HYDRODYNAMICS OF COPEPODS: A REVIEW
HOUSHUO JIANG1 and THOMAS R. OSBORN2,3
1
Department of Applied Ocean Physics and Engineering, MS 12 Woods Hole Oceanographic
Institution, Woods Hole, MA 02543, USA
E-mail:[email protected]
2
Department of Earth and Planetary Sciences, The Johns Hopkins University, Baltimore,
MD 21218, USA
3
Center for Environmental and Applied Fluid Mechanics, The Johns Hopkins University,
Baltimore, MD 21218, USA
(Received 1 October 2002; accepted 19 September 2003)
Abstract. This paper reviews the hydrodynamics of copepods, guided by results obtained
from recent theoretical and numerical studies of this topic to highlight the key concepts.
First, we briefly summarize observational studies of the water flows (e.g., the feeding currents) created by copepods at their body scale. It is noticed that the water flows at individual copepod scale not only determine the net currents going around and through a
copepod’s hair-bearing appendages but also set up a laminar flow field around the copepod.
This laminar flow field interacts constantly with environmental background flows. Theoretically, we explain the creation of the laminar flow field in terms of the fact that a free-swimming copepod is a self-propelled body. This explanation is able to relate the various flow
fields created by copepods to their complex swimming behaviors, and relevant results
obtained from numerical simulations are summarized. Finally, we review the role of hydrodynamics in facilitating chemoreception and mechanoreception in copepods. As a conclusion, both past and current research suggests that the fluid mechanical phenomena
occurring at copepod body scale play an important role in copepod feeding, sensing,
swarming, mating, and predator avoidance.
Keywords: chemoreception, copepod, feeding current, hydrodynamics, mechanoreception,
numerical simulation, self-propelled
1. Introduction
Calanoid copepods live in water environments. Water flows are created,
whenever the copepods feed and/or swim by rapid beating of their antennae, mandibular palps, maxillules and maxillae (i.e., the cephalic appendages), elicit an escape reaction resulting from the combined actions of the
antennules and swimming legs, or even sink freely through the water column by stopping all the activities of the appendages. (This is because most
of them are negatively buoyant.) The water flows so created are crucial for
the survival of the copepods, as they have to engage in various survival
tasks of feeding, predator avoidance, and mating in the three-dimensional
water environments (e.g., Yen and Strickler, 1996; Yen, 2000).
Surveys in Geophysics 25: 339–370, 2004.
2004 Kluwer Academic Publishers. Printed in the Netherlands.
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The study of the water flows created by copepods and associated interactions with environmental background flows forms the scope of the
hydrodynamics of copepods. Generally, the studies of the hydrodynamics
of copepods may be divided into three research directions: (1) the water
flows at a copepod’s appendage scale, i.e., the water flows around and
through a copepod’s hair-bearing appendages, (2) the water flows at the
scale size of an individual copepod (e.g., the feeding current created by a
copepod hovering in the water column, the flow field around a swimming
copepod, and the vortical flow structure shed in the wake of a copepod
eliciting an escape reaction), and (3) the interaction between the water
flows created by a copepod and the environmental background flows surrounding it (e.g., the manner in which the small-scale turbulence around a
copepod erodes the laminar feeding current created by the copepod).
Important questions are the following: (i) How does a copepod alter its
feeding current by adjusting its body orientation and the forcing which it
applies to the adjacent water, in response to a turbulent eddy or turbulence-induced shear of a scale comparable with the size of the copepod?
(ii) In general, how does a copepod change its swimming behavior and therefore change the flow field around its body in response to the small-scale
turbulence? (iii) How does the interaction between the flows created by a
copepod and the environmental background flows affect the copepod’s sensory mechanisms such as mechanoreception and chemoreception?
The study of the water flows at a copepod’s appendage scale has been
reviewed by Jørgensen (1983), LaBarbera (1984) and Shimeta and Jumars
(1991), mainly focusing on the mechanisms of suspension feeding. In addition, Childress et al. (1987) utilized a number of highly simplified models
of appendage motion, such as the movement of Stokeslets, spheres or
stalks, to set up an average scanning current in Stokes flow in a suitable
far-field formulation; they discussed the possible applications of these models in understanding the feeding efficiency and strategies of small organisms
such as copepods. Some more recent studies have discovered that different
aspects of morphology and behavior are important in determining the leakiness of a hair-bearing appendage at different Reynolds numbers, and have
provided insights about the function of arrays of hair-like olfactory antennae (e.g., Koehl, 1992, 1995, 1996; Loudon et al., 1994).
As to the study of the interaction between the water flows created by a
copepod and the environmental background flows surrounding it, experimental studies have documented the behavioral responses of copepods to
laboratory-generated turbulence (e.g., Costello et al., 1990; Marrasé et al.,
1990; Saiz and Alcaraz, 1992; Hwang et al., 1994; Caparroy et al., 1998).
Marrasé et al. (1990) revealed the difference in the flow field around a tethered copepod under two different background flow conditions: a non-turbulent condition and a turbulent condition. Kiørboe and Saiz (1995)
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provided a simple analysis of the erosion of copepod feeding current by
the small-scale turbulence. Osborn (1996) proposed a conceptual model of
the interaction between a copepod’s feeding current and the surrounding
small-scale turbulence, in which copepod feeding is considered as turbulent
diffusion of the food in towards the region where the feeding current serves
to capture the food well before it is identified. Although there is a large literature on the effect of the small-scale turbulence upon the encounter rate
between predators and prey (see the reviews in Dower et al. (1997), and
Lewis and Pedley (2000)), only some speculations about the interactions
between the copepod-created water flows and the environmental background flows can be found from the up-to-date literature (e.g., Strickler,
1985; Granata and Dickey, 1991; Yamazaki, 1993; Yamazaki and Squires,
1996; Strickler et al., 1997). Studies of the interactions in a more dynamic
way are still needed. That is, future studies are needed to investigate the
spatial and temporal variations of the flow field around a copepod under
the influence of environmental background flows at suitable spatial and
temporal scales. Since one of these two research directions has been
reviewed extensively by other researchers and the other has not yet been
investigated extensively, we choose not to include them in this review.
The main purpose of this paper is to review (from the viewpoint of
hydrodynamics) the study of the water flows at individual copepod scale.
The content includes (1) descriptions of the flow fields obtained from
observational studies, (2) understanding the creation of the flow fields
based on the evidence from both observations and theoretical analyses,
(3) numerical simulations of the flow fields, and (4) effects of the flow fields
on copepod sensory mechanisms. As has been pointed out at the very
beginning, the water flows at individual copepod scale play an important
role in copepod feeding, predator avoidance, and mating. It is noteworthy
that the water flows at individual copepod scale not only determine the net
water flows going around and through a copepod’s hair-bearing appendages but also set up a laminar flow field around the copepod; the created
laminar flow field is constantly under the influence of environmental background flows.
