Burrow Ventilation in the Tube-Dwelling Shrimp Callianassa Subterranea (Decapoda: Thalassinidea):II. The Flow in the Vicinity of the Shrimp and the Energetic Advantages of a Laminar Non-Pulsating Ventilation Current

Thalassinid shrimps characteristically create and inhabit burrows in the sea bed. These burrows are regularly ventilated for respiratory purposes or to filter the flow through the burrow for food (Atkinson and Taylor, 1988). The ventilation flow is generated by metachronal beating of three or four pairs of abdominal appendages, the pleopods (Farley and Case, 1968; Dworschak, 1981). Burrow ventilation is assumed to be energetically expensive and always occurs periodically (Atkinson and Taylor, 1988; Farley and Case, 1968; Torres et al. 1977; Felder, 1979; Dworschak, 1981; Mukai and Koike, 1984; Scott et al. 1988; Forster and Graf, 1995; Stamhuis et al. 1996). The predominantly filter-feeding Upogebiae are estimated to spend up to half their time on burrow ventilation for feeding purposes (Dworschak, 1981). The non-filter-feeding thalassinids, e.g. most of the Callianassidae, only ventilate their burrows occasionally, to renew the burrow water for respiration (Farley and Case, 1968; Stamhuis et al. 1996). Ventilation is performed in longer bouts with shorter intervals in the Upogebiae compared with the Callianassidae (Dworschak, 1981; Mukai and Koike, 1984; Forster and Graf, 1995; Stamhuis et al. 1996). Filter-feeding thalassinids, e.g. Upogebia pusilla and Upogebia major, use pumping rates of 33–50 ml min⁻¹ (Dworschak, 1981; Koike and Mukai, 1983). In these species, ventilation mainly serves feeding purposes and is occasionally performed for respiration only (Scott et al. 1988).

The Callianassidae usually inhabit extended burrows and have other feeding strategies (Griffis and Suchanek, 1991). Water is pumped through the burrow mainly for respiration. Occasionally, sediment is expelled from the burrow by pumping, causing a plume at the sediment surface (e.g. Suchanek, 1983; de Vaugelas, 1985; Stamhuis et al. 1996). Ventilation pumping rates of 0.6–5.5 ml min⁻¹ have been observed in C. japonica (Koike and Mukai, 1983; Mukai and Koike, 1984).

Flow through a burrow may be assisted directly by the ambient flow or indirectly as a result of ‘chimney effects’ at elevated exhalant openings (Vogel, 1978, 1994). This may reduce the ventilation costs in some upogebian species (Allanson et al. 1992). Flow generation mechanisms in burrow-living animals have been studied mainly in tube-living worms (e.g. MacGinitie, 1939; Chapman, 1968; Brown, 1975, 1977; Riisgaard and Larsen, 1995). Flow generation by metachronally beating pleopods (or other appendages) is observed in thalassinids, but the resultant flow inside the burrow has not previously been studied quantitatively.

The thallassinid shrimp Callianassa subterranea creates and inhabits an extensive burrow in the seabed (Witbaard and Duineveld, 1989; Atkinson and Nash, 1990; Rowden and Jones, 1995; Stamhuis et al. 1997). The shrimp ventilates its burrow every 14 min for 1.3 min, which is approximately 8 % of its time budget (Stamhuis et al. 1996). This may account for a significant part of its energy budget. The ventilation flow is produced by active pumping with three pairs of pleopods in an ad-locomotory metachronal pattern at a frequency of approximately 1 Hz (Stamhuis and Videler, 1997a). The present paper describes quantitatively the ventilation flow in the burrow and in the vicinity of a pleopod-pumping C. subterranea. Flow fields in front of, around and behind the shrimp are analyzed and processed to velocity profiles. The flow is examined for pulsation, and the energetic advantages of different ventilation strategies are evaluated.

Callianassa subterranea (Montagu) of approximately 40 mm total length were collected from box core sediment samples at the Oyster Grounds, central North Sea, approximately 53°45′N and 4°30′E. A sampling trip was made in September 1992 on the Dutch research vessel ‘Pelagia’. Each specimen was stored and transported to the laboratory in a separate jar. In the laboratory, each animal was allowed to construct a burrow in a 5 or 10 l plastic container largely filled with sediment from the sampling site and stored submerged in seawater aquaria at 12 °C. For details of the collection procedures, transport, storage and handling conditions, see Stamhuis et al. (1996).

