Introduction

Almost all scleractinian corals are carnivorous, but most species rely primarily on zooxanthellae for energy (Muscatine and Hand 1958; Muscatine and Porter 1977). However, symbiotic algae alone cannot replace nitrogen, phosphorus, and other essential nutrients needed by the coral host; corals must acquire these from other sources, such as zooplankton, particulate organic matter (POM), or dissolved organic matter (DOM) (reviewed by Muscatine and Porter 1977). The prey captured by corals have only been examined in detail for four species of corals, all Caribbean (Montastraea cavernosa (Porter 1974); Meandrina meandrites (Johnson and Sebens 1993); and M. cavernosa and Madracis mirabilis and Porites porites (Sebens et al. 1998). Even in these studies, questions remain as to the contribution of the marine snow and other hard to measure particulates.

Laboratory and in situ enclosure studies have investigated stomach contents, particle ingestion rates, and flow rates across entire cnidarian colonies (Sebens 1984; Sebens et al. 1997; Sebens and Johnson 1991; Abelson et al. 1993). Although these studies provide critical information on ultimate feeding success, they did not examine the role of polyp morphology in the cnidarian prey capture process. The mechanisms involved in the trapping and transferring of particles to the mouth are still largely a matter of conjecture.

For those corals that appear to filter feed on large, suspended food packets, the filter feeding apparatus consists of circular or longitudinal arrays of delicate, hydrostatically supported tentacles of various sizes and shapes. In many species, these tentacles are photosensitive and remain contracted during the day. This makes direct observations of their role in feeding inherently difficult and may explain why there are so few studies addressing this question (Price 1973; Lewis and Price 1975). Quantitative measurements of parameters affecting encounter and retention of particles have not been recorded for coral tentacles even though examination of the process is deemed critical to a full understanding of the feeding process (Shimeta and Jumars 1991). Thus, information necessary to model capture rates is still lacking for corals.

Because water motion in needed for vigorous coral growth (Darwin 1842; Jokiel 1978; Sebens and Done 1992), it seems most likely that corals have evolved behavior and morphological features to control flow at the level of the colony, polyp, and tentacle. Rubenstein and Koehl (1977) proposed that most filter feeding mechanisms around individual filter elements are operating in flow regimes of low Re (< 40) where viscous forces become increasingly important and eventually dominate when Re < 1. Particles in most suspension feeders are captured using inertial impaction, gravitational deposition, or most commonly, direct interception (Shimeta and Jumars 1991). In calculating Re, most coral studies have described flow in reference to a freestream velocity measured above the colony and used colony diameters or heights as characteristic lengths (Patterson 1984; Helmuth and Sebens 1993). However, these Re values are not applicable to individual coral polyps or tentacles where flow may be dominated by local turbulence and strong velocity gradients. Nowell and Jumars (1984) also suggested that freestream velocity values should not be used to calculate Re for feeding elements, as it is the flow impinging on the filtering element that determines the dynamics of particle interception.

The soft tissue structure of the polyps reflects the complexity of the corallites. The tentacles, which can be considered as the fundamental feeding elements, are also found in a wide variety of sizes, shapes, and complex configurations. How these patterns are related to feeding and other behavioral functions is not understood, nor have their influence on microscale flow dynamics received attention except for some preliminary work by Price (1973). This study examines the role of tentacle length and posture in the feeding of corals and in particular addresses the following questions:

  1. (1)

    Are the tentacle lengths correlated with the flow habitat where each species is most commonly found?

  2. (2)

    What are the approximate Re for flow around tentacles, and is there a predictable range of Re across which they appear to function?

  3. (3)

    Are deflection, retention, and contact dependent on tentacle posture?

  4. (4)

    Could elongated "sweeper tentacles" enhance filter feeding?

  5. (5)

    What are the synergistic consequences of different tentacle arrangements found in polyps?

Dynamic similarity states that the flow patterns around physically similar objects will be the same if the Re of the two systems, the organism in nature and the physical model in the laboratory, is the same (Vogel 1983). Physical modeling of tentacles not only allows working at larger scales for easier observation, but also for isolation and manipulation of their transient positions. We now describe how physical models were implemented to answer the questions posed above.

Materials and methods

Models of coral tentacles

Morphometric measurements of tentacles were collected from underwater macro-photographs (magnification 1:1, 1:2, and 1:3) of 27 Caribbean coral species found in Barbados, and St. Vincent and the Grenadines (Table 1). The base, middle, and distal tentacle diameters, as well as tentacle lengths, were measured from photographic transparencies using a dissecting microscope. Tentacles, being hydrostatically supported soft tissue structures, are inherently variable in form. Tentacle lengths and diameters are affected by different flow regimes, irradiance levels, and diver disturbance (personal observations). Consequently, measurements of at least 10 tentacles in five different polyps were averaged from within several polyps of a single colony and between two different colonies.

Table 1 Tentacle lengths, Reynolds numbers (Res), depth distribution, and diurnal polyp expansion, of 27 Caribbean corals
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The characteristic length used to calculate the Reynolds number (Re) was taken as the greatest length of an object in the direction of the flow. Because tentacle positions vary across a polyp and colony, the tentacle length was used as this characteristic length for Re calculations. The length of the tentacle is an appropriate characteristic length as the moving water in proximity to the tentacle feels the viscous forces exerted on it, and vice versa. As noted below, we gathered flow speeds from the region next to the tentacles for the computation of Re, as our concern is how flow around tentacles impacts particle capture.

