Lophelia pertusa coral samples were collected from the Tisler reef located in the Ytre Hvaler National Park (NE Skagerrak). Collection took place on December 3^rd, 2018, using a remotely operated vehicle (ROV, Ocean Modules V8 Sii). All necessary permits were in place (see Supplementary Information section 1 ). The corals were sampled from colonies at 100 – 120 m water depth. Collected samples were brought to the Tjärnö Marine Laboratory, University of Gothenburg, where the sex of each sample was determined through dissection of polyps. The corals were distributed, mixing male and female fragments, into six 18-L tanks connected to a piping system, allowing flow through of 50 µm filtered sea water with a salinity of 30.3 – 34.5 g kg^-1 and a temperature of 7 – 8°C. The corals were fed twice a week with frozen zooplankton.

Larvae for this study were produced during three spawning events, on February 14^th, 15^th and 23^rd, 2019. The three larval batches are hereafter referred to as B1, B2 and B3 respectively, numbered with respect to the chronology of spawning dates. Spawned egg and sperm were collected from the tanks and kept in 3 L glass jars for 2 – 3 days. The developed embryos were subsequently transferred into 5 µm filtered seawater in 2-L Erlenmeyer flasks. Larvae were cultured at 8°C and densities of 0.5 – 1.0 larvae mL⁻¹, until the experiments were carried out on March 5^th, 6^th and 14^th for B1, B2 and B3 respectively. The larvae were 19 days old when tested and were, by then, fully developed swimmers, striving upwards in the water column. Based on observations reported by Larsson et al. (2014) and by Strömberg and Larsson (2017), we assume that larvae were swimming at their maximum speed at the time of the experiments. Pre-competency was considered probable based on the upwards swimming behavior and lack of cnidocytes required for attachment to surfaces (Strömberg et al., 2019). Larvae at this age have not yet a fully developed mouth, meaning that they are not yet able to ingest food particles (Strömberg and Larsson, 2017).

A grid-stirred Plexiglas® tank with dimensions 32 cm × 32 cm × 70 cm (width × depth × height) was specifically constructed for the experiments ( Figure 1A ). The front and side walls of the tank were transparent while the back wall and bottom plate were opaque black. During the experiments, the water height was 67 cm in the tank. A transparent Plexiglas® lid covered the upper water surface. Turbulence was generated by two horizontally oriented Plexiglas® grids ( Figure 1B ), oscillating jointly with an amplitude of 5 cm along the vertical dimension. Grid mesh size was 32 mm ( Figure 1C ) and the bars of the grid had a square 8 mm × 8 mm cross section. The outer ends of the grids were “open” with the bars extending 15.5 mm from the outermost bar-crossings. The two grids were mounted 30 cm apart, equidistantly in relation to the center of the water column. Narrow steel rods, 8 mm in diameter, were connected to the corner bar-crossings of the grids as well as to a DC stepping motor (VEXTA, model BLUM440-GFS, Oriental Motor Co. Ltd. Japan) which generated the oscillating motion. Grid oscillation frequency was adjusted by a motor driver (VEXTA, model BLUD40C). All experiments were carried out in a thermo-regulated space where the ambient temperature was kept at 8.0 – 8.5°C. Water temperature during the trials was 8.1 – 8.3°C and the salinity was 33.2 – 34.0 g kg^-1.

Flow velocities within the tank were measured using particle image velocimetry (PIV). The PIV system from LaVision (Germany) consisted of a 1600 × 1200 pixel camera (Imager Pro X with a 50 mm Nikkor lens) and a double pulsed Nd : YAG laser (Quantel Evergreen 70, 70 mJ at 532 nm). The system allowed for single frame- or double frame capture at a maximum frequency of 15 Hz. During single frame capture, the system captures single image frames at a set frequency. Double frame capture implies that pairs of image frames are captured at a set frequency, with a very short time in between frames within pairs. Flow velocities may be calculated from particle displacement between paired images collected using single frame capture or from particle displacement between frames within image pairs collected during double frame capture. Neutrally buoyant hollow glass spheres (HGS−10, Dantec Dynamics), with an average diameter of 10 µm, were used as tracer particles at a concentration of about 7.5 × 10³ particles mL⁻¹.