To record the ventilation current of C. subterranea, individual animals were placed in a simple artificial burrow, a U-shaped glass tube of 8 mm diameter with two turning chambers at the ends of the horizontal section (Fig. 1). The burrow was submerged in a glass aquarium (width 5 cm) containing artificial sea water. The temperature of the experimental aquarium was kept at 12 °C by mounting it against a flat water-cooled heat exchanger, using ordinary hair-styling gel as a contact agent. Neutrally buoyant polystyrene particles with a diameter of approximately 25 μm were added to the water in the aquarium. The particles were illuminated by a vertical laser light sheet, approximately 0.5 mm thick, using a red light Krypton laser (wavelength 647 nm, P_max 1 W). The laser sheet coincided with the central plane of the glass tube. Images of the illuminated particles were taken using a high-resolution video camera equipped with a macro lens, mounted normal to the light sheet. The camera was electronically shuttered to prevent motion blur. The video frames were recorded using a U-matic-SP video recorder with access to each of the separate fields of a video frame (i.e. 25 frames s⁻¹, 50 fields s⁻¹).

The flow generated by a ventilating C. subterranea in the horizontal glass tube was recorded in four areas: in front of the animal, around the beating pleopods, directly behind the telson and further behind the animal (Fig. 2). The normal ventilation posture of C. subterranea allowed mainly lateral views but, since the shrimps sometimes turn around their longitudinal axis during ventilation, some views from the ventral and dorsal aspects were recorded as well. Ventilation flows generated by five different animals were recorded, and all showed the same flow patterns. The results from one animal are presented.

To prevent video interlace blurring, single fields were used for analysis. The first fields of two successive video frames were digitized to 768×512 pixel images which were enhanced by background equalization and contrast stretching (TIM image-processing environment, DIFA Vision Systems). Displacements of particles were obtained at sub-pixel accuracy by applying a combination of particle-tracking velocimetry (PTV) and sub-image correlation particle image velocimetry (SCPIV) (Stamhuis and Videler, 1995). The flow patterns in front of and behind the experimental animals were analyzed using SCPIV, the flow around the beating pleopods had to be analyzed using PTV because of the large velocity gradients. Velocity vector maps derived from the particle displacement data were processed to complete flow fields by two-dimensional spline interpolation, after vector validation. The resulting vector flow fields consist of arrays of vectors describing the velocity magnitudes and directions of the local flow. Vector averaging in the direction of the longitudinal axis of the tube resulted in average local flow profiles. Gradient variables derived from the velocity flow fields were used to study and describe the flow morphology (Stamhuis and Videler, 1995). Pulsation of the flow was studied by tracking single particles in the main stream over time.

The flow in the tube in front of a pumping C. subterranea is unidirectional (Fig. 3). The velocity profiles in the tube’s median plane are almost perfectly parabolic throughout the tube, indicating fully developed laminar ‘Hagen–Poiseuille’ flow. No irregularities or backflows near the tube walls indicating major oscillations are found (Fig. 4).

Tracking of individual particles in the main stream in time shows the flow to be practically non-pulsatile (Fig. 5, region I). The maximum core velocity is approximately 4.0±0.2 mm s⁻¹ (mean ± S.D., N=29), the mean velocity in the tube is therefore 2.0±0.1 mm s⁻¹.

Immediately in front of the abdomen, the flow is confined to the narrow space between the tube wall and the shrimp’s thorax (Fig. 6, left part). The velocity near the tube wall is increased compared with the flow velocity in front of the animal (Fig. 4) because of the reduced cross-sectional area (Fig. 7A). Ventral to the abdomen, the flow is dominated by the oscillating pleopods (Fig. 6, middle part). During the power stroke, each pleopod acts like an oar accelerating a mass of adhering water during the first part of the power stroke. In the lower part of the tube (see Fig. 6), the water is mainly accelerated by the distal part of the pleopods and the extended pleopodal rims, which enter this region during the power stroke only. The water mass around the pleopod is shed in a ventro-caudal direction during the second half of the power stroke (Fig. 8A first pleopod, Fig. 8B second pleopod). Shedding of the water mass is facilitated when water is squeezed from the spaces between neighbouring pleopods as they approach one another (due to metachrony), mainly during the second half of the power stroke (Fig. 8B, between the second and third pleopods). Acceleration and shedding of bodies of water results in significant velocity gradients in the area of the beating pleopods (Fig. 5, region II). The net result of the pleopod action is an average water displacement converging towards the lower tube wall with an increasing flow velocity in a caudal direction (Fig. 7B–D). The water leaves the area of the pumping pleopods only through the narrow opening underneath the telson because the uropods close off the rest of the tube diameter. The water is ejected as a jet with a mean velocity approximately eight times the velocity of the undisturbed flow in front of the shrimp (Fig. 6, right part; Fig. 7D,E).