2. Observations of the flow field at individual copepod scale
More than twenty years ago, a high-speed microcinematographic technique
based on a Schlieren optical pathway was used to observe the world of
zooplankton such as copepods (Strickler, 1977, 1985; Alcaraz et al., 1980).
In some earlier applications of this technique (e.g., Strickler and Bal, 1973;
Strickler, 1975a, b, 1977; Kerfoot et al., 1980), the ‘‘footprints’’ created by
free-swimming copepods were registered on film. In fact, these ‘‘footprints’’
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have visualized the hydrodynamic disturbances created by the copepods at
their body scale. The idea underlying this technique is direct visual observation, which now has been widely used by researchers to study the feeding, swimming, breeding, and predator–prey interactions of zooplankton,
and their interactions with environmental conditions. On the other hand,
this technique directly contributed to an important finding – many calanoid copepods create feeding currents – and made possible the quantification of the feeding currents. By analyzing the images taken on the film or
later on the digital videotapes, researchers were able to measure the flow
field (e.g., the feeding currents) created by copepods.
2.1. For a tethered copepod
Many laboratory experiments used tethered copepods and measured the
feeding currents created by them (e.g., Koehl and Strickler, 1981; Vanderploeg and Paffenhöfer, 1985; Paffenhöfer and Lewis, 1990; Yen and Fields,
1992; Fields and Yen, 1993; Yen and Strickler, 1996; Fields and Yen,
1997; van Duren et al., 1998). Obviously, ‘‘tethering’’ made the data gathering much easier. Here, we adopt the descriptions by Fields and Yen
(1993) of their measurement of the flow field around a tethered Pleuromamma xiphias (3.5 mm prosome length) to show the three-dimensional
flow structure of the feeding current created by a tethered copepod
(Figure 1). A maximum velocity of 38 mm s)1 occurred at the base of the
downward swing of the second antennae just lateral to the sides of the
body. Lateral symmetry was found in the flow field with water velocity
decreasing rapidly from the head to the distal tips of the antennules. Asymmetry in the flow field was present between the dorsal and ventral side of
the copepod with the 1 mm s)1 velocity isoline approximately 1.5 times
further from the body ventrally than dorsally. The hydrodynamic disturbance defined by the 1 mm s)1 velocity isoline was located as far as
4.1 mm above the head, 4.6 mm lateral, 5.6 mm ventral and 3.6 mm dorsal
to the copepod. The lower extent of the 1 mm s)1 velocity isoline could
not be identified; however, the lower portion of the 7 mm s)1 velocity isoline was found 7.5 mm directly below the head.
2.2. For a free-swimming copepod
However, the experimental technology has also allowed free-swimming copepods to be followed so that the flow field around the free-swimming
copepods can be obtained (e.g., Strickler, 1982, 1985; Greene, 1988; Tiselius and Jonnson, 1990; Yen et al., 1991; Bundy and Paffenhöfer, 1996).
HYDRODYNAMICS OF COPEPODS: A REVIEW
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Figure 1. Feeding current of a tethered Pleuromamma xiphias. Velocity contour plots from (a) a dorsal
view; (c) a lateral view. The labels in (a) and (c) are in mm s)1. Particle trajectories from (b) a dorsal
view; (d) a lateral view. (From Fields and Yen, 1993.)
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Strickler (1982) reported his measurement of the flow field around
free-swimming Eucalanus crassus. During feeding bouts of 10–30 s, the
structure of the flow field (i.e., the feeding current) around E. crassus was
constant. The flow field in front of the mouthparts showed a double shear
field, one extending laterally from the median plane and another parallel to
the median plane. Once an alga was entrained into this flow field, its path
through it was determined (indicating the laminar property of the flow
field). Strickler (1982) also pointed out the flow difference between the
feeding mode and the cruising mode of E. crassus, i.e., no anterior double
shear field was created during cruising. Greene (1988) illustrated the structure of the feeding current created by a hovering Neocalanus cristatus; the
feeding current structure looks visually similar to that due to a point force
in an infinite domain [see Figure 6.4.1a in Pozrikidis (1997)]. Tiselius and
Jonnson (1990) measured the flow field created by copepods among three
different feeding strategies: (1) slow-swimming or stationary suspension
feeding (Temora longicornis, Pseudocalanus elongatus, and Paracalanus parvus), (2) fast-swimming interrupted by sinking periods (Centropages typicus
and Centropages hamatus), and (3) motionless sinking combined with short
jumps (Acartia clausi). It was found that flow fields were similar for all suspension-feeding species, but the anterior velocity gradient moved closer to
the copepod in fast-swimming species. By tracing the paths of entrained
algae, Yen et al. (1991) reconstructed the velocity field of the feeding current created by a hovering Euchaeta rimana. The velocity field was actually
a two-dimensional velocity vector field on the dorsal–ventral plane nearly
perpendicular to the stretched antennules and also parallel to the body
axis. Based on this velocity field, some characteristics of the velocity gradient field such as vorticity, shear, and squared rates of strain were calculated. Furthermore, by assuming axisymmetry of the feeding current (not
necessarily a good approximation here), Yen et al. (1991) were able to calculate the viscous energy dissipation per E. rimana feeding current as
9.3 · 10)10 W individual)1.
Bundy and Paffenhöfer (1996) utilized high-resolution video observations of free-swimming adult female copepods to characterize the flow
fields created by Centropages velificatus (an omnivore with strong tendencies toward carnivory), and Paracalanus aculeatus (a herbivore). For the
purpose of comparison, the flow fields around tethered copepods were also
measured. The velocity vectors were calculated on the dorsal–ventral plane,
so that the obtained flow fields were two-dimensional. Large differences in
flow geometry were found between tethered copepods and free-swimming
copepods. This was attributed to the fact that, for free-swimming copepods, flow field velocity and geometry are controlled by the balance of
forces (drag, negative buoyancy, and forces exerted on the water by the
appendages) (Strickler, 1982), while, for tethered copepods, tethering will
HYDRODYNAMICS OF COPEPODS: A REVIEW
345
Figure 2. Lateral view of the feeding current of a free-swimming Paracalanus aculeatus female. (a)
Flow velocity contour plot. The contour interval is 1 mm s)1. (b) Flow velocity vector plot. Single
large arrow represents the copepod’s swimming direction. Note that the frame of reference is fixed on
the copepod. (From Bundy and Paffenhöfer, 1996.)
alter the balance of these forces. Since different species may have different
configurations of the balance of forces, it is not surprising that large differences in the geometry of flow fields were found between species. They also
observed that a free-swimming copepod creates a flow field with areas of
high velocity (larger than its swimming velocity) located in a short distance
away from the body surface, and in most situations ventrally or anteriorventrally to the body surface (Figure 2).