The laser was mounted to the side of the tank ( Figure 1A ), emitting a 1 mm thick laser sheet aligned with the center of the water column. The camera, mounted horizontally perpendicular to the laser, had a field of view (FOV) with a spatial extent of 86.3 mm × 64.8 mm, fixed in the center of the water mass. The process of finalizing the experimental setup involved testing the system with several alternative grid separation distances and FOV sizes. The chosen settings were proven to produce relevant levels of turbulence while keeping the secondary flow low and, at the same time, allowing larvae to be identified and tracked within the FOV. Due to technical limitations of the PIV system, separate experiments were required for the two purposes of estimating turbulence and study larval swimming.

Four turbulence levels, hereafter referred to as T₁, T₂, T₃ and T₄, were generated by oscillating the grids at frequencies of 0.045 Hz, 0.4 Hz, 0.8 Hz and 1.18 Hz respectively. Estimations of turbulent energy dissipation rates, ϵ, were based on two sets of PIV measurements for each turbulence level. All individual PIV recordings made for this part of the study were proceeded by a 10-minute resting period and a 10-minute spin-up period. Each set of PIV measurements lasted 10 minutes.

PIV velocity vector fields (see Figure S1 for examples) and velocity gradient scalar fields were calculated using cross-correlation in the DaVis (version 8.4) software from LaVision. Image pairs were processed to calculate velocity vectors u and w in the horizontal (x) and vertical (z) direction respectively. For details on PIV data processing, see Supplementary Information section 2 . The turbulent energy dissipation rates were estimated directly from velocity gradient scalar fields, assuming the flow being axisymmetric about the vertical axis (z-dimension) as in George and Hussien (1991):

where v is the kinematic viscosity. The two-dimensional components of the strain rate tensor are time-averaged over the timespan of the PIV recording.

The effect of PIV particles and larval batch on vertical swimming velocity in still water was analyzed with a two-way unbalanced ANOVA using Type-III sums of squares. Both factors were considered fixed. Normal distribution and equal variances of the data were indicated by visual assessment and supported by results from Shapiro-Wilk tests and Levene’s test respectively.

The main objective of the turbulence experiments was to identify possible effects of turbulence on vertically directed swimming of pre-competent L. pertusa larvae. The null hypothesis, stating that 〈w _s〉_Tr = 0, was tested for each combination of turbulence level and larval batch using two-tailed one-sample t-tests. Statistical tests were not applied across turbulence levels. Results from Shapiro-Wilk tests supported normal distribution of data from each group tested except for batch B3 in treatment T₄ [W_B3,T4 = 0.778, p _B3,T4 = 0.025]. For this treatment the non-parametric Wilcoxon signed rank test was performed instead of a two-tailed one-sample t-test. All statistical tests were done in R (R Core Team, 2020) using built in functions as well as the packages car (Fox and Weisberg, 2019) and lawstat (Gastwirth et al., 2019). A significance level α = 0.05 was used throughout.

Turbulence in the grid-stirred tank increased with grid oscillation frequency ( Table 3 ) and estimated turbulent kinetic energy dissipation rates, ϵ, ranged from 9.03 × 10⁻⁹ to 1.05 × 10⁻⁵ m² s⁻³. Temperature and salinity during trials were 8.3°C and 33.3 g kg^-1 respectively, resulting in a kinematic viscosity, v, of 1.42 × 10⁻⁶ m² s⁻¹. Corresponding Kolmogorov length scales, η = (v ³/ϵ)^1/4, were 0.72 – 4.22 mm, implying that the distance, Δx, between PIV vector grid nodes was smaller than the size of the smallest energy containing eddies at all turbulence levels.