The velocity field directly behind the animal shows the high-velocity jet below a separation zone directly behind the telson (Figs 9, 10). In the separation zone, vortex-like backflow occurs with low velocity compared with that of the jet core. The jet coming from the opening underneath the telson continues to converge for a short distance downstream of the telson, the narrowest part (the ‘vena contracta’) being situated approximately 0.15 tube diameters behind the opening (Fig. 6, right side). From there, the jet diverges and the core velocity decreases because of the steep velocity gradient surrounding the jet core. The transverse velocity gradients are caused by shear between the jet core and the tube wall below the jet as well as between the jet and the slowly rotating separation zone above it (Fig. 9, colour coding). Because of the high rates of shear, the jet evolves towards a parabolic velocity profile within a distance of approximately 2.5 tube diameters behind the animal, which is less than one body length (see also Fig. 5, region III).

In Fig. 11, the animal had turned around its longitudinal axis, allowing a dorsal view of the abdominal region. This figure shows the blocking of the tube by the tail-fan, since the last abdominal segments, the uropods and the telson close off the tube almost completely, preventing leakage along the top and the sides. The flow passes only through the small opening ventral to the telson and emerges (in Fig. 11) some distance behind the telson, when it enters the central plane of the tube. The separation zone with low-velocity backflow is visible directly behind the telson in this figure.

Further downstream of the animal, the jet has faded and only small traces remain. (Fig. 12; area IV in Fig. 2). The flow profile in the tube gradually returns to the parabolic velocity profile normal for laminar flow (Fig. 13).

The flows in front of, around and behind a pumping C. subterranea are summarized in Fig. 14. This figure also shows reconstructed cross sections of characteristic positions in the tube to clarify further the morphology of the flow.

In this discussion, our results will be compared with theoretical and empirical predictions. The energetic implications of different flow regimes will be quantified and evaluated. Finally, our results will be compared with data in the literature on thalassinid ventilation flows.

For 1<Wo<3, the phase of the flow rate Q starts to lag behind the phase of the pressure gradient Δp₀, and the parabolic velocity profile becomes disturbed by the oscillatory motion of the fluid core. If Wo>3, Q lags more than 60 ° behind Δp₀, and inertial forces rule the flow, causing the velocity profile to flatten (Caro et al. 1978). The hydrodynamic resistance of a tube increases with Wo, causing a decrease in Q at values of W ⪢ o1.

In our experiments, Wo ⪢ 12.5 with D=0.01 m and ω=2π (pulsation frequency, f=1 Hz), predicting a strong pulsatory flow, an almost flat velocity profile, a phase shift between Q and Δp₀ of almost 90 °, and a strongly reduced flow rate of approximately 0.1Q_steady, where Q_steady is the non-pulsating laminar flow rate. However, the flow actually generated by C. subterranea resembles laminar flow with no trace of pulsation and no disturbance of the normal velocity distributions.

The fact that the flow in the tube is not pulsating can be explained from the geometry and kinematics of the ‘pump’. The uropods and telson constrict the tube diameter. This reduces the cross-sectional area by a factor of approximately 10, thereby increasing the local mean flow velocity by the same factor. Some distance before the constriction, the flow converges towards the small opening. Directly behind the constriction, the jet flow converges further until the ‘vena contracta’ and then diverges. The flow velocity in the jet decreases only gradually, because of separation and the consequential rotating water mass behind the telson. As a result, the high flow velocity persists over a trajectory much longer than the constriction itself. This high flow velocity causes inertial forces to prevail over viscous forces, the local Re increases to values near 150 and the local Wo decreases to values close to 1. The character of the flow therefore changes locally from viscosity-dominated to inertia-dominated, which suppresses the expression of pulsation.