3. Creation of the flow field at individual copepod scale: the significance
of ‘being self-propelled’
How does a copepod create a quasi-steady flow field at its body scale? To
answer this question, first, the characteristics of beating movements of the
cephalic appendages of copepods must be taken into account, as many
observations have shown that the creation of the flow field is closely
related to the beating movements (e.g., Koehl and Strickler, 1981;
Paffenhöfer et al., 1982; Cowles and Strickler, 1983; Strickler, 1984; Price
and Paffenhöfer, 1986a). After revisiting some observational evidence
obtained by other researchers, Jiang et al. (2002b) have generalized that
two characteristics of the beating movements are responsible for the creation of a quasi-steady flow field at individual copepod scale. (1) The beating movements are rapid, i.e., the beating movements occur at a high
frequency, ranging from 20 to 80 Hz (e.g., Storch and Pfisterer, 1925; Cannon, 1928; Lowndes, 1935; Koehl and Strickler, 1981; Price et al., 1983;
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HOUSHUO JIANG AND THOMAS R. OSBORN
Price and Paffenhöfer, 1986a, b; Gill, 1987). (2) The cephalic appendages
usually operate in specific motion patterns during swimming and feeding,
displaying asymmetry in the propulsive stroke and the recovery stroke
(e.g., Gauld, 1966; Strickler, 1984). A high frequency of the beating movements ensures that the unsteadiness of the flow field can only
exist within a
pffiffiffiffiffiffiffiffi
short distance characterized by the viscous length scale v=x (where m is
the kinematic viscosity of the fluid, and x ¼ 2pf, where f is the beating frequency of the appendages) away from the surface of the appendages.
Therefore, at a scale of copepod body length, which is usually much larger
than the viscous length scale, the flow field is quasi-steady. On the other
hand, copepods usually live at low Reynolds numbers (e.g., Zaret, 1980;
Koehl and Strickler, 1981; Strickler, 1984; Naganuma, 1996); because of
the reversibility of the low Reynolds number flow, the asymmetry in
motion patterns of the appendages is of ultimate importance for copepods
to create a non-zero mean flow field at their body scale.
Next, factors that control the magnitude and geometry of the non-zero
mean flow field at a copepod’s body scale must be determined. These factors include the copepod’s excess weight, swimming behavior, and morphology. Stricker (1982) first pointed out that a copepod’s excess weight
(i.e., negative buoyancy) is important for the copepod to create a strong
feeding current. Intuitively, he suggested that the configuration of forces
acting on a free-swimming copepod determines the copepod’s body orientation and swimming velocity; further, he drew diagrams of different configurations of forces for several different copepod species. Along the same line,
Emlet and Strathmann (1985) argued that the drag on the main body of a
copepod also plays an important role in setting up the flow field around
the copepod. In fact, their argument emphasizes the role of the copepod’s
swimming behavior and morphology, since the drag is determined by the
swimming behavior (including the body orientation, and swimming direction and speed) and morphology (including the morphology of the main
body, and the morphology and motion pattern of the cephalic appendages).
Childress et al. (1987) indicated that the far-field flow associated with
the main body resistance decays much faster than the far-field associated
with counterbalancing the excess weight. Indeed, the far-field flow associated with the net force exerted by the copepod on the fluid (a force monopole) falls off as 1=r and is independent of the morphology. The far-field
flow associated with the main body resistance (a force dipole) falls off like
1=r2 and depends on the morphology and the details of how the copepod
is propelling itself (e.g., Childress, 1981; Pedley, 1997; Jiang et al., 2002b).
(Here, r is the distance from an origin inside the body.) The reason is the
following. When a neutrally buoyant copepod swims, the copepod applies
both drag (through body resistance) and thrust (through the beating move-
HYDRODYNAMICS OF COPEPODS: A REVIEW
347
ment of appendages) on the water, and the first-order effect due to one is
cancelled in the far-field by the first-order effect due to the other. However,
the intense currents associated with the details of how the copepod is propelling itself will be found in the immediate vicinity of the ‘‘scanning
machine’’ (a name given by Childress et al. (1987) to the beating appendages). Based on this, it is worth pointing out that if the ‘‘scanning
machine’’ is well separated from the body parts where most of the resistance originates, the currents around it will be very strong and wellextended, resembling ‘‘first-order scanning’’, their name for the motion
associated with overcoming the excess weight.
For example, a few calanoids such as those in the family Calocalanidae
have a long and huge tail-like appendage attaching to their urosome (see
Figure 2.2.1B in Huys and Boxshall (1991)). A small swimming speed of
the copepod’s body will result in a large drag originating from the tail-like
appendage. That force has to be balanced by the force exerted on the fluid
by the beating movement of the cephalic appendages (the ‘‘scanning
machine’’). Therefore, a strong, well-extended, first-order scanning-like
feeding current may be created around a relatively large volume around
the cephalic appendages (J.R. Strickler, pers. comm.). On the other hand,
the effect of tethering on the flow field around a copepod is discussed by
Childress et al. (1987). The effect of the tethering is twofold. First, the
tethering may restrain the normal swimming motion of the copepod and
therefore alter the drag. Second, if the tether force is not zero, the tethering
will change the thrust that the copepod applies to the water through the
beating movement of the cephalic appendages, and therefore modify the
flow that one interprets as the first-order scanning component.
The above descriptions about the effects of excess weight and main body
drag on the creation of the flow can be unified by the concept of being
self-propelled, i.e., a free-swimming copepod must beat its cephalic appendages in a certain way and therefore gain propulsion (equal in magnitude
but opposite in direction to the thrust) from the surrounding water in
order to counterbalance the drag force by the water and its excess weight.
Based on this concept, a self-propelled Stokes-flow model has been developed to calculate the flow field around a free-swimming, negatively buoyant, spherical copepod in steady motion through properly coupling the
Stokes equations, which govern the flow field around the spherical copepod
under the Stokes approximation, with the dynamic equation of the copepod’s spherical body (Jiang et al., 2002b). A point force is applied on the
water at a given position outside the spherical body, representing the net
effect of the beating movement of the copepod’s cephalic appendages. The
magnitude and direction of the point force (the thrust) is adjusted according to the copepod’s swimming behavior through the coupling between the
fluid dynamics and the body dynamics, so that the propulsion balances the
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velocity magnitude
(normalized by terminal velocity)
drag force by the water and the copepod’s excess weight. Although the
model is highly abstract, it reflects the key concept of being self-propelled.
Above all, analytical solutions of the model can be obtained for arbitrary
steady motion, such as hovering, sinking, or steady swimming at a given
speed along a given direction.