For this study, Re was computed for objects in moving water, following Vogel (1983):

$${\text{Re}}\left( {{\text{dimensionless}}} \right) = ({1}/\eta ) \, \left( {{\text{s cm}}^{{ - {2}}} } \right) \times {\text{characteristic length}}\;\left( {{\text{cm}}} \right)\;x\;{\text{flow speed }}\left( {{\text{cm s}}^{{ - {1}}} } \right)$$
(1)

For water, η = 0.01 cm2 s−1, approximately.

The range of tentacle types of both simple and meandrine polyps was typified by two postures: straight and curved. Since the flow over a reef is oscillatory and omni-directional, tentacles curved upstream into the flow during the first half of the oscillation are curved downstream with the flow in the next half oscillation. Thus, three postures were defined: straight, upstream-facing, and downstream-facing (Fig. 1). These generic postures were modeled in Super Sculpey™ approximately 10x life size (7 cm in length). Elongated sweeper tentacles, which are occasionally found on the periphery of Agaricia agaricites and Montastraea cavernosa colonies (Price 1973), were also modeled approximately 10x life size (Fig. 2).

Fig. 1
figure 1

Macro-photographs of Montastraea cavernosa (a) and Colpophyllia natans (b) followed by simplified top and side views of polyp models, and side views of the tentacle models with dimensions

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Fig. 2
figure 2

Vertical encounter zones around model tentacles (upper, middle, base) and the inner () (1.0 local tentacle radius) and outer horizontal region () (3.0 local tentacle radii from top of inner horizontal region) for the three postures of coral tentacles: straight (a), upstream-facing (b), and downstream-facing (c). Local tentacle diameters (white double-arrows) indicated on diagram inside the ellipses. Note that the total extent of the inner and outer horizontal regions totals to 4 tentacle radii and is height dependent. Also, the upstream horizontal region where encounter speeds were measured extends 10 cm for all models, thus farther than the 5 cm implied by the location of the model diagrams. For sweeper tentacles (d), closeness and horizontal regions are presented in top (e) and side (f) view

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Flow speeds

Microscale flow speeds were video-recorded over the surface of expanded colonies of Montastrea cavernosa, Colphophyllia natans, Siderastraea siderea, Meandrina meandrites, Diploria labyrinthiformis, and Dichocoenia stokesii, at 20 m depth at Conch Reef (24.57°N, 80.28°W) off Key Largo, Florida, USA. A Sony V-99 Hi-8 mm video camera in an underwater housing was weighted and held on the substrate at right angles to the oscillating flow, and then manually focused on polyps 10 cm from the macro lens port. An opaque PVC disk with a 2-mm-wide slit opening, fitted on a standard dive light, produced a collimated light sheet that illuminated a 1-cm depth of field (Fig. 3). The trajectories of five particles above each of the 12 different coral heads were measured using frame-by-frame video analysis.

Fig. 3
figure 3

Recordings were made of corals at night to measure micro-flow regimes around and above expanded tentacles. A collimated light sheet, oriented parallel to the flow, illuminated particles in the water and around a band of polyps. The width of the light sheet (perpendicular to the flow direction) just above the polyps was about 1 cm

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Flume

A transportable laminar flow 100-liter flume, two meters in length, was constructed for the project (Fig. 4). The working trough was made of four 50-cm-long clear acrylic sections (15 cm × 15 cm), bolted together in tandem. Flow speeds were controlled by a Bodine Series 400, 1/15 hp motor driving a 12-cm-diameter, double-bladed, plastic propeller. To straighten the flow, longitudinal plates were built within the return pipes to eliminate most of the secondary flow from the propeller. When the flow entered the flume, it passed through four honeycomb Aeroflex™ blocks (5 cm thick with 5 mm channels).

Fig. 4
figure 4

Portable laminar flume used to observe flow patterns around models of coral tentacles. Left inset: average speed profiles + SD (n = 30) as function of height in the upper, middle, and base vertical zones, as defined in Fig. 2. Right inset: key for the components of the recirculating flume

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The tentacle models were placed in the third section of the flume where flow was the most uniform. The wall boundary layer effects could be considered negligible since the projected surface area of the models normal to the flow was less than 2 percent of the cross-sectional area of the flume (Nowell and Jumars 1984; Denny 1988). To reduce the influence of the floor boundary layer, the tentacle was affixed 2 cm above a grid-marked PVC “substrate” platform, on a narrow (2-mm-dia.) stainless steel bolt.

Tracer particles and video analysis

To investigate the motion of particles around the models, finely chopped bean sprout disks (c. 1 mm thick), stained opaque with Tintex™ black fabric dye, were used. They had a mean (n = 50) sinking velocity of 0.25 cm s−1, similar to mucus flocks (0.2 cm s−1; Johannes 1967). The relative density (difference between the freshwater used in the flume and the particle) was of order 10–2 g cm−3, which places them close to invertebrate larvae (3.2 × 10–2 g cm−3; Salzen 1957) (Table 2). Scaled to the models, they are equivalent to particles 100–200 µm, or the size of many invertebrate larvae (Butman 1986).