Furthermore, the pleopod movements during the recovery stroke are not the opposite of those during the power stroke. During the power stroke, the pleopods are fully extended into the main stream. During the recovery stroke, they are ‘lifted’ out of the main stream and reduce the flow velocity relatively little. The pleopods therefore act like oars, and the flow in the area of the oscillating pleopods is mainly confined to the lower part of the tube (see also Stamhuis and Videler, 1997a). Consequently, hardly any pulsation is generated.

The pleopods move in an ad-locomotory metachronal wave with a phase shift of approximately one-third of a cycle. This phase shift increases the pulsation frequency by a factor of three, but reduces the amplitude of a pulsation by approximately the same factor. Theoretically, the frequency increase would double Wo but, since the amplitude is practically zero, the flow is hardly affected.

Finally, the pleopod pump system of C. subterranea has a slip component, unlike a piston pump with valves. A piston pump imposes pulsation on the fluid because the fluid has to follow the piston displacement. Moving pleopods do not close off the tube completely, so that water can still flow around the tips. This damps pressure differences and promotes steady flow.

In conclusion, C. subterranea applies a combination of mechanisms to minimize pulsation in the flow through its burrow. It constricts the tube with its tail-fan, thereby locally changing the morphology and character of the flow, and it employs a pump with metachronally moving oar-like pleopods.

Fig. 15 is a diagram of the streamlines of a modelled laminar non-pulsatile flow in a tube of comparable geometry to that in the present study with a C. subterranea present, but without oscillating pleopods. This prediction was generated by solving the Navier–Stokes equations numerically in two dimensions, at the flow rate and Reynolds number that apply to the burrow of C. subterranea (Forbes and Recktenwald, 1996). The diagram matches our observations of the flow in the vicinity of the shrimp, confirming the laminar non-pulsatile character of this flow.

Calculations of the dissipated mechanical energy for a tube with or without a constriction and with or without a pulsatory component in the flow yield estimates of the mechanical energy involved in C. subterranea ventilation at different flow regimes. The power necessary to maintain a steady laminar flow in a tube containing a pumping C. subterranea may be calculated by assuming that the animal in its tube resembles a straight cylindrical tube of length L_tot and diameter D₁ with two constrictions (Fig. 16).

The first constriction is a reduction of the tube diameter to 0.85D₁ over a distance of 5 cm, representing a reduction in cross-sectional area to approximately 70 % due to the shrimp’s body. The second constriction, immediately behind the first, reduces the tube diameter to 0.32D₁, representing a reduction in cross-sectional area by the uropods and the telson by a factor of 10.

When calculating the steady and the unsteady dissipated power with L_tot=0.45 m, D₁=0.01 m, f=1 Hz and the total dissipated power with unsteady flow p_tot,unsteady can be calculated: P_steady=0.061×10⁻⁶ W, Punsteady=0.579×10⁻⁶ W and Ptot,unsteady=Psteady+Punsteady= 0.640×10⁻⁶ W.

Hence, by constricting the tube with its tail-fan, C. subterranea theoretically doubles the dissipated power (P₀≈2P_steady), but requires only one-sixth of the power that would be needed to produce oscillatory flow in a tube without the tail-fan constriction (P_tot,unsteady≈6P₀). Keeping the flow steady and laminar by partially constricting the tube and confining the flow ventral to the metachronally beating pleopods is therefore probably an energetically advantageous ventilation strategy.

It should be noted that the dissipated power is not necessarily equal to the mechanical power invested by the pumping shrimp, which is usually higher because of the pump efficiency and the muscle efficiency, which are less than 1 (Stamhuis and Videler, 1997a).

