FLOW PATTERN AROUND THE RIGID CEPHALIC SHIELD OF THE DEVONIAN AGNATHAN ERRIVASPIS WAYNENSIS (PTERASPIDIFORMES: HETEROSTRACI)

Authors


Abstract

Abstract:  Palaeozoic armoured agnathans (or ostracoderms) are characterised by having an external, bone shield enclosing the anterior part of their bodies, which demonstrate great diversity of both forms and sizes. The functional significance of these cephalic shields remains unclear (they may have been a functional analogue of the vertebral column, or merely afforded protection). Here we assess the importance of the cephalic shield in terms of locomotion. In order to do this, we have studied flow patterns of the Devonian heterostracan Errivaspis waynensis (White, 1935), using an anatomically correct model of E. waynensis positioned at different pitching angles. The fluid flow was visualised in a wind tunnel, using planar light sheet techniques, adding vaporised propylene glycol to the fluid. The flow pattern over the cephalic shield of Errivaspis is dominated by the formation of leading-edge vortices (LEVs). When the model was positioned at angles of attack of -2 degrees or higher a pair of nearly symmetrical, counter-rotating primary vortices were produced, which flowed downstream over the upper surface of the cephalic shield. At moderate angles of attack, LEVs remained attached to the dorsal surface, but, as the angle of attack increased above 7 degrees, vortices began to separate from the surface at posterior locations. At a high angles of attack (around 12 degrees or 13 degrees), vortex breakdown (or vortex burst) occured. The body-induced vortical flow around the cephalic shield is very similar to the that described over delta wing aircraft. This strategy generates lift forces through vortex generation (vortex lift). Based on this analogue and knowing that Errivaspis lacked pectoral fins or any other obvious control surfaces, vortex lift forces added through this mechanism may have played a major role in the locomotion of these primitive fishes, not only to counteract the negative buoyancy of the fish, but also as a means of manoeuvring.

Living agnathans or jawless fishes (lampreys and hagfishes) represent only a minute portion of the once great morphological diversity that the group achieved in the past. They dominated vertebrate faunas during Ordovician, Silurian and Devonian times. Most of these Palaeozoic agnathans were armoured forms (e.g. heterostracans, osteostracans, galeaspids and pituriaspids), characterised by having a large, rigid external shield enclosing the anterior part of the body, whilst the rest of the body and the caudal fin were covered by scales. Although armoured agnathans have been extensively studied from the biostratigraphical, taxonomical and phylogenetic point of view (see Janvier 1996; and references therein), the functional significance of their rigid carapaces remains unclear. Mark-Kurik (1992) summarised previous interpretations on the function of the armour in these agnathans. However, she proposed that the carapaces of these agnathans should be considered “first of all from the aspect of locomotion”. The great diversity of shapes and sizes found among the cephalic shields of armoured agnathans (see Janvier 1996 for an overview), the development of fixed exoskeletal elements with clear hydrodynamic importance, as lateral expansions and dorsal spines or keels, their large rostrums, and the variation in the position of the branchial openings, especially in heterostracans, support Mark-Kurik’s (1992) hypothesis.

Little is yet known about the hydrodynamics of the cephalic shield in armoured agnathans (but see, e.g. Kermack 1943; Bunker and Machin 1991), but a recent detailed studies on the flow patterns around some species of boxfishes, a group of living teleosteans that also have the anterior region of their bodies encased in rigid bony carapaces (Bartol et al. 2002, 2003, 2005) provided new insights. Bartol et al. (2002, 2003, 2005) proved that the rigid carapaces produce leading-edge vortices (LEVs) capable of generating self-correction trimming forces during swimming trajectories in boxfish. These regions of attached vorticity are strongly correlated with regions of low pressure, producing suction forces on these areas, which are significant for trim control. Thus, the carapaces of these fish play an essential role in their hydrodynamic stability of swimming.