Table 2 Size, density, and sinking velocity for various marine suspended particulates and tracer particles (sprout slices, n = 50) used for the study
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Video recordings were made using a Sony video camera. A mirror above the flume allowed for simultaneous recording in both the vertical (xz-axis) and horizontal (xy-axis) planes. Frame-by-frame (1/30th s) analyses (position resolution 1 mm) of the paths of 10 particles encountering each vertical zone of the three tentacle postures were performed in both the horizontal and vertical planes from pre-encounter to several tentacle diameters post-encounter (Fig. 2).

Defining horizontal regions and vertical zones of influence

Horizontal travel

Two scales of horizontal (xz-axis) particle travel were used. A coarse scale divided the horizontal recordings into four, 5-cm, equidistant horizontal regions (I–IV) from pre-encounter to post-encounter. Because the behavior of particles close to the tentacle is important in determining the probability of capture by the tentacle, a second scale consisting of an inner region, extending one local radius downstream, and an outer region, extending to three radii beyond this (Fig. 2) was defined.

Vertical travel

The vertical aspect of the tentacle was divided into three equal vertical zones, termed upper, middle, and base. For the straight tentacle, this made the upper zone from 4.8 to 7.2 cm; the middle zone from 2.4 to 4.8 cm; and the base zone from 0.0 to 2.4 cm. In the two curved models, the dimensions for the upper, middle, and base vertical zones were 3.6–5.4 cm, 1.8–3.6 cm, and 0.0–1.8 cm, respectively (Fig. 3).

Computation of particle travel parameters

Particle trajectory distribution

Particles encountering the tentacles within any of the three vertical zones hypothetically could go through any of the inner and outer horizontal regions. Particles that passed through these horizontal regions were expressed as a percentage of the potential 10 particles that hypothetically could enter each vertical zone.

Vertical deflection

The vertical deflection was measured as the difference between inner horizontal region entry point and the region (inner or outer) exit point on the z-axis, with upward deflections positive and downward flections negative. Particle travel paths were not recorded below the tentacle base.

Horizontal deflection: encounter width and particle spread

The cross-stream width of an ensemble of particles before they encountered the tentacles models was measured from path tracings performed 5 cm in front of the tentacle. We call this cross-stream width and the encounter width, and we categorized these widths by the particle approach position on the xy-plane in three horizontal radial regions: (i) within 1.0 local tentacle diameter; (ii) between 1.0 and 1.5 local tentacle diameters; and (iii) beyond 1.5 local tentacle diameters.

Similarly, the cross-stream width post-encounter with the tentacle was measured from an ensemble of particles at approximately five local diameters dl, downstream of the models. The width was taken as the distance from the central axis of the tentacle to the position of the furthest trace path on either side. This distance was then doubled and then transformed into a dimensionless post-encounter spread ratio (ds):

$$d_{s} \left( {{\text{dimensionless}}} \right) = {\text{post - encounter spread }}\left( {{\text{cm}}} \right)/{\text{pre - encounter diameter }}\left( {{\text{cm}}} \right)$$
(2)

For example, if the furthest post-encounter spread measured was 3.6 cm at the base vertical zone of the tentacle, where the local diameter is 2.4 cm, the dimensionless spread value ds is 2(3.6 cm)/2.4 cm, or 3.0.

Time and retention value (r)

The actual time ta, a particle spent within a given region, was measured with a resolution of 1/30 s. The speed at which the particle approached the tentacle (measured 10 cm upstream of the tentacle over 10 frames of video), we call the encounter speed ve. We endeavored to set this speed to approximately 5 cm s−1 in the middle of the base zone, but it ranged 4.5–7.5 cm s−1 because of differences of particle release height in the boundary layer and variations in the flume speed controller (inset, Fig. 4). To allow use of particles approaching at speeds other than 5 cm s−1, we compensated for this experimental variability by normalizing the tracking times of the particles as follows. The time a particle spent in each region was multiplied by the ratio of the actual encounter speed to a standardized speed vs of 5.0 cm s−1. We thus defined a transformed time (tt):

$$t_{t} \left( {\text{s}} \right) = t_{a} (v_{e} /v_{s} )$$
(3)

Thus, if a particle encountered the tentacle at 7 cm s−1, then the actual time that this particle spent in each region would be multiplied by a factor of (7/5) to yield the transformed time.

To calculate retention effects, in the absence of the physical model, it was assumed that particles would have continued in straight-line paths at the (adjusted) freestream velocity. Thus, any distance a particle traveled along the horizontal axis would have a theoretical freestream time ts-value.

We then defined a dimensionless retention value (r):

$$r\left( {{\text{dimensionless}}} \right) = \, t_{t} \left( s \right)/t_{s} \left( s \right)$$
(4)

If an r-value is < 1, the particle must have been accelerated as it traveled around the tentacle. Note, if the r-value > 1, this cannot be equated to a reduction in speed as actual travel distance in a vortex could be much longer than a straight-line freestream distance. However, higher values of r indicate an increase of time spent in the vicinity of the tentacle which would increase the probability of particle capture. In the event of a particle stalling, or prolonged contact against the tentacle surface, the stall time was subtracted from the calculation. This makes the calculation of the r-value conservative. Also, when a particle dropped below the tentacle base (“0” on the z-axis), tracking was terminated.