For a few thalassinid species, mainly Upogebiae, pumping flow rates are reported in combination with some information on an animal’s posture and pleopod beating pattern (Dworschak, 1981; Allanson et al. 1992; Scott et al. 1988; Forster and Graf, 1995; Stamhuis and Videler, 1997a). The main differences between Upogebiae and Callianassidae regarding ventilation are the number of pleopods active in pumping, the morphology of the tail-fan, the mechanism of flow regulation and the average time spent pumping. Upogebiae, at least the filter-feeding species, spend much more time pumping (up to 45 %) than the Callianassidae as a result of their need to generate a flow for feeding purposes (Dworschak, 1981; Scott et al. 1988). In the Upogebiae, the uropods are approximately the same size as the telson with equally long setae, whereas in the Callianassidae the telson is smaller than the uropods and has very short setae (Stamhuis and Videler, 1997a). The ventilation flow in Upogebia operculata and Upogebia sp. is adjusted by changing the posture of the whole tail-fan (Scott et al. 1988), which is probably the case in most Upogebiae. C. subterranea does not change the posture of the tail-fan during pumping and, since the other Callianassidae have a similar tail-fan morphology, this is probably also the case in the other Callianassidae. The Upogebiae have four pairs of paddle-like pleopods, which are all used in pumping, but no records exist, to our knowledge, on motion patterns or phase shifts between pleopod pairs. As in C. subterranea, the Callianassidae have only three pairs of pleopods involved in pumping, with a phase shift of approximately one-third of a cycle (Stamhuis and Videler, 1997a). The flow rates during pumping in Upogebia pusilla are 2–4 times as high as in C. subterranea and C. japonica of the same size, at approximately the same or an even lower pleopod beat frequency (Dworschak, 1981; Stamhuis and Videler, 1997a; Forster and Graf, 1995; Mukai and Koike, 1984).

These data on ventilation in thalassinid species indicate that the mechanism of minimizing pulsation in the ventilation flow in thalassinids may be applied in various ways. Our hydrodynamic predictions support this view. If the pleopod beat frequency and, consequently, the flow velocity is increased, it may be energetically advantageous to widen the constriction, since the hydrodynamic resistance of the constriction increases with the square of the velocity (third term in equation 3) and the dissipated power increases with the cube of the velocity. The other advantages of a high flow velocity are not necessarily affected by this strategy, since the increased flow velocity with a less narrow constriction will make inertial forces prevail over viscous forces. This, in combination with the increase in pump frequency, probably suppresses the expression of pulsation. Such a ventilation strategy is observed in Upogebia operculata and Upogebia sp. (Scott et al. 1988), and was also observed in C. subterranea during occasional heavy pumping to flush sediment out of the burrow. C. subterranea increased the pleopod beat frequency by a factor of approximately three and partly lifted its tail-fan while flushing out excavated sediment (see also Stamhuis et al. 1996).

Forster and Graf (1995) recorded ventilation activity of adult C subterranea in mesocosms and found a rather different ventilation pattern from the one described in the present study. They measured the flow using a thermistor probe in inhalant or exhalant openings of burrows and found a pulsating flow with a pulsation frequency of 0.15 Hz, which they observed to correlate with the pleopod motions (1 beat cycle per 7 s). They found the mean flow rate to be 1.8±1.1 ml min⁻¹ (mean ± S.D.). These results on pleopod beat frequency, flow rate and the pulsating character of the flow are all contrary to our results: we found a non-pulsating flow with a mean flow rate of 9.4±1.5 ml min⁻¹ at a pleopod beat frequency of 0.9±0.2 Hz (see also Stamhuis and Videler, 1997a). We observed the ventilation behaviour of more than 20 animals during behavioural studies (Stamhuis et al. 1996) and recorded pleopod beat frequencies from five individuals during the experiments presented here. The beat frequency during ventilation appeared to be typically approximately 1 Hz in all animals. We rarely observed pleopod movement of very low frequency, which we did not classify as ventilation activity. Some animals did display these slow motion patterns on occasions, others never did. Owing to the very low beat frequency, the resulting low-velocity flow showed pulsatility, and obviously viscous forces dominated the flow. We suspect that Forster and Graf (1995) recorded this type of pleopod motion and the consequent flow pattern.

Our results on the dissipated power in the ventilation flow are of the same order of magnitude as estimated by Allanson et al. (1992) for Upogebia africana and by Gust and Harrison (1981) for the alpheid shrimp Alpheus mackayi, when accounting for differences in size and pumping rates. In those studies, however, the pressure drops at the entrance and at constrictions were not taken into account. Depending on the flow velocity and the dimensions of the constrictions, this may cause underestimations of the dissipated power by a factor two or more.

The present results on the velocity distributions and morphology of the flow in the vicinity of a pleopod-pumping C. subterranea will be used to model pleopod pumping energetics in tube-living thalassinids in companion paper (Stamhuis and Videler, 1997b).

We cordially thank Professor T. J. Pedley (University of Cambridge) for guidance on the fluid dynamics of tube flows, especially on entrance effects and oscillatory flow. We are indebted to Ulrike Müller for critically reading the first draft of the manuscript.