The results obtained from the self-propelled Stokes-flow model are consistent with intuition and observational evidence. Intuitively, the net force
exerted by a free-swimming copepod in steady motion on its surrounding
water must be equal to its excess weight in spite of the swimming behavior,
because the copepod is self-propelled. Concerning the decay of the velocity
field around a negatively buoyant copepod, this indicates that the velocity
field should decay in the far-field to the velocity field generated by a point
force of magnitude of the copepod’s excess weight in an infinite domain
(termed the ‘‘point force’’ model). Fortunately, the self-propelled Stokesflow model is able to reproduce this important property in velocity decay.
It is clearly shown that the velocity magnitudes for different swimming
behaviors (e.g., hovering, forward swimming fast or slowly) decay to the
velocity field generated by the point force model (Figure 3). On the other
hand, observations have shown that the geometry of the flow field around
a free-swimming copepod varies significantly with different swimming
behaviors. (A review of copepod swimming behaviors as well as the associated flow fields is given in Jiang et al. (2002b).)
The observations have been confirmed by the modeling study, in which
the streamtube through the capture area of the copepod is used to visualize
the flow geometry. Specifically, the streamtube associated with a copepod
swimming slowly (i.e., swimming at a speed at least several times smaller
point force model
standing-still model
forward swimming model (u=4.4 mm/s)
forward swimming model (u=1.1 mm/s)
X (normalized by sphere radius)
Figure 3. Velocity decay for different swimming behaviors. The velocity magnitudes have been normalized by the terminal velocity of the spherical copepod (4.4 mm s)1 for the present case). (From Jiang
et al., 2002b.)
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HYDRODYNAMICS OF COPEPODS: A REVIEW
(a)
(b)
t=–2.5s
-2.0
Z (mm)
Z (mm)
4.0
t=–1.2s
2.0
t=–0.5s
t=–0.1s
t=0.0s
0.0
t=0.0s
t=–0.1s
Vsinking=4.4 mm/s
0.0
6.0
t=–0.5s
t=–1.2s
-4.0
-6.0
-2.0
-8.0
-4.0
-2.0
0.0
2.0
4.0
6.0
t=–2.5s
-4.0
-2.0
0.0
X (mm)
2.0
4.0
X (mm)
(c)
(d)
6.0
Z (mm)
Z (mm)
t=–2.5s
2.0
t=–0.1s
0.0
t=–0.1s
t=0.0s
0.0
t=–2.5s
t=–0.5s
4.0
t=–1.2s
t=–0.5s
t=–1.2s
5.0
t=0.0s
Vswimming=4.4 mm/s
-5.0
Vswimming=1.1 mm/s
-2.0
-2.0
0.0
2.0
X (mm)
4.0
6.0
0.0
5.0
10.0
X (mm)
Figure 4. Lateral view of the streamtube through the capture area of a spherical model copepod (a)
hovering (like a helicopter) in the water, (b) sinking freely at its terminal velocity (4.4 mm s)1),
(c) swimming forward (in positive x-direction) at a speed of 1.1 mm s)1, and (d) swimming forward (in
positive x-direction) at a speed of 4.4 mm s)1. Note that the frame of reference is fixed on the copepod.
(From Jiang et al., 2002b.)
than the copepod’s terminal velocity of sinking, termed the slow-swimming
behavior) resembles the streamtube of a copepod hovering in the water. In
both situations, the cone-shaped and wide streamtube transports water to
the capture area of the copepod, and a feeding current is created
(Figure 4a and c). Conversely, when a copepod swims at a speed equal to
or greater than the terminal velocity (termed the fast-swimming behavior),
the streamtube is cylindrical, long and narrow and the corresponding flow
field is not a feeding current (Figure 4d). In addition, when a copepod
sinks freely, the flow comes from below relative to the copepod and the
streamtube is much narrower and longer than hovering and swimming
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HOUSHUO JIANG AND THOMAS R. OSBORN
slowly, but shorter than swimming fast (see Figure 4b). Again, the flow
field around a free-sinking copepod is not like a feeding current. The differences in the flow geometry with the different swimming behaviors are
due to the relative importance between the two factors in generating the
flow field: the copepod’s swimming motion and the requirement to counterbalance the copepod’s excess weight. Here, comparing the actual swimming
velocity with the terminal velocity of sinking distinguishes between slowswimming and fast-swimming among species, and also measures the relative importance between the two factors in generating the flow field.
Modeling free-swimming copepods as self-propelled bodies not only
serves as an imperative to obtaining a correct spatial decay of the flow field
and understanding the relationship between swimming behavior and flow
geometry, but also plays a crucial role in reproducing the key aspects of the
flow field, which have been revealed by observational studies. These key
aspects include the double shear field (Strickler, 1982), the spatial configuration of the velocity gradient field such as vorticity, shear, and squared rates
of strain (Yen et al., 1991), and the spatial configuration of the velocity field
such as the locations of velocity maximums relative to the body surface
(Bundy and Paffenhöfer, 1996) and asymmetry (e.g., ventral–dorsal asymmetry). For instance, the self-propelled Stokes-flow model is able to reproduce an important flow characteristic reported by Bundy and Paffenhöfer
(1996), i.e., an area of high flow velocities (larger than its swimming velocity) is located a short distance away from the body surface, and in most situations ventrally or anterior-ventrally to the body surface (Figure 5b and
d). On the contrary, the Stokes-flow field due to the translating motion of a
solid sphere, termed the towed body model, cannot reproduce this flow
characteristic; the velocity maximum (equal to the translating velocity) is
reached at the body surface when using a stationary frame of reference
(Figure 5a and c). In addition, the self-propelled body model creates a flow
field with a ventral-dorsal asymmetry (Figure 5b and d), while the flow field
created by the towed body model is axisymmetric with respect to the body
axis along the direction of the translating motion (Figure 5a and c).
Some studies, although very heuristic for understanding the biological
aspects of copepod feeding and/or sensing, used the towed body model to
calculate the flow field created by a free-swimming copepod, not considering the free-swimming copepod as a self-propelled body. Tiselius and Jonsson (1990) used the towed body Stokes solution to model the flow field
around a swimming copepod and tried to understand the efficiency of hovering behavior compared with swimming behavior. In their study, the
clearance of a swimming copepod was simply calculated as the cross section of the copepod times swimming velocity. However, the most important contribution to the clearance by the beating movement of the
copepod’s cephalic appendages was neglected. In addition, for the same
HYDRODYNAMICS OF COPEPODS: A REVIEW
351
Figure 5. Contour plots of velocity magnitudes of the flow field calculated from (a) and (c) the towed
body model, and (b) and (d) the self-propelled body model. The velocities have been calculated using a
stationary frame of reference and the velocity magnitudes normalized by 4.4 mm s)1 (the terminal
velocity of the spherical copepod). In (a), the sphere (a towed body) translates in the negative x-direction at a speed of 1.1 mm s)1. In (b), the spherical copepod (a self-propelled body) swims backward in
the negative x-direction at a speed of 1.1 mm s)1. In (c), the sphere (a towed body) translates in the
negative x-direction at a speed of 4.4 mm s)1. In (d), the spherical copepod (a self-propelled body)
swims backward in the negative x-direction at a speed of 4.4 mm s)1. (From Jiang et al., 2002b.)
swimming velocity, the drag calculated from the towed body model is generally different from that calculated from the self-propelled body model (Jiang et al., 2002b). Similarly, Kiørboe and Visser (1999) applied the Stokes
solution of the flow around a fixed sphere to model the flow around a
moving plankter.