Particle contacts and rotations

Contacts of particles with the surface of the tentacle were recorded as either a direct frontal impact contact, or if the contact occurred on the downstream side of the tentacle, as a vortex contact. A rotation was defined as an event in which a particle looped or rotated around its axis as it moved horizontally.

Sweeper tentacle

Particles (n = 24) traveling along the elongated sweeper tentacle were tracked on the horizontal axis of the tentacle model through seven 5-cm horizontal regions (A–G) (Fig. 2). However, since the diameter of the sweeper tentacle decreased from the base to its tip, the proximity of the particle from the tentacle surface was divided by the local diameter of the tentacle (Fig. 2) to define a dimensionless closeness value (dcl):

$$d_{{{\text{cl}}}} \left( {{\text{dimensionless}}} \right) = {\text{proximity }}\left( {{\text{cm}}} \right)/{\text{local diameter }}\left( {{\text{cm}}} \right)$$
(5)

The straight-line three-dimensional diagonal distance between exit and entry points of the 5-cm horizontal regions was calculated and then summed to give a conservative estimate of the total travel distance of a particle. The particle retention r-value was calculated as the time spent in each region, transformed to the standardized encounter velocity of 5 cm s−1, and then expressed as a ratio of the freestream time for a particle to cover the same distance. Also, a particle path that crossed over the axis of the tentacle was recorded as a distinct “crossing” event.

Results

Tentacle posture, flow rates, and Re for tentacles

The length of normal tentacles ranged from 0.05 to 1.3 cm (Table 1) in the coral species examined. Sweeper tentacles, 4 and 20 times the length of normal tentacles were measured in Montastraea cavernosa (4–6 cm) and Agaricia agaricites (0.6–1.1 cm), respectively. Examination of the macro-photographs of both simple and meandroid corals indicated that polyps could be considered as having combinations of curved and straight tentacle whorls or rows. In the simple polyps, such as Montastraea cavernosa or Tubastraea coccinea, in addition to the curved tentacles, there are whorls of straight tentacles perpendicular to the plane of the oral disk, as well as horizontal-straight tentacles parallel to the plane of the oral disk (Fig. 1). In both these species, the vertical-straight tentacles were found to be double the length of the horizontal-straight tentacles (Table 1). In contrast, for the meandroid coral, such as in Diploria labyrinthiformis, the vertical-straight tentacles found on the thecal ridge were approximately 30% shorter than the more horizontal-curved tentacles (7.5 mm compared to 10.5 mm).

No correlation was found between the optimum depth at which a coral species was found and tentacle length (R2 =  − 0.08). Flow environments could only be divided qualitatively into three broad categories: fast-flow as found in exposed inshore shallow area (1–5 m depth); moderate-flow for the mid-reef area (5–20 m depth); and slow-flow deep-reef (20–35 m depth). In general, however, coral species found in the shallow and fast-flow habitat have short tentacles (< 0.15 cm) which remain expanded during the day and night. The moderate-flow mid-reef areas are dominated by longer tentacled species that fully expand their polyps at night. In the slow-flow deep habitats, short tentacled species seem to be dominant and they too generally expand their tentacles only at night. However, in this deeper zone, very long tentacled species, such as Mussa angulosa and Scolymia cubensis are also found, and they too fully expand only at night (Table 1).

Flow speeds over the colonies of Montastraea cavernosa, Colphophyllia natans, Siderastrea siderea, Meandrina meandrites, Diploria labyrinthiformis, and Dichocoenia stockesii, filmed at a depth of 20 m averaged 10.7 ± 3.2 cm s−1 (mean ± SD; n = 60), with an oscillatory period of 4.8 s (n = 5). Flow speeds within the tentacles and up to 5 cm above the expanded polyps showed no gradient. Numerous unidentified large zooplankton were attracted to the video light swimming at an average speed of 46 ± 20 cm s−1 (mean ± SD; n = 10). Using the similar flow rate of 10 cm s−1, the Re of the six species ranged from 120 to 1250 (Table 1). Since accurate flow rates are not available for all species, and to cover the range of flow speeds that they would normally experience, Re values were calculated at 5, 10, 25, and 50 cm s−1 (Table 1). All the calculated Res are ≫ and most are well above Re = 40, ranging up to 6250 (M. cavernosa, “top” tentacles).

Tentacle models

The average flow speed in the flume was set to be approximately 5.0 cm s−1, which gave a Re for the models as 3500. This is in the range of the Re encountered by medium to long tentacles in moderate- to high-flow environments and therefore produced similar flow characteristics. The boundary layer descriptions and turbulence intensities for this flume are given in dimensionless form in Patterson (1984).

Particle distribution through horizontal regions as percent occurrence

All particle traces (n = 90) are presented in a composite of posture and encounter vertical zones in Fig. 5, and percentage computations of particle trajectories are shown in Fig. 6. For the straight tentacle, all particles encountering the upper zone tended to stay within the upper encounter zones immediately after passing by the tentacles. Only one dropped into the outer middle zone within the outer region. Middle-zone encounters caused 10% of the particles to drop into the inner base horizontal region and 40% to pass through the outer base horizontal region. All particles encountering the base vertical zone passed through both inner and outer horizontal regions (Fig. 6).