Under these considerations, we have studied the flow pattern around the rigid cephalic shield of Lower Devonian pteraspidid Errivaspis waynensis (White, 1935) (Text-fig. 1), previously known as Pteraspis rostrata (Agassiz, 1835) var. waynensis and P. rostrata (Agassiz, 1835) var. toombsi (see Blieck 1984 for nomenclatural discussion). Pteraspidids are characterised by having a cephalic shield of dentine and acellular bone (aspidine), composed of 11 main cephalic plates separated by sutures, including paired cornual plates and a dorsal spine. The rest of the body and the caudal fin are covered by small scales. A single, common external branchial opening, covered by a branchial plate, is present on either side of the head armour, near the cornual plates. The mouth is surrounded by elongated, probably movable plates. Pteraspidids lacked paired and median fins except for the caudal one. They also present a system of deep, closed canals on the dorsal disc, probably related to the sensorial organs (Blieck 1984). Most pteraspidids show streamlined bodies, having a fusiform cephalic shield, which is ventrally bulged and dorsally more flattened and have a triangle-shaped planform with an elongate rostral plate, and a distally flexible body.

Figure TEXT‐FIG. 1..

 General aspect of Errivaspis. Abbreviations: bo, branchial opening; c, cornual plate; cf, caudal fin; d, dorsal plate (also dorsal disc); ds, dorsal spine; m, mouth; o, orbital plate; r, rostral plate; s, scales; v, ventral plate (also ventral disc). Adapted from White (1935).

This paper aims to describe the vortical flow pattern observed around the bone cephalic shield of Errivaspis waynensis, as well as to investigate its possible function in locomotion. This species was chosen because it has been the subject of previous work on its locomotion and life habits, and because it represents a generalised morphological type among pteraspidids, which makes our results potentially widely useful in interpreting other similar or related species.

Material and Methods

A generic, anatomically correct model of Errivaspis waynensis (Text-fig. 2) was initially made in clay based on the reconstruction displayed in the National Museums Scotland, and after available morphological reconstructions (Blieck 1984; Janvier 1996). From that, a two-part silicon cast was obtained, which was filled with fast hardening epoxy resin. Once ready, this 23 cm long model was polished to correct small surface imperfections. The material chosen proved suitable to be pierced with little holes for adding anchorages and weights.

Figure TEXT‐FIG. 2..

 Resin model of Errivaspis used in wind tunnel texts positioned at null angle of attack (α = 0º). Note that at the considered α = 0º, the leading edge of the cephalic shield (αl-e = 0º) sustains a positive angle of about 6º. A. Lateral view. B. Dorsal view.

The model was then mounted to a rigid rod that allowed for variation of the angle of attack and studied in the wind tunnel of the Instituto de Mecánica de Fluidos de la Facultad de Ingeniería, Universidad de la República (Montevideo, Uruguay). This facility is 17 m long, 2.25 m wide and 2 m high, with a maximum wind speed of 30 m/s. The pressure gradient can be adjusted by moving the vault vertically. It is also equipped with an anemometer and a system of visualisation based on light cuts (see below).

Despite the differences in the properties of both fluids (air in the case of the analysed model, water in the case of the fish when alive), several studies have demonstrated good agreement between wind and water tunnel dynamic tests (Erickson 1980; Wolffelt 1986; Malcolm and Nelson 1987; Suárez and Malcolm 1994). Thus, if the Reynolds number (Re) of the model in the wind tunnel is equivalent to the Reynolds number of the fish in water, the air flow round the model is dynamically similar to the water flow round the fish (Bunker and Machin 1991). This quantity is calculated as:

image

where l is a relevant length in metres, u is the velocity of the flow in m/s, ρ is the density of the fluid in kg/m3, and ν is the viscosity of the fluid in kg/m/s (ρ/ν is called the dynamic viscosity, η).