The numerical model of a two-dimensional flow field around two circular cylinders (which is actually a towed body model) was used to model the
situation of a free-swimming copepod approaching an inert particle (Bundy
et al., 1998). Since these studies did not consider a free-swimming copepod
as a self-propelled body, their quantitative results may need to be re-exam-
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ined. A so-called ‘‘spherical pump’’ solution (the Stokes flow for a translating sphere with a frame of reference fixed with respect to the far-field fluid)
was used to model the flow field of a copepod feeding current (e.g., Kiørboe and Visser, 1999). Although the velocity decay happens to be correct,
the spatial configurations of velocity field, deformation rate field and vorticity field (around the solid sphere) calculated from the model are apparently not comparable with available observational results around a
copepod (e.g., Yen et al., 1991; Bundy and Paffenhöfer, 1996). Visser
(2001) argued that, for the spherical pump model, the thrust is distributed
over a finite spherical volume of space. If this is the case, we can only
understand that the solid body in the spherical pump model is not the
copepod main body since a hovering negatively buoyant copepod only
applies thrust to a small volume of water where its cephalic appendages
are located, with its main body retarding the created feeding current. Thus,
the ‘‘spherical pump’’ model does not separate the main body resistance
from the thrusting effect of the beating movement of the cephalic appendages, which is, however, a requirement for a self-propelled body model.
Therefore, the model is still not a self-propelled body model. It is worth
noting that a specific form of the separation reflects a specific way in which
the copepod propels itself, which then can be used to reproduce the specific
‘‘footprint’’ left by the copepod.
4. Numerical simulations of the flow field at individual copepod scale
The equations governing the flow velocity vector field u(x) around a copepod in steady motion are approximately the steady Navier–Stokes equations and the continuity equation:
qu ru ¼ rp þ lr2 u þ fa
ð1Þ
ru¼0
ð2Þ
where q is the density of the seawater, l is its dynamic viscosity and p is
the flow pressure field. fa represents the force field (force per unit volume)
that models the net effect of the beating movement of the copepod’s cephalic appendages, and the volume integral of fa is the thrust (Jiang et al.,
2002b). The boundary conditions of Eqs.(1) and (2) are the no-slip boundary condition on the surface of the main body (denoted as X mb , i.e., the
body excluding the beating appendages):
u ¼ Vswimming ; at X mb
ð3Þ
HYDRODYNAMICS OF COPEPODS: A REVIEW
353
and the boundary condition at infinity:
u ! 0; at infinity
ð4Þ
Here, Vswimming is the swimming velocity of the copepod. That a copepod
is in steady motion means that it is hovering at a position (Vswimming=0),
swimming at a constant velocity (Vswimming=constant), sinking at its terminal velocity of sinking (Vswimming=Vsinking and fa=0), or tethered at a position (Vswimming=0). The dynamic equation of a copepod in steady motion
can be written as
Z
Wexcess þ F fa ðxÞdx þ Te ¼ 0
ð5Þ
x
where Wexcess is the excess weight of the copepod, F is the drag force
exerted by the flow field on the copepod’s main body, and Te is the force
acting on the copepod by the tethering, if any.
Eqs (1)–(5) are a set of equations that describe the dynamic coupling
between a copepod’s swimming motion and the water flows surrounding
the copepod. Apparently, along with the main body motion (i.e., the velocity and orientation of the main body), which determines the boundary condition at the body–fluid interface, the beating movement of the cephalic
appendages (represented here by fa) plays a key role in the dynamic coupling. The input parameters of the set of equations are the morphology,
swimming behavior, and excess weight of the copepod. Here, the morphology includes the main body morphology and the spatial distribution of the
cephalic appendages relative to the main body (represented here by the
spatial distribution of fa). The swimming behavior includes the swimming
speed and direction. The excess weight is determined from the excess density and body volume of the copepod. The mass density of some copepod
species is available (see Gross and Raymont, 1942; Lowndes, 1942; Greenlaw, 1977; Køgeler et al., 1987; Visser and Jónasdóttir, 1999; Knutsen
et al., 2001). Information on the density contrast of copepods with respect
to their natural seawater habitat can be found in Greenlaw and Johnson
(1982) and Knutsen et al. (2001).
Numerical simulation involving computational fluid dynamics (CFD) is
needed for a full solution of Eqs. (1)–(5). The output of the numerical simulation is a three-dimensional flow velocity vector field around the copepod, which is detailed enough for further uses, such as visualization of the
flow geometry, estimation of the feeding rate, and quantification of the
sensory field, etc.. Till now, an accurate measurement of the three-dimensional flow velocity vector field still challenges experimental biologists. One
of the virtues of numerical simulations is that parametric studies can be
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HOUSHUO JIANG AND THOMAS R. OSBORN
performed. That is, we can vary the input parameters, such as the morphology, swimming behavior, and excess weight of the copepod, and examine their effects systematically. Some problems (e.g., the relationship
between swimming behaviors and feeding efficiency, the relationship
between swimming behaviors and sensory mechanisms, and the size effect)
may be difficult to study experimentally. However, they can be attacked by
performing the numerical simulation.
4.1. For a tethered copepod
Eq. (5) is neglected and only Eqs. (1)–(4) are solved numerically in the simulation of the feeding current created by a tethered copepod. The magnitude and distribution of the force field fa is adjusted so that the flow
velocity field output from the simulation is reasonably matched to available
observational data of the feeding current around a tethered copepod. From
this flow field, the drag force F acting on the copepod’s main body by the
water is calculated, and then the tethering force Te can be evaluated from
Eq. (5). Following the above-described simulation process, a numerical
feeding current has been generated (Jiang et al., 1999). The magnitude and
spatial configuration of the simulated feeding current (Figure 6) are in
good agreement with those of the feeding current around a tethered Euchaeta norvegica observed by Yen and Strickler (1996). The geometry of the
entrainment region, as visualized by tracking particles in the feeding current to construct a streamtube through the capture area of the copepod, is
cone-shaped and wide. By calculating the viscous dissipation rates around
the copepod, the influence field of the simulated feeding current is shown
to be anisotropic, similar to the observational results obtained by Fields
and Yen (1993). In addition, by varying the distribution of the force field
fa, it is shown that a distributed force dissipates less energy, but results in
a higher entrainment rate than a concentrated force does. Therefore, for a
given amount of force, applying a more distributed force to the water is
energetically more efficient. This interesting finding may be used to account
for the evolution of the complex and delicate feeding appendages.