The estimated ϵ for set grid oscillation frequencies varied both spatially within the FOV and in-between trials ( Table 3 , Figure S2 ). For turbulence treatment T₄, the estimated in-between trials difference of ϵ was high and comparable to the difference in average ϵ between turbulence treatment T₃ and T₄. For T₁ through T₃, the in-between trials differences as well as the spatial variation of ϵ were small in relation to the relative differences of ϵ between turbulence treatments.

The two-way ANOVA revealed no significant differences in trajectory averaged vertical swimming velocity, 〈w _s〉_Tr, for any of the main factors, i.e., presence of PIV seeding particles [F_(1,76) = 0.06, p = 0.81] or larval batch [F_(1,76) = 0.63, p = 0.43]. The interaction between the factors PIV particles and larval batch was significant [F_(1,76) = 4.11, p = 0.046] because of opposite reactions to the presence of PIV particles for the two larval batches ( Figure 3 ). Larvae in B1 swam on average slower and larvae in B2 on average faster with added PIV particles. Thus, no general effect of the presence of PIV particles on larval vertical swimming performance could be detected.

The 〈w _s〉_Tr estimated for larvae in still water without PIV seeding particles will hereafter be referenced to when comparing with 〈w _s〉_Tr estimated in turbulence treatments. The no-particle estimates are used to allow still water comparison for all three larval batches. In still water, the mean 〈w _s〉_Tr was 0.36 ± 0.11 mm s⁻¹ (mean ± SD) across batches ( Figure 4 ).

Larval swimming in the grid-stirred tank changed with ϵ ( Figure 4 , Table 2 ). The statistical tests indicate that 〈w _s〉_Tr remained significantly positive (directed upwards) in turbulence levels T₁ and T₂ for all three larval batches ( Table 2 ). Across-batch averages of 〈w _s〉_Tr decreased by 24.8% and 30.0% in T₁ and T₂ respectively, compared to 〈w _s〉_Tr estimated from still-water trials ( Figure 4 ). In the two highest turbulence levels, T₃ and T₄, 〈w _s〉_Tr did not differ significantly from zero, except for those estimated from B3 in T₄ for which 〈w _s〉_Tr were significantly negative ( Table 2 ). More detailed statistics on larval swimming are given in Table S1 .

Adjusting the grid oscillation frequency, we generated turbulence with turbulent kinetic energy dissipation rates, ϵ, between 9.03 × 10⁻⁹ and 1.05 × 10⁻⁵ m² s⁻³ in the grid-stirred tank ( Table 3 ). The corresponding Kolmogorov length scales, η, ranged between 0.73 and 4.24 mm, implying that the spatial resolution, Δx = 0.43 mm, of the PIV velocity vector fields was consistently smaller than η. Elevated uncertainty in the estimations of ϵ with decreased turbulence level should be considered, due to the increased risk of estimation errors caused by noise as η increase in relation to Δx (Saarenrinne and Piirto, 2000; Tanaka and Eaton, 2007). By ensuring that the density of PIV seeding particles was sufficient and by adjusting the Δt between frames for optimal particle displacement, the risk for spurious vectors was reduced.

Variations of estimated ϵ, both spatially and in-between trials, indicate some degree of inhomogeneity of the turbulence in the central part of the grid-stirred tank ( Table 3 ; Figure S1 ). Such variations must be acknowledged when interpreting the results since they translate into variation in the turbulence experienced by observed larvae. They do not, however, undermine our possibilities to assess the directed swimming in turbulence since larvae were tracked from all parts of the FOV and during three trials per turbulence level.