Flow visualisation along the model was made adding smoke (vaporised propylene glycol, chosen because it is non-toxic and non-carcinogenic and does not contaminate or damage the test facility) to the fluid. Smoke was emitted from a thin tube place upstream from the model. The distribution of smoke particles was then visualised by illuminating a plane of the flow field (Text-fig. 3). The model was tested at different angles of attack (α, or pitch angles), covering a range from −20 to +20 degrees and at 1 degree increments. The null angle of attack (α = 0 degree) is defined in regard to the horizontal position, or geometric zero, of the fish. In this position, the leading edge of the cephalic shield sustains a positive angle of about 6 degrees (Text-fig. 2). For each studied angle of attack, the flow field was cut by transverse (YZ) planes placed at successive longitudinal positions from the anteriormost part of the model up to the end of the cephalic shield. Planes at different longitudinal positions were photographed and geometrically integrated to reconstruct the whole flow field along the model. The model was positioned in the wind tunnel at a wind speed of approximately 9 m/s, which resulted in Re of 1.45 × 105. This is the equivalent of a 0.23 m fish swimming in sea water at 20°C at about 0.65 m/s (approximately three body lengths per second), which can be considered realistic for a fish of that size.

Figure TEXT‐FIG. 3..

 Scheme of the test in the wind tunnel to observe the flow through the model of Errivaspis. Black arrows indicate the direction of the flow. The light sheet allows the visualisation in that longitudinal plane.

Results

Smoke flow visualisation provided a good global qualitative description of flow around the model. The flow on the dorsal surface of the model was dominated by vortical structures created at the rounded leading edges of the cephalic shield, this is summarised in Plates 1 and 2. At some angles of attack (see below) the flow is characterised by a pair of nearly symmetrical, counter-rotating vortices formed roughly parallel to the leading edges. These remain attached to the dorsal surface of the model. The formation, attachment and decay of these leading-edge vortices depend on the angle of attack. Thus, at more negative values of attack than -2 degrees, signs of vortical structures were not observed (Pl. 1, figs 1, 4, 7, 10). Regions of attached vorticity started developing at α = -2 degrees, at a longitudinal location about 2 cm from the rostral tip. The vortex core was well defined at α = 0 degree (Pl. 1, figs 2, 5, 8, 11). From α = 0 degree to α = 7 degrees (Pl. 1, figs 2–3, 5–6, 8–9, 11–12; Text-fig. 4), two attached counter-rotating (from the rear of the model, clockwise in the right side and counterclockwise in the left side) vortices formed on the dorsal surface of the model. These vortices remain fixed along the entire dorsal disc until the posterior edge of the cephalic shield, behind the space between the dorsal spine and the cornual plates, some 11 cm from the tip (Pl. 1, figs 11–12). The strength and circulation of the vortices intensified as the angles of attack increased. At angles of attack of more than 7 degrees, the vortex core began to separate from the body at posterior locations. The longitudinal positions at which vortices left the body depended on the angle of attack. Thus, at α = 8 degrees the vortices began to detach slightly from the body at the level of the cornual plates (Pl. 2, fig. 10). At α = 11 degrees vortices detached from the body more anteriorly, near the branchial openings, some 9 cm from the rostral tip, and they were clearly separated from the model near the cornual plates (Pl. 2, figs 8, 11), revealing occasionally vortex burst (or vortex breakdown, see below). The breakdown of the vortex core is evident above the posterior portion of the carapace at α = 14 degrees (Pl. 2, fig. 12). The breakdown point moves forward as the angle of attack increased. At α = 19 degrees vortices separated from the body and the bursting of the vortex core occurred immediately after they formed, about 3 or 4 cm from the rostral tip.

Figure EXPLANATION OF PLATE 1.

Figure EXPLANATION OF PLATE 1.