Fig. 5
figure 5

The particle traces through the inner (< 1.0 local tentacle diameter) () and outer (3.0 local tentacle radii from top of inner) () horizontal regions of the three tentacle posture models, in the upper, middle, and base approach sections. Travel along the vertical (x–z axes) and horizontal (x–y axes) planes is shown for the same particle sets (n = 10 for each vertical zone and each posture). The dimensionless spread ratio values (ds) are expressed as mean for N = 10 particles traced

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Fig. 6
figure 6

The distribution of particles (% occurrence) through the inner and outer horizontal regions as defined in Fig. 5 after encountering the different tentacle postures within the three vertical zones (upper, middle, base). Arrows denote direction of flow at midpoint of the vertical encounter zones. In each vertical zone, 10 particles were traced for each tentacle posture

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Particles that encountered the upper vertical zone of the upstream-facing tentacle resulted in particles passing through all six post-encounter horizontal regions. Middle-zone encounters also spread particle distribution, but mostly in the outer middle and base horizontal regions. Base encounters resulted in particles remaining in the base vertical zone.

Particles encountering the downstream-facing tentacle influenced flow reacted quite differently. Upper-zone encounters caused 100% of the particles be retained in both upper horizontal regions. However, middle-zone encounters caused 30% of the particles to be deflected upwards into the upper inner horizontal region and 20% into the upper outer horizontal region. Very few dropped into the base horizontal regions. Base-zone encounters caused particles to be deflected into all six horizontal regions.

Deflection: horizontal and vertical

Vertical deflection

Vertical deflection values across the inner and outer horizontal regions are presented in Fig. 7. The straight tentacle produced a downward deflection in all three vertical encounter zones with the middle zone having a slightly greater effect. The upstream-facing tentacle produced strong downward displacement of particles along its entire length, with the upper horizontal regions causing a strong deflection of an average of 3.8 cm, of the 5.4 cm high model. For the downstream-facing model, there was effectively no downward vertical displacement in either the upper or middle vertical zones. However, there was strong upward lift from the base-zone encounters of 1.2 cm.

Fig. 7
figure 7

Vertical deflection of particles across the inner and outer horizontal regions following encounter with the different tentacle postures. Downward deflection is (−) and upward deflection is (+). Mean ± standard deviation (cm) of particles

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Horizontal deflection

Most of the particles (79%) that were influenced by the tentacle models approached within one tentacle diameter irrespective of the approach height (Fig. 8). Of the remainder, 12% were within 1.5 diameters and 9% beyond this width.

Fig. 8
figure 8

Horizontal post-encounter spread ds (dimensionless), of particles encountering the three tentacle postures in the three vertical zones (upper, middle, and base). The spread is indicated by the arrows and bar, after which particles rejoined the freestream, or remained below the model bases (n = 10 for each zone). Mean ds shown for each zone and overall mean for each tentacle posture. Note that the origins of the three tentacle postures now share a similar origin for ease of interpretation of the post-encounter spread

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The average post-encounter spread values across the three vertical zones were similar for all three tentacle postures (straight, ds = 2.9; upstream-facing, ds = 3.0; and downstream-facing, ds = 3.8). However, the spread for each vertical zone showed a different pattern from one posture to another (Fig. 8).

Particle retention (r)

Coarse-scale retention: horizontal regions

Retention was only slightly positive in the first encounter horizontal regions of all three postures (r = 1.1) but was immediately increased in the subsequent two post-encounter regions (Fig. 9). The upstream-facing tentacle produced the strongest effect in both post-encounter horizontal regions II and III (r = 1.8 and 2.5, respectively). In the straight tentacle regions, r = 1.7 (II) and r = 1.6 (III), and the downstream-facing tentacle retention was slightly less, where both r-values equaled 1.5. By horizontal region IV (beyond 10 cm), most particles, except for those that had dropped below the baseline, were returning to freestream velocities.

Fig. 9
figure 9

Retention r-values and standard deviations of particles passing through the horizontal encounter regions of the three tentacle models. (The limitations of the video setup did not permit measurements in the upstream-facing Region IV.) Note that the origins of the three tentacle postures now share a similar origin for ease of interpretation of the post-encounter spread

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Fine-scale retention—inner and outer horizontal regions

Straight tentacle: Upper-zone encounters had moderate average retention of inner r-value = 1.7 and outer r-value = 1.4, except for one particle that accelerated through the outer middle horizontal region for an r-value = 0.5 (Fig. 10). Middle-zone encounters had a relatively low inner retention r-value (r = 1.2) but had a much higher outer value (r = 2.9). One particle was retained in the inner base region for a long period for an r-value of 14.0. Particles encountering the base zone gave similar retention values in both the inner and outer horizontal regions (r-value = 1.5).

Fig. 10
figure 10

Retention r-values in the inner and outer horizontal regions following particle encounters (n = 10) with the different tentacle postures in the three vertical zones (upper, middle, base). N above the bars indicates the number of particles (of the 10) that were deflected into each horizontal region

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Upstream-facing tentacle: Average upper-zone encounters r-value was 1.6 (Fig. 10) with most particles traveling downward where they were strongly retained in the inner middle and base horizontal regions (middle r = 7.9, and base r = 4.6). Middle-zone encounter particles experienced more uniform retention (inner r = 1.2 and outer r = 1.1), with a consistent higher value in the outer base region (r-value = 2.6). Base-zone encounters were moderate (inner r = 1.2 and outer r = 1.9); however, particles that dropped below the xz-axis were not recorded.