4.2. For a free-swimming copepod
To simulate the flow field created by a free-swimming copepod in steady
motion, Eqs. (1)–(5) have to be solved together such that the model is a
self-propelled body model. Given the main body morphology, spatial distribution of the force field fa (the spatial distribution resembles that of a
real copepod’s cephalic appendages), and excess density of the copepod,
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HYDRODYNAMICS OF COPEPODS: A REVIEW
1.5 mm/s
1.5 mm/s
2 mm
Figure 6. Contours of velocity magnitudes of the simulated feeding current around a tethered copepod.
The contour plot is drawn along a plane 0.3 mm ventral to the copepod. The contour levels are (1.50,
2.00, 3.00, 4.00, 5.00, 6.00, 7.00, 8.00, 9.00, 10.0, 11.0, 12.0, 13.0, 14.0, 15.0, 16.0, 17.0, 18.0, 18.5)
mm s)1.
the magnitude of the force field fa and the body orientation of the copepod
are determined for different swimming behaviors (characterized by their
swimming speed and direction). Then, the flow field around the copepod is
determined. The above-described simulation process has been performed
by Jiang et al. (2002a). The numerical results confirm the conclusions
drawn from the theoretical analysis using Stokes-flow models by Jiang
et al. (2002b) about the relationship between swimming behaviors and flow
geometry, i.e., the geometry of the flow field around a free-swimming copepod varies significantly with different swimming behaviors (Figure 7).
Above all, the simulated feeding current is comparable with available
observational data, especially in the spatial configuration of the feeding
current: by comparing a simulated velocity vector field around a forward
swimming copepod (Figure 7b) with an observed velocity vector field also
around a forward swimming copepod (Figure 2b), it is shown that the
numerical simulation is able to reproduce the key features of an observed
feeding current, such as the location of velocity maximum and the spatial
configuration of the shear layer around the copepod. Here, the high veloc-
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HOUSHUO JIANG AND THOMAS R. OSBORN
ity area extends for up to a body length ventrally/anterior-ventrally away
from the body surface.
The spatial configuration of the shear layer around a copepod is shown
to be different for different swimming behaviors (e.g., hovering/slow-swimming, fast-swimming, or sinking freely, see Figure 7). Each swimming
behavior is associated with a specific three-dimensional flow structure. For
example, for a hovering copepod (Figure 8), the streamtube through the
area above the antennules does not overlap with that through the capture
area. The flow above the antennules is decelerated when approaching the
antennules, because it has to satisfy the no-slip boundary condition (i.e.,
zero velocity) at the surface of the antennules. In contrast, the flow going
through the capture area is accelerated when approaching the capture area,
since here the no-slip boundary condition is the beating movement of the
cephalic appendages, the net effect of which is an accelerated flow. Further
parametric studies reveal that the behavior of hovering or swimming slowly
is energetically more efficient in terms of relative capture volume per
energy expended than the behavior of swimming fast. That is, for the same
amount of energy expended a hovering or slow-swimming copepod is able
to scan more water than a fast-swimming one does. It is also found that
the behavior of hovering or swimming slowly is hydrodynamically quieter
than the behavior of swimming fast or sinking freely. That is, the influence
field is smaller for the flow field created by a hovering/slow-swimming
copepod than by a fast-swimming/free-sinking copepod, provided that the
excess weight of the copepod is the same.
4.3. For two copepods in close proximity
When two copepods are in close proximity or approaching each other,
the flow field created by the movement of one copepod is transmitted
through the fluid medium and affects the flow field around, as well as
the hydrodynamic force and torque on the other copepod. This is the
hydrodynamic interaction between two copepods, which was first studied
by Jiang et al. (2002c) using a numerical simulation method. Their results
show that, when two copepods are in close proximity, the hydrodynamic
interaction between them distorts the geometry of the flow field around
each copepod (Figure 9a) and changes the hydrodynamic force on each
copepod. The hydrodynamic interaction also results in a hydrodynamic
signal, which can be measured as a distribution of flow velocity difference
along each copepod’s antennules (Figure 9b). Parametric studies show
that the hydrodynamic interaction as well as its resulting hydrodynamic
signal is a function of the separation distance between the two copepods,
their relative body positions and orientations, and their relative swimming
HYDRODYNAMICS OF COPEPODS: A REVIEW
357
(b)
(a)
Vswimming=1.047 mm/s
(d)
Vsinking=4.187mm/s
(c)
Vswimming=4.187 mm/s
Figure 7. Velocity vector plots along the median plane of a model copepod (a) hovering in the water;
(b) swimming forward at a speed of 1.047 mm s)1; (c) swimming forward at a speed of 4.187 mm s)1;
(d) sinking freely, with the anterior pointing upward, at its terminal velocity (4.187 mm s)1 and along
its body axis for this case). The frame of reference is fixed on the copepod.
velocities. The numerical method may have further usage in understanding the swarming behavior of zooplankton, nearest neighbor distances
(NND) in a zooplankton swarm, and the energetic advantage of
maintaining swarm integrity.
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HOUSHUO JIANG AND THOMAS R. OSBORN
Figure 8. Streamtubes for a model copepod hovering in the water. Two streamtubes are drawn: the
streamtube through an area right above the copepod’s antennules and the streamtube through the
copepod’s capture area. The dashed line connecting the stars is the streamline passing through the center of the capture area. Note that the copepod’s body has been made transparent in order to show the
portion of the streamtube ventral to the copepod. (From Jiang et al., 2002d.)
5. Hydrodynamics and copepod sensory mechanisms
Behavioral, morphological and physiological studies have revealed that
copepods are able to perceive food particles, prey, predators and conspecifics (including mates) via mechanoreception and/or chemoreception
(for reviews see Atema, 1988; Lonsdale et al., 1998; Mauchline, 1998;
Visser, 2001; see also Doall et al., 1998; Kiørboe and Visser, 1999;
Moore et al., 1999; Paffenhöfer and Loyd, 2000; Jiang et al., 2002d, and
references therein). Since the water environment surrounds the copepods
359
HYDRODYNAMICS OF COPEPODS: A REVIEW
(a)
z (mm)
4
2
t =–12.0s
t =–7.0s
t =–12.0s
t =–7.0s
t =–3.0s
t =–1.0s
t =–3.0s
t =–1.0s
t=0.0s
0
t=0.0s
–2
–4
–2
0
y (mm)
2
4
(b)
The paired dotted lines represent the
velocity magnitude of the solitary copepod
+/- 20 µm/s. Any velocity magnitude outside
these dotted lines can be detected, based on a
detection threshold of 20 µm/s velocity difference.