 Figs 1–12. Smoke flow visualisation over Errivaspis model at Re of 1.45 × 105 I. The flow is visualised in two dimensions by using planar light sheet techniques adding vaporised propylene glycol to the fluid. Model was positioned at pitch angles of –5° (1 4, 7, 10), 0° (2, 5, 8, 11) and +5° (3, 6, 9, 12), as is indicated in the upper side of the plate. For each angle of attack (columns) the flow field was cut by successive transverse (YZ) planes (files). The longitudinal locations of the transverse plane are indicated in the left side of the plate. Each plot is a representative photogram captured from a running film taken from the rear of the model. At angles of attack of more than -2º (see text) the leading edge of the cephalic shield generates a pair of nearly symmetric, counter-rotating (clockwise in the right side and counterclockwise in the left side) primary vortices which remains attached to the dorsal surface of the model.

Figure TEXT‐FIG. 4..

 Reconstruction of the whole flow field over Errivaspis cephalic shield at pitch angles of 5º. The position and aspect of the vortices is based on a geometrical integration of transverse planes at different longitudinal positions (see Pls  1 and 2). A. lateral view. B. dorsal view. In A, the leading edge vortices are cut by four successive transverse planes.

Figure EXPLANATION OF PLATE 2.

Figure EXPLANATION OF PLATE 2.

 Figs 1–12. Smoke flow visualisation over Errivaspis model at Re of 1.45 × 105 II. The flow is visualised in two dimensions by using planar light sheet techniques adding vaporised propylene glycol to the fluid. Model was positioned at pitch angles of +8° (1, 4, 7, 10), +11° (2, 5, 8, 11) and +14° (3, 6, 9, 12), as is indicated in the upper side of the plate. For each angle of attack (columns) the flow field was cut by successive transverse (YZ) planes (files). The longitudinal locations of the transverse plane are indicated in the left side of the plate. Each plot is a representative photogram captured from a running film taken from the rear of the model. At pitch angles of attack of +8º, the vortex core began to separate from the body at posterior locations (8, 9, 11). At angles of attack of +14º and more positives (see text) breakdown of the vortex core occurs at posterior locations of the model (12).

In summary, the flow pattern around the rigid cephalic shield of Errivaspis is strongly dominated by the formation of leading-edge vortices At angles of attack above -2 degrees, the transverse flow separated from the leading edges and formed a pair of nearly symmetric, counter-rotating primary vortices which flow downstream over the upper surface of the cephalic shield. The vortices formed nearly parallel to the leading edges and remained attached to the dorsal surface. Under the primary vortex, the formation of a secondary vortex spiralling opposite to it could also be observed but not as clearly as the primary vortices. The formation this secondary vortex is due to viscosity effects when the fluid is trapped between a surface with friction and the primary vortex (Tormalm 1995). As the angle of attack increased the leading-edge vortices began to separate from the model at posterior locations and at a sufficiently high angle of attack (about 12 degrees or 13 degrees), these leading edge vortices underwent a dramatic disorganisation, associated with a sudden radial expansion of the vortex core, known as vortex breakdown (Werlé 1954; see also Mitchell and Delery 2001; Lucca-Negro and O’doherty 2001, for updated reviews), which result in the destruction of the vortices.

Discussion

Vortex lift forces in Errivaspis

The vortical flow pattern observed around the rigid cephalic carapace of Errivaspis is very similar to the vortical flow over a delta wing (e.g. Bertin and Smith 1989; Anderson 1991) and summarised in several review articles (see Lee and Ho 1990; Gursul 2005 and references therein). Delta wings (after the Greek letter delta, Δ) are swept-back wings that have a planform in the shape of a triangle. Delta wings are present in several aircraft such as the supersonic airliner Concorde, the US space shuttle or the modern Eurofighter Typhoon. The flow structure on the upper side of a delta wing is dominated by vortical regions created at the leading edge. As the angle of attack increases, separation starts from the leading edge and produces a pair of virtually symmetrical vortices which remains attached to the upper surface of the wing and have a conical shape growing streamwise. The leading-edge vortices induce a field of low pressure over the wing, producing a suction effect, which results in an increase in lift usually referred to as non-linear or vortex lift (Polhamus 1966). At high angles of attack the vortex core bursts (see above) and the suction effect disappears (Wentz and Kohlman 1968).