We noted that the variation in estimated trajectory averaged vertical swimming velocities, 〈w _s〉_Tr, increased with turbulence ( Figure 4 ; Table S1 ). This may partly be explained by the increased spatial variance of the flow velocities generated within the grid-stirred tank. Such an increase may alter the range of water motion experienced by individual larvae, but moreover it will add uncertainty to the interpolation of flow velocities into larval positions. Interpolation performance tests showed that errors tend to increase with increasing turbulence, although the average difference between interpolated and measured vertical velocities was close to zero for all turbulence treatments. Interpolation errors of this kind do therefore not disallow assessment of larval swimming along the vertical axis.

Our hypothesis was based on the on the argument that turbulent water movements would repeatedly tilt swimming larvae away from their preferred orientation. Larvae swimming with constant speed but in random directions would lead to a decrease in their mean absolute w_s and an increase in the variation. The data is thus consistent with this argument, but the turbulence-dependent uncertainty of the velocity interpolation procedure implies that we cannot make rigorous conclusions regarding speed or directionality of larval swimming in higher turbulence. Our results concerning the influence of turbulence on the vertical swimming in L. pertusa larvae remain solid even though the mechanism/s causing the observed effect could not be identified. A reduction in vertical swimming speed may indeed be attributed to a loss of orientation as suggested by the hypothesis, but it may alternatively be caused by e.g., a reduced swimming activity or a combination of disturbance and altered behavior.

Our experiments were designed to appropriately address the question of how vertical swimming in L. pertusa larvae may be affected by turbulence that they encounter during their pelagic phase. The turbulence intensities to which larvae were exposed in the experiments were therefore intended to be comparable to those encountered in the water column of the open ocean. Field measurements have shown that ϵ of the open ocean typically range between 10⁻¹¹ and 10⁻⁴ m² s⁻³ (e.g., Kiørboe and Saiz, 1995; Fuchs and Gerbi, 2016; Bendtsen and Richardson, 2018; Franks et al., 2022). Corresponding η between 13 and 0.4 mm imply that the smallest energy containing eddies of marine turbulent flows are commonly larger or much larger than the size of L. pertusa planulae. This suggests that L. pertusa larvae are likely to experience turbulence as temporally varying sub-microscale shear in their natural environment.

Below the mixed layer, away from ocean boundaries, ϵ is commonly very low, reflecting weak turbulent mixing, while turbulence may be elevated by several orders of magnitude near boundaries. In a data synthesis presented by Franks et al. (2022), the authors found median ϵ of about 10⁻¹⁰ m² s⁻³ below 100 m depth while rates higher than 10⁻⁸ m² s⁻³ rarely occur below 150 m. Dissipation rates higher than 10⁻⁷ m² s⁻³ were reported as uncommon between 50 and 20 m depth whereas values between 10⁻⁶ and 10⁻⁵ m² s⁻³ are reached during brief events, lasting 10 min or less.

Although not covering the entire span of ϵ observed in the ocean, those generated within the grid-stirred tank were shown to be relevant to the objective of our study. Ranging from roughly 10⁻⁸ m² s⁻³ to 10⁻⁶ m² s⁻³, they compared to ϵ closer to the upper end of the spectrum encountered in the open ocean. Larval vertical swimming was affected by the generated turbulence, with trajectory averages, 〈w _s〉_Tr, of upwards directed swimming speed decreasing with increasing ϵ. In turbulence with dissipation rates of roughly 10^-8 and 10^-7 m² s⁻³, 〈w _s〉_Tr were decreased by 22% and 39% respectively, compared to 〈w _s〉_Tr estimated for larvae swimming in still water ( Figure 4 ). Over this interval, where ϵ increased by one order of magnitude, there was only a small reduction of 〈w _s〉_Tr, from 0.28 to 0.22 mm s^-1. In turbulence with ϵ ≥ 2.28 × 10^-6 m²s^-3, upwards directed swimming was not observed. When exposed to such turbulence, 〈w _s〉_Tr were not significantly different from zero except for those estimated from B3 in T₄ for which significant, relative downward movement was observed.