Downstream-facing tentacle. Particles encountering the downstream-facing tentacle within the different vertical zones produced very different retention values, but generally produced strong retention, particularly in the inner vertical zones for particles approaching the middle and base vertical zones (Fig. 10). Upper-zone particles were only slightly retained close to the lee surface (inner r = 1.7; and outer r = 1.8), and none dropped into lower vertical zones. Middle-zone encounters indicated a marked retention and upward influence. Particles spent little time (inner r = 1.1; and outer r = 2.7) in the middle vertical zone, but many traveled upwards into the upper vertical zone where they experienced strong retention (inner r = 10.9; and outer r = 2.5). Particles approaching the base vertical zone demonstrated a similar influence of strong vertically entrainment and retention (inner r = 1.8; and outer r = 4.8). Those that traveled upwards close to the tentacle and were particularly strongly retained in the middle vertical zone (inner r = 16.8; and outer r = 9.7), and somewhat less, but still strong in the upper vertical zone (inner r = 9.2; and outer r = 1.8). Outer retention in the base and middle horizontal regions was moderate.

Tumbles and contacts

Almost all particles had paths that rotated or looped following an encounter with the tentacle models (Fig. 11a). The vertical straight model produced the least events (77%) and the upstream- and downstream-facing slightly more (87 and 93%, respectively). There was no significant influence of the encounter heights.

Fig. 11
figure 11

Rotations (a) and contacts (b) of particles following encounter with tentacle models in each vertical zone

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For particles that encountered the three tentacle models, 61% contacted the model. Of these, 91% directly impacting the frontal surface and 9% contacted the lee side as they traveled in vortices. Again, there was no significant influence of the encounter heights.

Frontal contacts accounted for 100% (n = 16) in the straight tentacle, 88% (n = 11) in the upstream-facing tentacle, and 92% (n = 26) in the downstream-facing tentacle. Overall, the downstream-facing tentacle experienced that highest frequency of contact (Fig. 12).

Fig. 12
figure 12

Tracer particles (n = 24) around the 35-cm-long sweeper tentacle model. The shaded “closeness” area is 2.0 local diameters wide (a and b). Other sub-figures: c closeness values along tentacle; d straight-line travel distances between horizontal regions (A-G); e retention r-values; f percentage of particles that contacted, rotated, or crossed the tentacle axis within each horizontal region

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Sweeper tentacle

Almost all the particles (21) that encountered the sweeper tentacle (n = 24) tended to travel along the length of the tentacle and remain within the arbitrary “closeness” envelope despite the effects of gravitational fall (Fig. 12a-c). The mean distance away from the tentacle surface was only slightly greater than the local diameter (mean = 1.1; SD = 0.73). Summing the straight-line distances between exit and entry points along the horizontal regions (A–G) indicated that particles followed courses 20% longer than a freestream straight-line path (Fig. 12d). Retention values along the horizontal regions ranged from r = 1.05–1.43, with a mean r = 1.31 (Fig. 12).

During this travel, particles behaved much differently than if they had remained in the freestream (Fig. 12d). Every particle tumbled, contacted, and crossed over (or under) the tentacle axis at least once. Activity was highest at mid-length, with activity dropping off in the last two regions (Fig. 12f).

Discussion

Flow regimes and length of coral tentacles

A compilation (Table 1) of depth distribution (Goreau and Wells 1967) and ecozones (Liddell and Ohlhorst 1987) did not give a significant correlation between tentacle length and depth (R2 =  − 0.08). This result suggests that either there is no correlation, or that the data are inadequate to answer the question. However, distribution is apparently further complicated by the role of phenotypic plasticity in some species. Individual colony morphology appears to allow, at least in two common Caribbean species, Madracis mirabilis (Sebens 1997) and Agaricia agaricites (Helmuth and Sebens 1993), to live across a wide depth range of the same Jamaican reefs. Madracis mirabilis (2–22 m depth) changes branching in response to the local micro-flow conditions. These studies indirectly support the hypothesis that tentacle length and microscale flow values are linked, but further confirmation will require morphological descriptions of individual colonies, as well as micro-flow measurements at the polyp level.

In the corals examined, tentacle lengths spanned a range of 0.05–1.3 cm, with sweeper tentacles up to 4 (A. agaricites) and 20 (M. cavernosa) times longer (Table 1). The inherent flexibility of tentacles, especially in the mid-range and longer tentacles (0.53–1.2 cm), allows them to bend in response to flow or when feeding (Fig. 13), but in general their postures can be described as either straight, or curved.

Fig. 13
figure 13

Examples of common coral species found across a typical Caribbean reef in the shallow-reef (a, b), mid-reef (c, d, e, f), and deep-reef (g, h, i, j) zones, showing the wide variation in soft tissue structure and tentacle sizes

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Smaller tentacled corals (0.05–0.23 cm) found in shallow fast-flow environments (10–25 cm s−1) have Re ~ 100–500. The longer (0.36–1.01 cm) tentacled species have Re (300–3000) (Table 1). These values indicate that corals live in a world of turbulent rather than laminar flow (LaBarbera 1984). Although the tentacle models used in this study are in the upper range (Re = 3500), they are well within the prerequisite “same order of magnitude” of Re to reflect the same flow patterns (Vogel 1983). We can assume, therefore, that the microscale flow patterns produced by the models are like those produced by mid-sized coral tentacles.