The high degree of similarities between the vortical flow pattern observed around the rigid cephalic carapace of Errivaspis and that over a delta wing clearly suggest that, during forward swimming, the rigid cephalic shield of Errivaspis could have operated hydrodynamically in a similar manner as a delta wing do. Thus, the body-induced vortices generated over the dorsal surface of Errivaspis carapace must have induced a low pressure field and hence a suction effect, resulting in the generation of vortex lift forces.

The hydrodynamics of Errivaspis was originatelly studied by Kermack (1943). According to this author, since the animal must have been denser than water and lacked pectoral fins, the lift that counteracted the weight of fish in water must have been obtained by an inclination of the whole body (positive angle of attack), using it as an hydrofoil during forward movement. However, as noted by Belles-Isles (1987), the hydrodynamic profile of the whole body of Errivaspis clearly differs from the typical hydrofoil or airfoil sections (i.e., a traditional wing, where the upper surface is curved whilst the lower one is flatter) and somewhat resembles an inverted wing profile (see Belles-Isles 1987; Text-fig. 3). In fact, the overall shape of Errivaspis’s cephalic shield (and many others pteraspidids) is similar to that of a typical delta-wing aircraft, having a delta-like planform with a more or less flatter upper surface, a forward projected conical nose and a curved ventral surface.

As our approach is qualitative, we cannot predict the exact values of the lift forces added by this mechanism during the locomotion of Errivaspis. However, it can be safely assumed that body-induced vorticity existed over Errivaspis cephalic shield, and these vortices were a functionally relevant source of energy during swimming, as is the case in living boxfishes (see Bartol et al. 2002, 2003, 2005). Taking into account that Errivaspis lacked pectoral fins and other obvious lift-generating surfaces, vortex lift forces added by this mechanism may have played a major role in counteracting the negative buoyancy of the fish. On the other hand, as stated above, Bartol et al. (2002, 2003, 2005) made it obvious that body-induced vorticity generates self-correcting forces for pitching and yawing motions contributing to the hydrodynamic stability of swimming trajectories in boxfishes. It is possible that vortical flows on Errivaspis also generates self-correcting forces to prevent undesirable movements of pitching and yawing during forward fast swimming or to deal with an environment of variable velocities.

Body-induced vorticity and branchial exhalent flows as a source of manoeuvring

Traditionally, the lack of pectoral fins, the presence of a heavy head shield and a ventrally placed mouth in Errivaspis have been interpreted as indicative of a bottom-living form with little manoeuvrability (e.g. White 1935). This idea was followed or slightly modified by later authors. Thus, Aleyev (1976) and Aleyev and Novitskaya (1983), based on Kermack’s approach (see above), proposed the idea of ‘intermittent’ locomotion of pteraspidids, so they could move actively only upwards and sinking passively downwards or settled on the bottom (Aleyev and Novitskaya 1983; Fig. 1). Contrary to this, Belles-Isles (1987) suggested that this fish must have kept a sustained periodic locomotion at high speeds, as in modern tunas and scombrids, based essentially in its external morphology and in its anteriorly placed centre of mass. Furthermore, this author inferred low manoeuvrability because of the lack of pectoral fins. Thus, he proposed Errivaspis to have been a filter-feeding transoceanic migrator in search of the plankton it fed on. More recently, Botella and Fariña (2004) noted that both biomechanical considerations and morphometric analysis place Errivaspis within the group of accelerating specialist fishes that use an efficient body and caudal fin (BCF) transient swimming strategy, capable of accelerating and making sudden changes of speed and direction, consistent with an active searching for and capture of small food items or escaping from predators.

