypothesis has been tested only in simplified 52 or idealised turbulence regimes that are well-suited to mathematical analysis and 53 simulation, but do not accurately reflect the turbulent environment that microbes 54 experience in, for example, lakes or oceans [37]. Experiments in steady vortices, for 55 example, fail to capture the complexity of real turbulence, which comprises many 56 unsteady vortices of different sizes emerging and dissipating constantly. More complex 57 simulations involving statistically steady-state isotropic turbulence are a more accurate 58 approximation of real world turbulence, but it remains the case that turbulence in, for with both non-motile (passive) and motile (gyrotactic) virtual microbes, we tested whether the proposed mechanism of turbulence-driven patchiness is realisable in flow 71 conditions comparable to those that a microbe would experience in a convective mixed 72 as shown in Fig. 1, and separately analysed patchiness in each depth region. Gyrotaxis and microbe patchiness within the simulated flow 99 We quantified patchiness using the "patch concentration enhancement factor" Q for the 100 1% most aggregated cells (f = 0.01, see Methods) to compare motile and non-motile 101 microbe accumulation into patches. Q is dimensionless, and captures the difference in 102 patch concentration between motile and non-motile microbes; the larger the Q value, 103 the more motile microbes were concentrated within patches than non-motile microbes. 104 The expected intensity of patchiness in our simulations can be determined from two 105 dimensionless parameters: the stability number Ψ, and the swimming number Φ (Fig. 2, 106 also see Discussion). Greater patchiness is expected when Ψ ≈ 1 and for large Φ.    reoriented quickly, and were thus more frequently able to overcome viscous torque to 143 orient themselves "upwards". Microbes with higher B were slow to reorient and thus 144 more vulnerable to "disorientation" due to viscous torque; they swam in more 145 continuously varying directions and more horizontally, on average, than low-B microbes. 146 We note that swim speed did not appear to impact the distribution of microbe 147 orientations.

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Microbe orientation is only part of the story underlying the patchiness trends  Within the Shallow (Fig. 6a,b) and Mid (Fig. 6c,d)    density 75% lower than that of the bottom layer, thus creating a stable stratification.

328
The density jump used here is much stronger than in lakes or the ocean, but was chosen 329 to limit turbulent entrainment and thus slow down the deepening of the mixed layer [53]. to descend, forming a convective mixed layer above the density interface (Fig. 7).

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In order to be able to resolve all the turbulent scales of motion, a kinematic viscosity 337 ν = 5 × 10 −6 m 2 s −1 was chosen, which is slightly higher than that of water. Reynolds number are: The computational grid was 720 × 720 × 360, which corresponds to 186,624,000 cubic 343 cells. Cell side-lengths were thus ∆x = ∆y = ∆ z ≈ 0.83 mm. The dissipation rate 344 peaked at ǫ = 2.66 × 10 −4 m 2 s −3 (see Fig. 1), which implies that the Kolmogorov 345 length scale is η K = (ν 3 /ǫ) 1/4 = 0.828 mm. This is the size of the smallest turbulent 346 eddy that is encountered in the flow. Since ∆x/η K ≈ 1, it follows that all the turbulent 347 scales of the flow were resolved, and the simulation can indeed be considered DNS.

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At t = 0s, the fluid was quiescent, after which the buoyancy flux was switched on. The velocity and density fields were obtained using the direct numerical simulation 353 code SPARKLE, which employs a symmetry-preserving fourth-order-accurate finite 354 volume discretization scheme, preserving mass, momentum and energy [56,57].

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SPARKLE solves the Navier-Stokes equations in 3D in the Boussinesq approximation: 356 where space is denoted as x = (x, y, z) and fluid velocity by where p is a unit vector describing the swimming direction, ω = ∇ × u is the fluid the sensitivity of patch formation to these biological parameters.

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OceanParcels -computing microbe trajectories 396 We computed motile and non-motile particle trajectories using the OceanParcels    Table 1 summarises the parameters for the OceanParcels simulations. smallest Voronoi polyhedron volume), and we used the concentrations within these patches to calculate, at every second, the 'patch concentration enhancement factor' Q: 437 where C is the median concentration among motile microbes inside patches, C P is the 438 median concentration among non-motile particles inside patches, and C M is a