Particle behavior following encounters with tentacles

Vertical deflection

Near-bed boundary layers in temperate waters have been reported to have strong vertical gradients (Vogel 1983; Nowell and Jumars 1984), and within this narrow layer seston rapidly changes particle concentration and composition, with the lighter, nutrient rich particles found mostly 5 cm above the seabed (Muschenheim 1987). Assuming a similar near-bed boundary layer exists over coral reefs, a vertical extension strategy of feeding elements would appear to be advantageous to many coral species. Indeed, Sebens et al. (1998) found that zooplankton capture in the field was greatly affected by morphology and polyp size and that predation on zooplankton was encounter limited.

The specific postures of tentacles result in significant changes in the vertical deflection over the surface of a coral polyp. The downward deflection of straight tentacles increases effective filtering height. In the simple polyps, the strong downward deflection of the upstream-facing tentacles would greatly increase particle flux toward the polyp oral region. The strong upward lift from downstream-facing posture, on the other hand, may be important in not only keeping particles within the filtering array of tentacles in the contiguous polyps, but prevent particles from accumulating below and between the polyps.

Horizontal encounter width and spread

The encounter width of particles was found to be slightly less than the width of the tentacle. However, given the repetitive nature of the tentacle arrays over the surface of a colony, particles traveling through this array would seem to have a high probability of impacting a tentacle surface. This possibility would become greater as the vertical-straight tentacles tend to drive particles downwards where the frontal area of impact increases with the width of the tentacle base. On the other hand, the average post-encounter spread ratio following encounter with a tentacle is large (ds = 3.2), which would cause particles to diffuse across a colony and consequently increase probability of impacting upon a tentacle.

Retention of particles

The finding that particles are retained in the wake of the model tentacles is predicted from basic fluid mechanics, although a “tapered cylinder” is not a simple condition and has not been investigated at these Res. The vortices formed at the lee surface of a cylinder are the agents responsible for the increased “holding time,” and in flow rates over Re = 40, they begin to shed irregularly (Vogel 1983; Blevins 1984). Analogous engineering studies have shown that this turbulence increases the heat transfer coefficient within the boundary layer of a cylinder by approximately 80 percent by the continual renewal of “fresh” fluid to the surface by the turbulent eddies (Kestin et al. 1961). This same mechanism has been hypothesized to be applicable to particle encounter through interception and impaction (Patterson 1991). The empirical results of this study, and in particular the retention values, support this prediction.

Retention in the immediate post-encounter regions was found for all three tentacle positions. It was particularly strong in region III behind the upstream-facing tentacle (r = 2.5), compared to the straight and downstream-facing models where the wake appeared to be disintegrating and retention values dropped to r = 1.6 and 1.5, respectively (Fig. 9). Retention of particles 1.5–2.5 times their freestream value has important implications to particle settlement over oral surfaces. Several species are believed to use mucus as a method of entrapping particles over their oral surface (Lewis and Price 1975) and increase in time would allow for significant settlement of many particles within the seston.

However, closer analysis found that retention was focused within one local tentacle diameter, especially in the downstream-facing tentacle, where retention r-values reached 10.9 in the upward third and 16.8 in the middle regions. This has significant implications to potential feeding success of a suspension feeder, as direct frontal interception of particles on the upstream collecting surface is not necessarily the only opportunity to trap a particle. These leeward vortices hold or often return the particles very close to the tentacle surface.

Rotation and tumbling of particles

All three tentacle postures increased the rotation of particles encountering tentacles. Since direct interception by a feeding element is dependent on particle diameter (Rubenstein and Koehl 1977), rotating and tumbling by any object in the flow field would increase the effective “width” of a particle by extending the particle beyond its freestream path and will increase probability of contact. The turbulence of the vortices results in inherent high standard deviations in all the parameters measured. Larger sample sizes would undoubtedly have reduced them, but despite these constraints, the overall patterns were consistent and have given insight and appreciation of the dynamics.

Capture rates

The results of this study could be incorporated into predictive models of capture rates by polyps, provided that retention efficiencies for particular particle types are assumed (or measured). Shimeta and Jumars (1991) note that maximization of encounter rate vs. encounter efficiency is affected differently by flow advection vs. size of the particle collector. As they note, “Retention converts encounter into capture and is therefore equally important to study.” Our work provides quantitative insights into the magnitude of localized encounter rate that could thus be used to provide a framework for a predictive capture rate model.

Sweeper tentacles

Sweeper tentacles have been found in several coral species (Price 1973; Chornesky and Williams 1983; Logan 1986; Lang 1973). Although the presence of sweeper tentacles is generally described as an aggressive response to contiguous neighbors, the sweeper tentacles of the M. cavernosa colony photographed in this study was not contiguous with another colony, and some of the polyps with sweeper tentacles were central in the colony. It is proposed that these tentacles had been extended for feeding, as results of this study support feeding as a potentially effective strategy.

Particles passing along sweeper tentacles remained closer to the tentacle surface, following erratic, but longer paths (20% longer on average), resulting in an overall average retention r-value = 1.3 (Fig. 12e). In addition, all particles were not only tumbled, but also made contact at least once with the tentacle surface.