Nowadays it is widely known from aeronautic experimental studies that leading edge vortices generated over a delta-wing aircraft can be controlled by applying different methods such as the use of flaps, leading-edge blowing, leading-edge suction, trailing-edge jet control, heating or using Micro-Electro-Mechanical System (see Huang et al. 2001; Gursul et al. 2006 and references therein). Using differential interaction between some of these devices and leading-edge vortices on both sides of the delta wing causes loading asymmetry, control forces and moments for all three axis about the aircraft, consequently they can effectively be used for manoeuvring (roll, pitch and yaw) control (see Rao 1986; Huang et al. 2001). Errivaspis (as other pteraspidids) have a single, common external branchial opening, covered by a branchial plate, on each side of the head armour. The exact location of these branchial openings with regard to the cephalic armour varies depending on the pteraspidid species considered, but they are usually strategically placed at the level of the leading-edge or even on the dorsal surface of the armour (see Blieck 1984; Mark-Kurik 1992; text-fig. 5). In those positions, exhalent jets through branchial openings affect longitudinal vorticity. Thus, body-induced vortical flow around the Errivaspis cephalic shield could potentially generate large manoeuvring forces with a small amount of gill effluent affecting attachment or separation of that vortices, in a similar way that vortices on a delta wing can be controlled by application of blowing along the leading edge of the wing (e.g. Wood and Roberts 1988; Gu et al. 1993). This mechanism could in some way compensate for the lack of obvious control surfaces (paired and intermediate unpaired fins) in pteraspidids.

Additionally, it is important to note that the dorsal surface of the carapace shows two symmetrical, slight concavities at both sides of the animal, near the end of the rostral plate. These slight concavities meet the leading edge at the level of the orbital plate, approximately above the eye, corresponding to the position in which the vortices are clearly formed. This morphology can be interpreted as a way of having the vortex permanently fixed in this point near the eye (Text-fig. 4), which in turn must have been convenient for keeping an optimal distribution of pressure around the eye and prevented the admittedly small eyeball from being deformed as flow passed along the body (Bartol et al. 2003, 2005).

Concluding remarks and future work

Our overall aim in this study was to describe the flow pattern around the bone cephalic shield of Errivaspis. The body-induced vortical flow observed around our model is very similar to the vortical flow over a delta wing, dominated by paired, nearly symmetrical, counter-rotating vortices, which are created at the leading edge and remain attached to the upper surface (but see above) growing downstream. This strategy generates lift forces through vortex generation (vortex lift). Despite our approach being qualitative, it can be safely stated that forces derived from body-induced vorticity existed over the cephalic shield of Errivaspis. Since Errivaspis lack pectoral fins and other obvious control surfaces, we hypothesise that vortex lift forces added by this mechanism during the locomotion may have played a major role not only in counteracting the negative buoyancy of the fish, but also as a source of manoeuvring.

Quantifying the magnitude of forces generated by longitudinal vortices on the dorsal surface of the carapace of Errivaspis and other pteraspidid species, and analysing the way in which branchial effluent affected attachment or separation of those vortices, producing a possible large torque for hydrodynamic control, are the aim of ongoing studies. For this, flow velocity measurements, pressure distribution measurements and force balance measurements are under way in three species of pteraspidids under different conditions. These studies will allow a better understanding of the role cephalic armours played in the hydrodynamic stability of swimming in these primitive agnathans. Moreover, we suggest that increased understanding of the swimming mode and manoeuvrability of this primitive fishes can provide an important source of inspiration for the development of biomimetic underwater vehicles.

Acknowledgments

Acknowledgements.  José Cataldo and Valeria Durañona, of the Instituto de Mecánica de Fluidos de la Facultad de Ingeniería, Universidad de la República (Montevideo, Uruguay) helped with many of the tests. Bobby Paton and Vicenta Carrión (National Museums Scotland) helped in the access to the collections at their charge. The artist of the Museum of the Universitat de València, Spain, Oscar San Isidro, helped in building the model and in the drawings. This work has been partially supported by a Postdoctoral Grant of the Spanish Government (H.B.).

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