3.4
3
4.8 mm
8m
m
4.10 m
m
Figure 9. (a) Ventral view of the two streamtubes respectively through the capture areas of the two copepods that are side-by-side, stationary and separated by a distance of 3.43 mm. (b) Velocity magnitudes along the line right above the antennules for the two side-by-side stationary copepods. The labels
in mm indicate the separation distance between the two copepods. (From Jiang et al., 2002c.)
as well as their items of interest, the flow field created due to the existence of both parties will affect the generation and transmission of
water-borne signals, whether the signals are mechanoreceptional or chemoreceptional.
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HOUSHUO JIANG AND THOMAS R. OSBORN
5.1. Chemoreception
The role of the copepod feeding current in copepod chemoreception has
been noticed for a long time (e.g., Alcaraz et al., 1980; Strickler, 1982).
The shear configuration of the feeding current created by a copepod hovering or slightly drifting in the water column will elongate the active space of
the chemicals around an entrained alga; this will enable the copepod to use
chemoreception to detect the presence, as well as the trajectory, of the alga
(Strickler, 1982). Strickler’s hypothesis was confirmed by Andrews (1983),
who developed a two-dimensional numerical model to calculate the deformation of the active space surrounding an alga in the low Reynolds number feeding current created by a copepod. The experiments done by Moore
et al. (1999) also confirm the hypothesis, further, they show that the deformation of the chemical signal can be different when entrained into feeding
currents of different shear configurations.
Copepod chemoreception capability has been compared among copepods of different swimming behaviors by using a three-dimensional algatracking, chemical advection–diffusion model to calculate the deformation
of the active space surrounding an entrained alga (Jiang et al., 2002d). It is
shown that an initially spherical active space will be more elongated when
entrained by the flow field around a hovering or slow-swimming copepod,
and that the copepod can have a few hundred milliseconds to respond to
the approaching alga (Figure 10a and b). Thus, a copepod in slow-swimming behaviors (including the behavior of hovering) is capable of using
chemoreception to detect individual algae entrained by the flow field. In
contrast, the advance warning time for a fast-swimming copepod is much
shorter (Figure 10c), so that the copepod is not able to rely on chemoreception for remote detection. The distinction is because the flow fields associated with different swimming behaviors have different velocity and shear
configurations. It is emphasized that not only the shear configuration but
also the velocity configuration of the flow field affect the advance warning
time. The former determines the deformation of the active space; the latter
determines the traveling time as well as trajectory of the alga. For a hovering or slow-swimming copepod, the flow streamlines are concentrated from
a large region toward a small region around the capture area, and therefore there are larger differences in speed between adjacent streamlines and
in speed as well as acceleration along streamlines. For a fast-swimming
copepod, since the flow geometry is cylindrical, narrow and long, the differences in speed between adjacent streamlines and in speed as well as
acceleration along streamlines are expected to be small. Thus, the deformation of the active space is more significant for a hovering or slow-swimming copepod than for a fast-swimming copepod. On the other hand, the
flow velocity magnitudes around a fast-swimming copepod are generally
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HYDRODYNAMICS OF COPEPODS: A REVIEW
(a)
(b)
5 mm/s
5 mm/s
Vswimming=1.047 mm/s
t=0.000 s
t=0.000 s
t=1.920 s
t=1.800 s
t=3.494 s
t=3.550 s
t=3.998 s
(d)
t=3.744 s
Vsinking=4.187 mm/s
t=0.000 s
t=0.900 s
t=1.800 s
t=2.700 s
5 mm/s
t=3.600 s
t=3.996 s
t=3.904 s
(c)
t=3.998 s
t=1.740 s
t=1.500 s
t=1.000 s
t=0.500 s
t=0.000 s
Vswimming=4.187 mm/s
5 mm/s
Figure 10. Deformation of the active space surrounding an alga entrained by the flow field around a
model copepod (a) hovering in the water; (b) swimming forward at a speed of 1.047 mm s)1; (c) swimming forward at a speed of 4.187 mm s)1; (d) sinking freely, with the anterior pointing upward, at its
terminal velocity (4.187 mm s)1 and along its body axis for this case). The alga is on the median plane
of the copepod and to be entrained into the copepod’s capture area. The streamline is drawn through
the centers of the alga. The velocity vectors of the flow field relative to the copepod are drawn on the
median plane. (From Jiang et al., 2002d.)
much greater than those around a hovering or slow-swimming copepod
(the frame of reference is fixed on the copepod). Thus, the alga travels
much faster when entrained into the flow field created by a fast-swimming
copepod than by a hovering or slow-swimming copepod.
For these two reasons, the advance warning time for a fast-swimming
copepod is much shorter than for a hovering or slow-swimming copepod.
The velocity and shear configurations for a free-sinking copepod seem to
favor its chemoreception of an encountered alga (Figure 10d). It is also
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HOUSHUO JIANG AND THOMAS R. OSBORN
shown that advection by fluid motion dominates over diffusion during the
transport of the chemical signals inside the active space surrounding an
alga to the location of a copepod’s chemoreceptors.
5.2. Mechanoreception
Tremendous efforts have been made in order to identify and quantify the
hydrodynamic signals detected by copepods, and to determine signal
threshold strengths and the associated detection distances (e.g., Haury
et al., 1980; Fields and Yen, 1996, 1997; Viitasalo et al., 1998; Kiørboe
and Visser, 1999; Kiørboe et al., 1999; Fields et al., 2002). Kiørboe and
Visser (1999) have argued that prey detection relies on the magnitude of
the fluid velocity created by the prey, while predator detection depends on
the magnitude of one or several of the components of the fluid velocity
gradients (deformation rate, vorticity, acceleration) created by the predator. Most importantly, the hydrodynamic signals potentially detectable by
copepods may be the velocity differences caused by all these components.
Many studies have quantified the signal threshold strengths in terms of the
fluid deformation (or shear) rate at the copepod’s body scale. However, the
threshold deformation rate obtained ranges from 0.5 to 5 s)1 (Kiørboe
et al., 1999), which is probably too broad.