The rigid model is most likely to have different results than a live tentacle. Field observations, for example, found that the flexibility of these tentacles allows them to be swept back and forth in the oscillating currents, causing them not only to flutter, pass through a much greater volume of water, and in so doing, probably increase encounter probability.

Tentacle combinations in simple and Meandrine Polyps

Coral planulae have bilateral symmetry and research summarized by McFadden et al. (2021) makes a strong case for most Cnidaria as truly bilaterian. We note that after metamorphosis from a planula into a polyp, a secondary radial symmetry appears, and is flow direction independent, probably an adaptation for a sessile lifestyle (Malakhov 2016). In a simple polyp, such as Montastraea cavernosa, the tentacle whorls around the oral disk are a combination of straight and curved tentacles (Fig. 14). This configuration would cause particles approaching the upstream side of the polyp to be deflected downward by both the vertical-straight and upstream-facing tentacles. As the flow continues across the oral disk, the downstream-facing and vertical-straight tentacles will deflect particles almost horizontally to the next polyp rather than downward between the polyps (Figs. 14, 15). In addition, colonies of simple polyp species generally have curved surfaces; thus, exiting currents would primarily deflect particles directly into the upstream-facing and vertical-straight tentacles of the adjacent polyp, where again the particles are subjected to further retention and increased probability of contacts and rotation (Fig. 15).

Fig. 14
figure 14

Synergistic effect of tentacles and positions found around the oral disk of a simple coral polyp. The "upstream-facing" curved tentacles on the perimeter of the disk are first to encounter the current, along with whatever food packets it is carrying, and they deflect the current downward to the oral disk. As the current exits the oral disk area, it encounters mirror image "downstream-facing" curved tentacles whose base zone deflects current upwards. The current runs directly into the "upstream-facing” tentacles of the adjacent polyp and is re-filtered

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Fig. 15
figure 15

Synergistic composite of vertical particle deflection due to different postures of model tentacles on simple (e.g., Tubastraea) and meandrine (e.g., Colpophyllia) polyps. Particles deflect toward the oral disks in both models, and oscillating currents simply reverse the flow with the same results

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In meandroid corals, tentacle ridges can be described, at least in general, as having a double hedgerow of tentacles on the edge of the thecal walls; one set of vertical-straight alternating with a second set of tentacles curved inwards across the thecal ridge (Fig. 15). In the composite vector drawing of this scenario, it is proposed that over meandroid polyp surfaces, vertical-straight tentacles again would influence particles downward into the thecal valleys where the oral surface and mouths are located. The curved tentacles, on the other hand, would seem to keep the thecal wall free from accumulating particles as they deflect particles upward across the thecal wall where they then meet an upstream-facing tentacle hedgerow that deflects particles downwards toward the oral valley (Fig. 15). The process is simply reversed with the same results in the next flow oscillation.

To further understand feeding mechanisms and distribution of corals, more information is needed on the microscale flow conditions in the field over individual colonies. Only a few such studies have been made with limited numbers of species, depth ranges, and flow habitats (Shashar et al. 1996; Hench and Rosman 2013; Stocking et al. 2018). Recently, Shavit et al. (2022) achieved in situ measurements using particle image velocimetry (PIV) around a massive species (Dipsastraea favus), when the polyps were expanded and contracted. They noted that when tentacles were expanded, the flow altered substantially into a canopy flow (sensu Nepf 2012) very different from the boundary layer flow present when tentacles were contracted. Many of their observations on increased residence time, velocity fluctuations, and mixing around the tentacles are congruent with observations of flow around our flexible models.

A recent review on the turbulence characteristics over coral reefs makes a strong case that such further work is needed, e.g., the role of spatial variation from upstream colony wakes on momentum flux (Gardella and Edmunds 2001; Davis et al. 2021). Hench and Rosman (2013) observed strong recirculation zones induced by the colonies themselves and enhanced Reynolds stresses in the shear layers around the periphery of wakes. How these colony-induced aspects of the flow field affect particle capture and mass transfer remains an active area of research.

The momentum boundary layer and diffusive boundary layers around corals are affected similarly by details of flow around corals, including the polyps. The momentum boundary layer is about an order of magnitude thicker than the diffusive boundary (Shashar et al. 1996), but both respond to changes in the flow field in a qualitatively similar way. Mass transfer of dissolved substances to coral colonies has been shown to be dependent on morphology and flow regime (Patterson et al. 1991; Patterson 1992a, b). Inasmuch as mass transfer and particle flux respond similarly to the flow field, more work is needed on small-scale details of the flow at the level of the polyp. Indeed, laboratory experiments (Reidenbach et al. 2006) and modeling based on field measurements shows the importance of flow in enhancing mass flux in branched coral colonies (Kaandorp et al. 1996; Chang et al. 2014).

Because coral tentacles exhibit such a diversity of shape and size, they most likely have several functions which vary between species. Malul et al. (2020) recently showed that the elasticity of the tentacles results in motions that are out-of-phase with oscillatory flows, thereby enhancing mass transfer around the polyp. Microscale flow modulation by tentacles within polyps is but one of their functions, and physical modeling allows insight into this process. Future research should integrate studies of coral form and function for both particle capture and mass transfer to better understand the physiological limits to coral performance in this era of climate change.