The average vertical swimming velocity of 0.36 mm s^-1, recorded for 19-days-old larvae in our still water experiments, is lower than the 0.48 mm s^-1 previously recorded for a batch of 27-days-old planulae in the same temperature (Strömberg and Larsson, 2017). Differences between methods, larval age and/or larval batches may explain the discrepancy. Larsson et al. (2014), measured horizontal swimming velocities in short sequences under a dissecting microscope at 8–9°C and registered 0.23, 0.51 and 0.53 mm s^-1 for 7-, 14- and 21-days-old larvae respectively. These observations indicate that one week old larvae are still not fully developed swimmers while 2 weeks old larvae are. Besides the age of larvae, ambient temperature may affect swimming speed. Brooke and Young (2003) noted that swimming speed approximately doubled between 5 and 15°C for planulae of Oculina varicosa, which are of the same size as L. pertusa planulae. Since L. pertusa is a cosmopolitan species found at low to high latitudes and at various depths, its larvae may encounter a large range of temperatures. Adult corals of this species typically thrive at 4–12°C (Rogers, 1999), but water temperatures above their benthic habitats can be very different. Predictions of larval swimming and larval dispersal in L. pertusa are further complicated by the temperature dependent larval development (Strömberg and Larsson, 2017). These complications suggest that relative measures of the effect of turbulence on vertical swimming speed can be more helpful than absolute numbers.

Vertical swimming velocities were positive in turbulence treatment T₁ and T₂ ( Figure 4 ), suggesting that pre-competent L. pertusa larvae perform vertical migration throughout most of the oceanic water column where turbulence is typically weak to moderate (ϵ ≤ 2.07 × 10^-7 m² s⁻³). In T₁, where ϵ ≈ 10^-8 m² s⁻³, the average 〈w _s〉_Tr was roughly 0.3 mm s^-1. Neglecting possible effects of temperature, such a velocity translates to a vertical swimming rate of approximately 26 m d^-1. Active locomotion may thereby enable larvae from most known reefs to reach the mixed layer within a few days to weeks following fertilization. Larvae in the upper ocean will be transported by faster and more dispersive currents [e.g., wind- and wave driven currents (Röhrs et al., 2012)] than those residing in deeper layers where currents are typically slower, primarily density driven and more topographically steered. Ontogenetic vertical migration, and a resulting drift at depths much shallower than those of spawning, has been confirmed for larvae of the deep-sea mussel “Bathymodiolus” childressi (Arellano et al., 2014). The observed pattern was suggested to explain genetic similarities across large geographical distances and biophysical modelling indicated that the depth of larval transport may indeed have a strong impact on dispersal (McVeigh et al., 2017). Analogous modelling results, as well as genetic data, have been documented for L. pertusa (Dahl, 2013; Fox et al., 2016), adding to the notion that effective vertical migration is a mechanism that may strongly impact larval dispersal for deep-sea species with an extensive planktonic phase.

Larvae spawned at shallow sites, such as those located in the North Sea and the Skagerrak, may spend a major part of their pre-competency period within the mixed layer. In this region, during spring when many larvae are likely to be pre-competent, the temperature tends to be lower within the mixed layer than deeper down. For these larvae, time spent in the upper ocean may consequently enhance their dispersal by speeding up their drift as well as by slowing down their development rate.

Following our findings, further detailed studies on the body composition, body density distribution and swimming mechanism in L. pertusa planulae would be of great value. Studies of larval body shape plasticity and possible associated responses to environmental conditions such as turbulence may also reveal highly interesting traits of ecological importance. Our work has shown that pre-competent larvae of the cold-water coral L. pertusa maintain directed swimming in weak to moderate oceanic turbulence, thus allowing them to perform extensive vertical migration in their natural habitat. The mechanics behind the trait is however still to be explored and any future work on the topic would likely reveal information applicable to a wider range of larvae with similar morphology.