Our speculation on this is that the hydrodynamic signals might be better
measured at the place where copepod mechanoreceptors are located or distributed, such as along the antennules. This is because essentially the bending of setae on copepod sensory organs enables the detection, and the
bending is essentially due to the change of the flow field around the setae
(Jiang et al., 2002c). However, a fairly accurate measure of the flow field
around a copepod seta or even along the antennules is difficult. On the
other hand, 20 lm s)1 in the velocity difference between the tip and base
of a seta is enough to elicit a neural response from the antennules of copepods (Yen et al., 1992). Using this threshold in velocity difference and a
numerical simulation method, Jiang et al. (2002c) have quantified the
hydrodynamic signals, resulting from an approaching copepod of comparable size, along a line right above the antennules of a copepod.
Generally, the hydrodynamic disturbances (the signals) between two copepods (of comparable size) in close proximity are different from those
between a copepod and its prey (of a much smaller size) or predator (of a
much larger size). Since its size is much smaller than the copepod, the prey
has less influence on the flow field around the copepod (Figure 11a). The
hydrodynamic signals generated by the prey can only bend a very limited
number of setae on the copepod’s antennules, and hence the array of setae
along the copepod’s antennules detects the prey as localized velocity distur-
HYDRODYNAMICS OF COPEPODS: A REVIEW
363
bances. In contrast, an approaching predator of a relatively large size may
totally destroy the organized flow field around the copepod (Figure 11b).
The copepod detects the predator when the spatially varying and temporally
fluctuating velocity disturbances at the copepod’s whole body scale stimulate the full array of mechanoreceptors on the copepod. Hwang and Strickler (2001) have suggested that copepods may use a simple form of pattern
recognition to distinguish between sources of signals, prey or predators.
Along the same line, pattern recognition may also be used by copepods
to detect conspecies of comparable size, where the velocity disturbances at
their partial body scale are detected (Figure 11c). As such, different deflection patterns of the array of mechanoreceptors in response to different signal sources enable a copepod to distinguish among a small prey, a giant
predator or a copepod of comparable size. Finally, it is worth noticing that
the signals between two copepods of comparable size may not necessarily
be symmetric, i.e., one copepod can detect the presence of the other copepod, while the latter cannot detect the former (see Figure 11d in Jiang
et al., 2002c).
5.3. Effects of morphology
The effects of morphology can be divided into the effects of the main body
and the effects of the appendages. Of the effects of the main body, the
effect associated with size is the dominant one. Given the size of the main
body, changes in the body shape have limited effects on the flow field
around the body in the low Reynolds number regime (Panton, 1996). On
the other hand, the local flow field around the body is largely dependent
on the distribution and moving pattern of the appendages relative to the
main body. Thus, it is not surprising that the results from the theoretical
analyses using Stokes-flow models of a sphere with a point force (Jiang
et al., 2002b) are so close to the results obtained from the numerical simulations using a realistic copepod body shape (Jiang et al., 2002a). The
sphere and the realistic copepod body shape are of similar size, and the
magnitude and distribution (relative to the main body) of the forces, which
represent the net effect of the appendages, are also similar.
Furthermore, the distribution and moving pattern of the appendages
may reflect a copepod’s sensory requirements, in that they create flows
going across the sensors on the copepod (e.g., Yen and Stricker, 1996).
Correspondingly, the sensors may be distributed to fit for monitoring the
changes in the key aspects of the flow field. Observational evidence of the
locations of copepod chemoreceptors and mechanoreceptors supports the
interplay of flow structure and sensor morphology (e.g., Fields and Yen,
1993; Lenz and Yen, 1993; Moore et al., 1999). The experiments done by
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HOUSHUO JIANG AND THOMAS R. OSBORN
Figure 11. Illustrations of the three perspectives of copepod mechanoreception as predator, prey and
conspecies, respectively. (a) Detection of the local flow disturbance due to the jumping motion of a
small prey; the streamlines are drawn using a frame of reference fixed on the copepod’s body. (b)
Detection of the flow disturbance at the copepod’s whole body scale due to the swimming motion of
an approaching predator (the fish); the streamlines are drawn using a frame of reference fixed on the
fish’s body. Note that the streamlines shown in (b) are just for the purpose of illustration; there are
some situations in which the streamlines are different from here, such as the situation that a fish generates suction to draw a copepod into its open mouth. [(a) and (b) are modified from Figure 1 in Jumars
(2000); copepod drawing from Williamson (1987) and fish drawing from Drucker and Lauder (1999).]
(c) Detection of the flow disturbance at partial body scale due to the presence of a nearby conspecific
copepod (of comparable size); the streamlines are drawn using a frame of reference fixed on one of the
two copepods.
HYDRODYNAMICS OF COPEPODS: A REVIEW
365
Fields et al. (2002) further show that each seta, whether long or short,
responds to only a portion of the overall range of flow velocity in the copepod’s habitat, suggesting that the ensemble of setae of different morphologies and lengths may function as a unit to decode the intensity and
directionality of complex hydrodynamic signals.
6. Summary
(1) Associated with their complex swimming behaviors, body morphology,
and negative buoyancy, water flows are created at the body scale of
calanoid copepods. The created water flows not only determine the net
currents going around and through the hair-bearing appendages of the
copepods but also set up a laminar flow field around them. The laminar flow field interacts constantly with the environmental background
flows.
(2) Physically, the creation of the water flows at copepod body scale can
be explained in terms of the fact that free-swimming copepods are selfpropelled bodies. That is, a free-swimming copepod must gain propulsion from the surrounding water in order to counterbalance its excess
weight and the drag force exerted by the water. This also explains the
observations that the flow field around a free-swimming copepod varies
significantly with the different swimming behaviors.
(3) Understanding the hydrodynamics at copepod body scale is helpful to
understand many aspects of copepod feeding, swimming, sensing and
swarming behaviors.
(4) Numerical simulation is a useful tool to study the small-scale biological–physical interactions (i.e., the organism–organism and organism–
environment interactions at the scale of the individual).
(5) Future research directions of the hydrodynamics of copepods may
include:
The interaction between the water flows created by a copepod and its
surrounding environmental background flows, such as small-scale turbulence.
The effect of small-scale turbulence on copepod sensory mechanisms.
The effect of the hydrodynamics on the mate locating processes.
The hydrodynamics of copepod nauplii.
Acknowledgements
H.J. gratefully acknowledges the Postdoctoral Scholar Program at the
Woods Hole Oceanographic Institution (WHOI), with funding provided by
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HOUSHUO JIANG AND THOMAS R. OSBORN
the Dr. George D. Grice Postdoctoral Scholarship Fund. T.R.O. is supported by the Office of Naval Research. The authors thank Dr. Mark Grosenbaugh and an anonymous reviewer for valuable advice and comments.
Thanks are due to Dr. David Fields for his kind help in preparing Figure 1
from his original work. H.J. also gratefully acknowledges the support from
the Penzance Endowed Fund in Support of Assistant Scientists at WHOI.
This is Contribution Number 10721 from WHOI.
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